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Module 5 Nonlinear Dielectrics Introduction

So far we have discussed linear dielectrics whose dielectric constant increases linearly with theapplied field accompanied by an increase in the polarization depending upon the presence ofpolarization mechanisms in the materials

In addition there are a few special classes of dielectric materials which show large dielectricconstants non-zero polarization in the absence of electric field and nonlinearity in the dielectricconstant These also show extraordinary special effects such as

Coupling of strain and electric field (piezoelectric ceramics)

Temperature dependence of the polarization (pyroelectric ceramics) and

Presence of large polarization in absence of electric field ie spontaneous polarization(ferroelectric ceramics)

Most of these materials happen to be oxides and as you can very well understand now theseproperties will be greatly affected by the defect chemistry and process variables

The presence of these features makes these materials extremely useful for a variety of applicationssuch as sensors actuators transducers temperature detectors imaging permanent data storage etcIn this module we will discuss origin of these properties with a crystallographic and thermodynamicframework and associated mathematical representations along with a few examples of materials anddevices

The Module contains

Classification based on Crystal Classes

Ferroelectric Ceramics

Piezoelectric Ceramics

Pyroelectric Ceramics

Summary

Suggested Reading

Principles of Electronic Ceramics by L L Hench and J K West Wiley

Principles and applications of ferroelectrics and related materials M E Linesand A M Glass Oxford University Press

Electroceramics Materials Properties Applications by A J Moulson and JM Herbert Wiley

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Module 5 Nonlinear Dielectrics Classification based on Crystal Classes

52 Classification based on Crystal Classes

Out of a total of 32 crystal point groups (see the course related to structure of materials) 21 arenon-centrosymmetric ie crystals not having a center of symmetry

The term centrosymmetric refers to a space group which contains an inversion center as one of itssymmetry elements ie for every point (x y z) in the unit cell there is an indistinguishable point (-x -y -z)

Crystal class

CentrosymmetricPoint groups

Noncentrosymmetric Point groups

Polar Non-polar

Cubic m3 m3m none 432 m 23

Tetragonal 4 orm

4 or mmm 4 4mm 2 m 22

Orthorhombic mmm mm2 222

Hexagonal 6 orm

6 or mmm 6 6mm 2m 622

Trigonal m 3 3m 32

Monoclinic 2 or m 2 m none

Triclinic 1 none

Total Number 11 groups 10 groups 11 groups

Out of these 21 point groups except group 432 crystals containing all other point groups exhibitpiezoelectric effect ie upon application of an electric field they exhibit strain or upon application ofan external stress charges develop on the faces of crystal resulting in an induced electric field

Out of these 20 non-centrosymmetric point groups 10 belong to polar crystals ie crystals whichpossess a unique polar axis an axis showing different properties at the two ends

These crystals can be spontaneously polarized and polarization can be compensated throughexternal or internal conductivity or twinning or domain formation

Spontaneous polarization depends upon the temperature Consequently if a change in temperatureis imposed an electric charge is developed on the faces of the crystal perpendicular to the polaraxis This is called pyroelectric effect All 10 classes of polar crystals are pyroelectric

In some of these polar non-centrosymmetric crystals the polarization along the polar axis can bereversed by reversing the polarity of electric field Such crystals are called ferroelectric ie these arespontaneously polarized materials with reversible polarization

So by default all ferroelectric materials are simultaneously pyroelectric and piezoelectric Similarlyall pyroelectric materials are by default piezoelectric but not all of them are ferroelectric

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Figure 51 Classificatin of piezo- pyro- and ferro-electrics

In the subsequent sections we will discuss about the ferroelectric pyroelectric and piezoelectricmaterials explaining the fundamental physics some key materials and applications

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

53 Ferroelectric Ceramics

Ferroelectric effect was first observed in Rochelle salt KNaC4H4O64H2O by Czech scientist Roger

Valasek in 1921 Afterwards for years the discovery did not raise much excitement possibly due tothe world war However after a few decades renewed technological interest led to much moreextensive studies and a better understanding

In the subsequent years many materials were discovered and were of technological interest as theywere employed into a variety of applications Among various categories of ferroelectric materialsfollowing stand out either due to interest in the structure or in the properties

Tri-glycine sulfate and isomorphous materials

Pottasium dihyrogen phosphates and isomorphous materials

Barium titanate and other perovskite structured compounds such as KNbO3 PbTiO3 etc

Complex oxides such as Aurrivillious compounds

Rochelle Salt and similar compounds

Ferroelectric Sulfates

Among the above perovskite related compounds have been studied most primarily due to theirexciting properties and reasonably high transition temperatures making them attractive for variousapplications

In the following section we will look some of the structural and thermodynamic features of thesematerials with main emphasis on perovskite compounds for the sake of illustration

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

531 Permanent Dipole Moment and Polarization

These materials consist of net permanent dipole moment ie finite vector sum of dipole momenteven in the absence of electric field This requires the material to be non-centrosymmetric whereasdipole moment would be forced to be zero in a centrosymmteric material due to symmetryconsiderations

On top of this there must be a spontaneous polarization as well which means the centers of positiveand negative charges in a crystal would never be the same

The following is the figure showing the crystal structure of a perovskite structured material such asBaTiO3 Here in cubic structure (A) the dipole is zero while in tetragonal form (B) the dipole

moment is finite This displaced position of the central atom is the energetically stable position iethe free energy is minimum

Figure 52 Cubic and tetragonal perovskite structures with dipolemoment in latter represented by an arrow due to movement ofcentral B ion up or down along c-axis

When this kind of ferroelectric material is switched ie subjected to a bipolar electric field it exhibitsa polarization vs electric field plot as shown below You can see that there is finite polarization in theabsence of electric field ie two equal and opposite values +Pr or -Pr also called remnant

polarization These two values can be connected with the position of a central atom in the octahedra in the figureabove So when you apply field in the direction the central atom moves up with respect to oxygenoctahedral and when you change the polarity it comes down in the opposite direction the extent ofdisplacement being similar

The plot shows a hysteresis which is important for applications such as memory devices We willexplain the details of this phenomenon in the subsequent sections

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Figure 53 A typical ferroelectric hysteresisloop

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

532 Principle of Ferroelectricity Energetics

The movement of central atom in the above structure can explained in terms of a potential energydiagram

Figure 54 Potential energy well and crystal structure for an ABO3structured ferroelectric

This situation can be explained in terms of a potential energy between two adjacent low energysites There are two equilibrium positions in which a B ion can stay but to change from one state toanother energy must be provided to overcome an energy barrier ΔE These energy wells further tiltto the left or right depending upon the polarity of the electric field ie in the non-zero field statemaking on configuration more stable than another However a coercive field which is the fieldrequired to bring the polarization back to zero is needed when you switch to other direction of thefield

Ferroelectric materials follow Curie-Weiss law which is expressed as

(51)

Here N is the number of dipoles per unit volume of the material a is dipolar polarizability and Tc is

defined as the Ferroelectric transition temperature or the Curie temperature

Ferroelectric behaviour is observed below the Curie Temperature above which the ferroelectricphase converts into a paraelectric phase which always has higher symmetry than the ferroelectricphase (for example transformation of low symmetry tetragonal BaTiO3 to higher symmetry cubic

BaTiO3 at about 120oC while heating) and ferroelectricity disappears A paraelectric state is

essentially a centrosymmetric higher symmetry state where dipoles are randomly oriented in acrystal giving rise to zero polarization

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Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

533 Proof of Curie-Weiss Law

We can now say that in a ferroelectric material reversible spontaneous alignment of electric dipolestakes place by mutual interaction This happens due to a local field E which is increased by dipolealignment in the direction of field Interestingly this phenomenon happens below a criticaltemperature Tc when crystal enters into nonsymetric state where thermal energy cannot randomize

the electric dipoles presumably due to dipole-dipole interactions and local field

Following the basic principles we developed in module 4 polarization P can be expressed as

(52)

Where local field E = E + P3e0 as given by Clausius-Mossotti relationship and er is the relative

dielectric permittivity and a is total polarizability Substitution for E in (52) results in

ie

or

(53)

Since we know that susceptibility we get

(54)

Equation (54) shows that both χ and er must approach 8 when Na3e0 approaches 1

This can be assumed to be a right condition for ferroelectrics as near the ferroelectric transition theyexhibit very large susceptibilities and dielectric constant At this point we can also ignore theelectronic ionic and interface polarizations assuming that dipolar polarizability is too high such thatad gtgt ae + ai + aint at a critical temperature Tc Here define a = ad = CkT where C is Curiersquos

constant This is the right sort of relation as we have already seen the temperature dependence ofdipolar polarization in section (453)

Hence we can further write

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OR

(55)

Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

we get

OR

(56)

Thus by now modifying equation (54) Curie-Weiss law can be expressed as

(57)

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

534 Thermodyanamic Basis of Ferroelectric Phase Transitions

Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

(58)

where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

(59)

where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

Converse piezoelectric effect is expressed as

(510)

Where dijkt is in mV

Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

(511)

where Pi is the vector of pyroelectric coefficient in cm-2K-1

Displacement is expressed as

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(512)

So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

For a ferroelectric system the free energy G can be expressed in terms of ten variables as

(513)

where Px Py Pz are the components of the polarization are the stress

components and T is the temperature

We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

(514)

Note that only even powers are taken because energy is same for plusmnPS states

Here a b c are the temperature dependent constants and E is the electric field

The equilibrium is found by establishing ie

(515)

ie

E = (516)

If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

If we ignore higher power terms then

(517)

leading to

(518)

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which is the same expression that we encountered for linear dielectrics

According to Landau-Devonshire theory near the Curie point (T~T0) we assume

a = a0 (T - T0) (519)

As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

(520)

In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

535 Case I Second order Transition

When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

second order transition (do not get confused between T0 and Tc as the distiction will become clear

in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

polarization can be expressed as

(521)

showing that the polarization decreased to zero at T = T0 as shown in figure 58

Dielectric susceptibility at T lt T0 can be estimated as

(522)

Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

values near T0

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Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

(523)

Now substituting in (523) yields

(524)

Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

536 Case ndash II First Order Transition

Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

now more than T0 This gives rise to the following free energy vs polarization plot

Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

(525)

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On the other hand field E must also be zero for the polarization to be spontaneous ie

(526)

The polarization and susceptibility at Tc are obtained by solving two equations and are given as

(527)

and

(528)

The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

temperature higher than Tc the sample will be in paraelectric state This results in thermal

hysteresis when these materials are thermally cycled across Tc

If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

Solid State Physics AJ Dekker Macmillan Publishing

Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

537 Ferroelectric Domains

In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

or 90deg domain walls

Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

Now the question is Why is there a domain wall

The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

splitting of the material into oppositely oriented domains or

compensation of the electrical charge via electrical conduction through the crystal

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Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

by transmission electron microscopy

Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

538 Analytical treatment of domain wall energy

Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

(529)

where Uc effect of applied field on the domain energy

Up and Ux bulk electrical and elastic energies

Ud depolarization energy and

Uw domain energy

Ud is the energy related to the internal field set up in the crystal by the polarization and not

compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

(530)

Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

is the polarization at the center of the domain

Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

width (d) and crystal volume (V) and is given as

(531)

To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

wrt domain wall thickness d ie dΔGdd = 0 resulting in

(532)

Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

539 Ferroelectric Switching and Domains

Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

microCcm2and E is electric field across the sample in Vcm The process is something like this

Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

Further increase of electric field in the opposite direction will cause complete reversal of orientation

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of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

>

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

5310 Measurement of Hysteresis Loop

Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

and coercive field Ec

A ferroelectric materials shows polarization of the order of 50-100 microCcm2

Figure 5 15 Schematic representation of sawyer-tower circuit

Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

Because the distorted octahedra are coupled together in ferroelectric form there is a very large

spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

5312 Applications of Ferroelectrics

In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

(above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

where their dielectric constant increases linearly with temperature they can be used for cameraflashes

53121 Nonvolatile Memories

Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

53122 Camera Flashes

In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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Module 5 Nonlinear Dielectrics

Summary

Summary

In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

5474 Actuators

In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

You can have it in two forms

Direct Piezo Actuators with strokes lower than 100 microns or so and

Amplified Piezoelectric Actuators which can yield millimeter long strokes

Some of the examples of applications are

Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

5475 Frequency Standards

Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

Quartz clocks

Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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Module 5 Nonlinear Dielectrics

Summary

Summary

Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

54 Piezoelectric Ceramics

Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

Pb(ZrTi)O3)

An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

541 Direct Piezoelectric Effect

Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

(533)

where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

542 Reverse or Converse Piezoelectric Effect

The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

(534)

where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

Figure 520 Direct and Converse PiezoelectricEffects

The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

543 Poling of Piezoelectric Materials

As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

The values of piezoelectric coefficient of some materials are given below

Material Piezoelectric Constant d(pmV)

Quartz 23

Barium Titanate 100-149

Lead Niobate 80-85

Lead zirconate titanate 250-365

So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

544 Depolarization of Piezoelectrics

Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

polarization or rather result in alignment of dipoles gets lost

Figure 522 Animation on depolarization offerroelectrics

(Courtesy copy DoITPoMS University of Cambridge)

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Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

545 Common PIezoelectric Materials

5451 Barium Titanate (BaTiO3)

This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

5452 Pb(ZrTi)O3 or PZT

PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

The phase diagram of PZT is shown below

Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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few poling directions available making it a useful piezoelectric

Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

546 Measurement of Piezoelectric Properties

Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

(535)

Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

(536)

Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

547 Applications of Piezoelectric Ceramics

Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

5471 Power Generation

Gas Lighter

Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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Power Transformer

A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

Figure 526 Schematic of a piezoelectrictransformer

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Module 5 Special Dielectrics Piezoelectric Ceramics

5472 Piezoelectric Sensors

Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

Other sensor applications are

Detection and generation of sonar waves

To detect detonation in automotive engine by sampling the vibrations of the engine block

To detect the precise moment of fuel injection in an automotive engine

Detection of acoustic emissions in acoustic emission testing

Microbalances as very sensitive chemical and biological sensors

Strain gauges

Medical applications using ultrasound waves

Kidney stone treatment

In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

Figure 527 Ultrasonic waves creation and

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kidney stone treatment and ultrasound imagingof the fetus

(Courtesy copy DoITPoMS University of Cambridge)

5473 Ultrasound Imaging Using Transduction Effect

Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

55 Pyroelectric Ceramics

Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

551 Difference between Pyroelectric and Ferroelectric Material

Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

552 Theory of Piezoelectric Materials

From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

(537)

Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

Assuming electric field E as constant differentiating the above equation with temperature leads to

(538)

Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

we write

Δ OR

Δ (539)

Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

(540)

The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

553 Measurement of Pyroelectric Coefficient

One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

(541)

Where Ip is the pyrocurrent and is given as

(542)

where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

respectively

Figure 530 Circuit for measuring pyroelectriccoefficient

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Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

554 Direct and Indirect Effect

Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

Since change in the polarization can also be expressed as depending

upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

Figure 531 Direct-Indirect effect animation

(Courtesy copy DoITPoMS University of Cambridge)

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Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

555 Common Pyroelectric Materials

Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

The most common materials are tabulated below

Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

LiTaO3 single crystal Hexagonal 665 -230

075Pb(Mg13-Nb23)O3-025PbTiO3

(PMN-PT) Ceramic

Perovskite 150 -1300

Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

Triglycine sulphate

(NH2CH2COOH)3H2SO4

Sulphate 49 -280

Polyvinylidene fluoride (PVDF) film Polymer 80 -27

5551 Triglycine Sulphate (TGS)

High pyroelectric coefficient

Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

Can be modified to withstand temperatures above Curie point without depoling

Used in thermal imaging cameras

5552 Polyvinylidene Fluoride (PVDF)

Poor pyroelectric coefficient

Readily available in large areas of thin film

More stable to heat vacuum and moisture than TGS mechanically robust

Low heat conductivity and low permittivity

High loss tangent

Commonly used for burglar alarms

5553 Perovskite Ferroelectric Ceramics

Generally robust and insensitive to moisture and vacuum

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High pyroelectric coefficient and low loss

Better operation near TC

Strong dependence on composition

As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

556 Common Applications

5561 Burglar Alarms

Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

Figure 532 Working of an IR intruder alarm

(Courtesy copy DoITPoMS University ofCambridge)

5562 Infrared or Thermal Imaging

Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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A typical photograph generated from IR imaging looks like this

Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

Here is a simple explanation of how IT imaging using pyroelectrics works

A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

Figure 534 Process of imagecreation

5563 Pollutant Control

The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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Figure 535 Gas detection using a pyroelectricdetector

(Courtesy copy DoITPoMS University of Cambridge)

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Module 5 Nonlinear Dielectrics

Summary

Summary

Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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    Module 5 Nonlinear Dielectrics Classification based on Crystal Classes

    52 Classification based on Crystal Classes

    Out of a total of 32 crystal point groups (see the course related to structure of materials) 21 arenon-centrosymmetric ie crystals not having a center of symmetry

    The term centrosymmetric refers to a space group which contains an inversion center as one of itssymmetry elements ie for every point (x y z) in the unit cell there is an indistinguishable point (-x -y -z)

    Crystal class

    CentrosymmetricPoint groups

    Noncentrosymmetric Point groups

    Polar Non-polar

    Cubic m3 m3m none 432 m 23

    Tetragonal 4 orm

    4 or mmm 4 4mm 2 m 22

    Orthorhombic mmm mm2 222

    Hexagonal 6 orm

    6 or mmm 6 6mm 2m 622

    Trigonal m 3 3m 32

    Monoclinic 2 or m 2 m none

    Triclinic 1 none

    Total Number 11 groups 10 groups 11 groups

    Out of these 21 point groups except group 432 crystals containing all other point groups exhibitpiezoelectric effect ie upon application of an electric field they exhibit strain or upon application ofan external stress charges develop on the faces of crystal resulting in an induced electric field

    Out of these 20 non-centrosymmetric point groups 10 belong to polar crystals ie crystals whichpossess a unique polar axis an axis showing different properties at the two ends

    These crystals can be spontaneously polarized and polarization can be compensated throughexternal or internal conductivity or twinning or domain formation

    Spontaneous polarization depends upon the temperature Consequently if a change in temperatureis imposed an electric charge is developed on the faces of the crystal perpendicular to the polaraxis This is called pyroelectric effect All 10 classes of polar crystals are pyroelectric

    In some of these polar non-centrosymmetric crystals the polarization along the polar axis can bereversed by reversing the polarity of electric field Such crystals are called ferroelectric ie these arespontaneously polarized materials with reversible polarization

    So by default all ferroelectric materials are simultaneously pyroelectric and piezoelectric Similarlyall pyroelectric materials are by default piezoelectric but not all of them are ferroelectric

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    Figure 51 Classificatin of piezo- pyro- and ferro-electrics

    In the subsequent sections we will discuss about the ferroelectric pyroelectric and piezoelectricmaterials explaining the fundamental physics some key materials and applications

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    53 Ferroelectric Ceramics

    Ferroelectric effect was first observed in Rochelle salt KNaC4H4O64H2O by Czech scientist Roger

    Valasek in 1921 Afterwards for years the discovery did not raise much excitement possibly due tothe world war However after a few decades renewed technological interest led to much moreextensive studies and a better understanding

    In the subsequent years many materials were discovered and were of technological interest as theywere employed into a variety of applications Among various categories of ferroelectric materialsfollowing stand out either due to interest in the structure or in the properties

    Tri-glycine sulfate and isomorphous materials

    Pottasium dihyrogen phosphates and isomorphous materials

    Barium titanate and other perovskite structured compounds such as KNbO3 PbTiO3 etc

    Complex oxides such as Aurrivillious compounds

    Rochelle Salt and similar compounds

    Ferroelectric Sulfates

    Among the above perovskite related compounds have been studied most primarily due to theirexciting properties and reasonably high transition temperatures making them attractive for variousapplications

    In the following section we will look some of the structural and thermodynamic features of thesematerials with main emphasis on perovskite compounds for the sake of illustration

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    531 Permanent Dipole Moment and Polarization

    These materials consist of net permanent dipole moment ie finite vector sum of dipole momenteven in the absence of electric field This requires the material to be non-centrosymmetric whereasdipole moment would be forced to be zero in a centrosymmteric material due to symmetryconsiderations

    On top of this there must be a spontaneous polarization as well which means the centers of positiveand negative charges in a crystal would never be the same

    The following is the figure showing the crystal structure of a perovskite structured material such asBaTiO3 Here in cubic structure (A) the dipole is zero while in tetragonal form (B) the dipole

    moment is finite This displaced position of the central atom is the energetically stable position iethe free energy is minimum

    Figure 52 Cubic and tetragonal perovskite structures with dipolemoment in latter represented by an arrow due to movement ofcentral B ion up or down along c-axis

    When this kind of ferroelectric material is switched ie subjected to a bipolar electric field it exhibitsa polarization vs electric field plot as shown below You can see that there is finite polarization in theabsence of electric field ie two equal and opposite values +Pr or -Pr also called remnant

    polarization These two values can be connected with the position of a central atom in the octahedra in the figureabove So when you apply field in the direction the central atom moves up with respect to oxygenoctahedral and when you change the polarity it comes down in the opposite direction the extent ofdisplacement being similar

    The plot shows a hysteresis which is important for applications such as memory devices We willexplain the details of this phenomenon in the subsequent sections

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    Figure 53 A typical ferroelectric hysteresisloop

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    532 Principle of Ferroelectricity Energetics

    The movement of central atom in the above structure can explained in terms of a potential energydiagram

    Figure 54 Potential energy well and crystal structure for an ABO3structured ferroelectric

    This situation can be explained in terms of a potential energy between two adjacent low energysites There are two equilibrium positions in which a B ion can stay but to change from one state toanother energy must be provided to overcome an energy barrier ΔE These energy wells further tiltto the left or right depending upon the polarity of the electric field ie in the non-zero field statemaking on configuration more stable than another However a coercive field which is the fieldrequired to bring the polarization back to zero is needed when you switch to other direction of thefield

    Ferroelectric materials follow Curie-Weiss law which is expressed as

    (51)

    Here N is the number of dipoles per unit volume of the material a is dipolar polarizability and Tc is

    defined as the Ferroelectric transition temperature or the Curie temperature

    Ferroelectric behaviour is observed below the Curie Temperature above which the ferroelectricphase converts into a paraelectric phase which always has higher symmetry than the ferroelectricphase (for example transformation of low symmetry tetragonal BaTiO3 to higher symmetry cubic

    BaTiO3 at about 120oC while heating) and ferroelectricity disappears A paraelectric state is

    essentially a centrosymmetric higher symmetry state where dipoles are randomly oriented in acrystal giving rise to zero polarization

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    Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    533 Proof of Curie-Weiss Law

    We can now say that in a ferroelectric material reversible spontaneous alignment of electric dipolestakes place by mutual interaction This happens due to a local field E which is increased by dipolealignment in the direction of field Interestingly this phenomenon happens below a criticaltemperature Tc when crystal enters into nonsymetric state where thermal energy cannot randomize

    the electric dipoles presumably due to dipole-dipole interactions and local field

    Following the basic principles we developed in module 4 polarization P can be expressed as

    (52)

    Where local field E = E + P3e0 as given by Clausius-Mossotti relationship and er is the relative

    dielectric permittivity and a is total polarizability Substitution for E in (52) results in

    ie

    or

    (53)

    Since we know that susceptibility we get

    (54)

    Equation (54) shows that both χ and er must approach 8 when Na3e0 approaches 1

    This can be assumed to be a right condition for ferroelectrics as near the ferroelectric transition theyexhibit very large susceptibilities and dielectric constant At this point we can also ignore theelectronic ionic and interface polarizations assuming that dipolar polarizability is too high such thatad gtgt ae + ai + aint at a critical temperature Tc Here define a = ad = CkT where C is Curiersquos

    constant This is the right sort of relation as we have already seen the temperature dependence ofdipolar polarization in section (453)

    Hence we can further write

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    OR

    (55)

    Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

    we get

    OR

    (56)

    Thus by now modifying equation (54) Curie-Weiss law can be expressed as

    (57)

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    534 Thermodyanamic Basis of Ferroelectric Phase Transitions

    Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

    These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

    Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

    (58)

    where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

    is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

    Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

    (59)

    where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

    Converse piezoelectric effect is expressed as

    (510)

    Where dijkt is in mV

    Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

    (511)

    where Pi is the vector of pyroelectric coefficient in cm-2K-1

    Displacement is expressed as

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    (512)

    So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

    From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

    For a ferroelectric system the free energy G can be expressed in terms of ten variables as

    (513)

    where Px Py Pz are the components of the polarization are the stress

    components and T is the temperature

    We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

    (514)

    Note that only even powers are taken because energy is same for plusmnPS states

    Here a b c are the temperature dependent constants and E is the electric field

    The equilibrium is found by establishing ie

    (515)

    ie

    E = (516)

    If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

    If we ignore higher power terms then

    (517)

    leading to

    (518)

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    which is the same expression that we encountered for linear dielectrics

    According to Landau-Devonshire theory near the Curie point (T~T0) we assume

    a = a0 (T - T0) (519)

    As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

    (520)

    In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

    Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

    paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

    nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

    Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    535 Case I Second order Transition

    When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

    second order transition (do not get confused between T0 and Tc as the distiction will become clear

    in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

    Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

    Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

    The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

    retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

    polarization can be expressed as

    (521)

    showing that the polarization decreased to zero at T = T0 as shown in figure 58

    Dielectric susceptibility at T lt T0 can be estimated as

    (522)

    Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

    will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

    values near T0

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    Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

    This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

    (523)

    Now substituting in (523) yields

    (524)

    Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    536 Case ndash II First Order Transition

    Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

    now more than T0 This gives rise to the following free energy vs polarization plot

    Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

    The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

    is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

    Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

    In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

    free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

    (525)

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    On the other hand field E must also be zero for the polarization to be spontaneous ie

    (526)

    The polarization and susceptibility at Tc are obtained by solving two equations and are given as

    (527)

    and

    (528)

    The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

    heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

    temperature higher than Tc the sample will be in paraelectric state This results in thermal

    hysteresis when these materials are thermally cycled across Tc

    If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

    Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

    Solid State Physics AJ Dekker Macmillan Publishing

    Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    537 Ferroelectric Domains

    In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

    Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

    The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

    directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

    or 90deg domain walls

    Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

    Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

    depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

    Now the question is Why is there a domain wall

    The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

    associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

    splitting of the material into oppositely oriented domains or

    compensation of the electrical charge via electrical conduction through the crystal

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    Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

    by transmission electron microscopy

    Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    538 Analytical treatment of domain wall energy

    Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

    (529)

    where Uc effect of applied field on the domain energy

    Up and Ux bulk electrical and elastic energies

    Ud depolarization energy and

    Uw domain energy

    Ud is the energy related to the internal field set up in the crystal by the polarization and not

    compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

    (530)

    Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

    is the polarization at the center of the domain

    Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

    width (d) and crystal volume (V) and is given as

    (531)

    To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

    in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

    wrt domain wall thickness d ie dΔGdd = 0 resulting in

    (532)

    Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    539 Ferroelectric Switching and Domains

    Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

    At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

    Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

    If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

    microCcm2and E is electric field across the sample in Vcm The process is something like this

    Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

    Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

    reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

    polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

    Further increase of electric field in the opposite direction will cause complete reversal of orientation

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    of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

    Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

    Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

    >

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    5310 Measurement of Hysteresis Loop

    Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

    The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

    crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

    This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

    and coercive field Ec

    A ferroelectric materials shows polarization of the order of 50-100 microCcm2

    Figure 5 15 Schematic representation of sawyer-tower circuit

    Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

    Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

    atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

    Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

    Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

    a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

    Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

    becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

    positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

    The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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    Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

    Because the distorted octahedra are coupled together in ferroelectric form there is a very large

    spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

    BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

    orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

    5312 Applications of Ferroelectrics

    In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

    Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

    (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

    Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

    where their dielectric constant increases linearly with temperature they can be used for cameraflashes

    53121 Nonvolatile Memories

    Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

    two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

    Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

    53122 Camera Flashes

    In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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    Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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    Module 5 Nonlinear Dielectrics

    Summary

    Summary

    In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

    can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

    and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

    binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

    One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

    5474 Actuators

    In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

    In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

    You can have it in two forms

    Direct Piezo Actuators with strokes lower than 100 microns or so and

    Amplified Piezoelectric Actuators which can yield millimeter long strokes

    Some of the examples of applications are

    Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

    Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

    Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

    Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

    In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

    As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

    5475 Frequency Standards

    Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

    Quartz clocks

    Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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    Module 5 Nonlinear Dielectrics

    Summary

    Summary

    Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

    54 Piezoelectric Ceramics

    Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

    Pb(ZrTi)O3)

    An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

    For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

    541 Direct Piezoelectric Effect

    Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

    (533)

    where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

    542 Reverse or Converse Piezoelectric Effect

    The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

    (534)

    where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

    Figure 520 Direct and Converse PiezoelectricEffects

    The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

    543 Poling of Piezoelectric Materials

    As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

    The values of piezoelectric coefficient of some materials are given below

    Material Piezoelectric Constant d(pmV)

    Quartz 23

    Barium Titanate 100-149

    Lead Niobate 80-85

    Lead zirconate titanate 250-365

    So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

    Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

    field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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    Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

    544 Depolarization of Piezoelectrics

    Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

    polarization or rather result in alignment of dipoles gets lost

    Figure 522 Animation on depolarization offerroelectrics

    (Courtesy copy DoITPoMS University of Cambridge)

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    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

    545 Common PIezoelectric Materials

    5451 Barium Titanate (BaTiO3)

    This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

    used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

    Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

    1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

    must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

    5452 Pb(ZrTi)O3 or PZT

    PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

    The phase diagram of PZT is shown below

    Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

    The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

    lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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    few poling directions available making it a useful piezoelectric

    Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

    546 Measurement of Piezoelectric Properties

    Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

    In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

    Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

    The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

    (535)

    Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

    (536)

    Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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    One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

    547 Applications of Piezoelectric Ceramics

    Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

    5471 Power Generation

    Gas Lighter

    Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

    Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

    One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

    Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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    Power Transformer

    A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

    An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

    Figure 526 Schematic of a piezoelectrictransformer

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    Module 5 Special Dielectrics Piezoelectric Ceramics

    5472 Piezoelectric Sensors

    Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

    Other sensor applications are

    Detection and generation of sonar waves

    To detect detonation in automotive engine by sampling the vibrations of the engine block

    To detect the precise moment of fuel injection in an automotive engine

    Detection of acoustic emissions in acoustic emission testing

    Microbalances as very sensitive chemical and biological sensors

    Strain gauges

    Medical applications using ultrasound waves

    Kidney stone treatment

    In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

    Figure 527 Ultrasonic waves creation and

    >

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    kidney stone treatment and ultrasound imagingof the fetus

    (Courtesy copy DoITPoMS University of Cambridge)

    5473 Ultrasound Imaging Using Transduction Effect

    Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

    55 Pyroelectric Ceramics

    Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

    Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

    Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

    551 Difference between Pyroelectric and Ferroelectric Material

    Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

    Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

    552 Theory of Piezoelectric Materials

    From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

    (537)

    Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

    Assuming electric field E as constant differentiating the above equation with temperature leads to

    (538)

    Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

    we write

    Δ OR

    Δ (539)

    Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

    Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

    (540)

    The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

    As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

    553 Measurement of Pyroelectric Coefficient

    One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

    (541)

    Where Ip is the pyrocurrent and is given as

    (542)

    where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

    respectively

    Figure 530 Circuit for measuring pyroelectriccoefficient

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    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

    554 Direct and Indirect Effect

    Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

    Since change in the polarization can also be expressed as depending

    upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

    Figure 531 Direct-Indirect effect animation

    (Courtesy copy DoITPoMS University of Cambridge)

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    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

    555 Common Pyroelectric Materials

    Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

    The most common materials are tabulated below

    Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

    LiTaO3 single crystal Hexagonal 665 -230

    075Pb(Mg13-Nb23)O3-025PbTiO3

    (PMN-PT) Ceramic

    Perovskite 150 -1300

    Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

    Triglycine sulphate

    (NH2CH2COOH)3H2SO4

    Sulphate 49 -280

    Polyvinylidene fluoride (PVDF) film Polymer 80 -27

    5551 Triglycine Sulphate (TGS)

    High pyroelectric coefficient

    Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

    Can be modified to withstand temperatures above Curie point without depoling

    Used in thermal imaging cameras

    5552 Polyvinylidene Fluoride (PVDF)

    Poor pyroelectric coefficient

    Readily available in large areas of thin film

    More stable to heat vacuum and moisture than TGS mechanically robust

    Low heat conductivity and low permittivity

    High loss tangent

    Commonly used for burglar alarms

    5553 Perovskite Ferroelectric Ceramics

    Generally robust and insensitive to moisture and vacuum

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    High pyroelectric coefficient and low loss

    Better operation near TC

    Strong dependence on composition

    As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

    RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

    556 Common Applications

    5561 Burglar Alarms

    Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

    Figure 532 Working of an IR intruder alarm

    (Courtesy copy DoITPoMS University ofCambridge)

    5562 Infrared or Thermal Imaging

    Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

    The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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    A typical photograph generated from IR imaging looks like this

    Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

    Here is a simple explanation of how IT imaging using pyroelectrics works

    A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

    This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

    Figure 534 Process of imagecreation

    5563 Pollutant Control

    The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

    Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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    Figure 535 Gas detection using a pyroelectricdetector

    (Courtesy copy DoITPoMS University of Cambridge)

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    Module 5 Nonlinear Dielectrics

    Summary

    Summary

    Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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      Figure 51 Classificatin of piezo- pyro- and ferro-electrics

      In the subsequent sections we will discuss about the ferroelectric pyroelectric and piezoelectricmaterials explaining the fundamental physics some key materials and applications

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      53 Ferroelectric Ceramics

      Ferroelectric effect was first observed in Rochelle salt KNaC4H4O64H2O by Czech scientist Roger

      Valasek in 1921 Afterwards for years the discovery did not raise much excitement possibly due tothe world war However after a few decades renewed technological interest led to much moreextensive studies and a better understanding

      In the subsequent years many materials were discovered and were of technological interest as theywere employed into a variety of applications Among various categories of ferroelectric materialsfollowing stand out either due to interest in the structure or in the properties

      Tri-glycine sulfate and isomorphous materials

      Pottasium dihyrogen phosphates and isomorphous materials

      Barium titanate and other perovskite structured compounds such as KNbO3 PbTiO3 etc

      Complex oxides such as Aurrivillious compounds

      Rochelle Salt and similar compounds

      Ferroelectric Sulfates

      Among the above perovskite related compounds have been studied most primarily due to theirexciting properties and reasonably high transition temperatures making them attractive for variousapplications

      In the following section we will look some of the structural and thermodynamic features of thesematerials with main emphasis on perovskite compounds for the sake of illustration

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      531 Permanent Dipole Moment and Polarization

      These materials consist of net permanent dipole moment ie finite vector sum of dipole momenteven in the absence of electric field This requires the material to be non-centrosymmetric whereasdipole moment would be forced to be zero in a centrosymmteric material due to symmetryconsiderations

      On top of this there must be a spontaneous polarization as well which means the centers of positiveand negative charges in a crystal would never be the same

      The following is the figure showing the crystal structure of a perovskite structured material such asBaTiO3 Here in cubic structure (A) the dipole is zero while in tetragonal form (B) the dipole

      moment is finite This displaced position of the central atom is the energetically stable position iethe free energy is minimum

      Figure 52 Cubic and tetragonal perovskite structures with dipolemoment in latter represented by an arrow due to movement ofcentral B ion up or down along c-axis

      When this kind of ferroelectric material is switched ie subjected to a bipolar electric field it exhibitsa polarization vs electric field plot as shown below You can see that there is finite polarization in theabsence of electric field ie two equal and opposite values +Pr or -Pr also called remnant

      polarization These two values can be connected with the position of a central atom in the octahedra in the figureabove So when you apply field in the direction the central atom moves up with respect to oxygenoctahedral and when you change the polarity it comes down in the opposite direction the extent ofdisplacement being similar

      The plot shows a hysteresis which is important for applications such as memory devices We willexplain the details of this phenomenon in the subsequent sections

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      Figure 53 A typical ferroelectric hysteresisloop

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      532 Principle of Ferroelectricity Energetics

      The movement of central atom in the above structure can explained in terms of a potential energydiagram

      Figure 54 Potential energy well and crystal structure for an ABO3structured ferroelectric

      This situation can be explained in terms of a potential energy between two adjacent low energysites There are two equilibrium positions in which a B ion can stay but to change from one state toanother energy must be provided to overcome an energy barrier ΔE These energy wells further tiltto the left or right depending upon the polarity of the electric field ie in the non-zero field statemaking on configuration more stable than another However a coercive field which is the fieldrequired to bring the polarization back to zero is needed when you switch to other direction of thefield

      Ferroelectric materials follow Curie-Weiss law which is expressed as

      (51)

      Here N is the number of dipoles per unit volume of the material a is dipolar polarizability and Tc is

      defined as the Ferroelectric transition temperature or the Curie temperature

      Ferroelectric behaviour is observed below the Curie Temperature above which the ferroelectricphase converts into a paraelectric phase which always has higher symmetry than the ferroelectricphase (for example transformation of low symmetry tetragonal BaTiO3 to higher symmetry cubic

      BaTiO3 at about 120oC while heating) and ferroelectricity disappears A paraelectric state is

      essentially a centrosymmetric higher symmetry state where dipoles are randomly oriented in acrystal giving rise to zero polarization

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      Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      533 Proof of Curie-Weiss Law

      We can now say that in a ferroelectric material reversible spontaneous alignment of electric dipolestakes place by mutual interaction This happens due to a local field E which is increased by dipolealignment in the direction of field Interestingly this phenomenon happens below a criticaltemperature Tc when crystal enters into nonsymetric state where thermal energy cannot randomize

      the electric dipoles presumably due to dipole-dipole interactions and local field

      Following the basic principles we developed in module 4 polarization P can be expressed as

      (52)

      Where local field E = E + P3e0 as given by Clausius-Mossotti relationship and er is the relative

      dielectric permittivity and a is total polarizability Substitution for E in (52) results in

      ie

      or

      (53)

      Since we know that susceptibility we get

      (54)

      Equation (54) shows that both χ and er must approach 8 when Na3e0 approaches 1

      This can be assumed to be a right condition for ferroelectrics as near the ferroelectric transition theyexhibit very large susceptibilities and dielectric constant At this point we can also ignore theelectronic ionic and interface polarizations assuming that dipolar polarizability is too high such thatad gtgt ae + ai + aint at a critical temperature Tc Here define a = ad = CkT where C is Curiersquos

      constant This is the right sort of relation as we have already seen the temperature dependence ofdipolar polarization in section (453)

      Hence we can further write

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      OR

      (55)

      Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

      we get

      OR

      (56)

      Thus by now modifying equation (54) Curie-Weiss law can be expressed as

      (57)

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      534 Thermodyanamic Basis of Ferroelectric Phase Transitions

      Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

      These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

      Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

      (58)

      where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

      is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

      Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

      (59)

      where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

      Converse piezoelectric effect is expressed as

      (510)

      Where dijkt is in mV

      Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

      (511)

      where Pi is the vector of pyroelectric coefficient in cm-2K-1

      Displacement is expressed as

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      (512)

      So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

      From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

      For a ferroelectric system the free energy G can be expressed in terms of ten variables as

      (513)

      where Px Py Pz are the components of the polarization are the stress

      components and T is the temperature

      We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

      (514)

      Note that only even powers are taken because energy is same for plusmnPS states

      Here a b c are the temperature dependent constants and E is the electric field

      The equilibrium is found by establishing ie

      (515)

      ie

      E = (516)

      If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

      If we ignore higher power terms then

      (517)

      leading to

      (518)

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      which is the same expression that we encountered for linear dielectrics

      According to Landau-Devonshire theory near the Curie point (T~T0) we assume

      a = a0 (T - T0) (519)

      As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

      (520)

      In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

      Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

      paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

      nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

      Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      535 Case I Second order Transition

      When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

      second order transition (do not get confused between T0 and Tc as the distiction will become clear

      in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

      Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

      Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

      The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

      retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

      polarization can be expressed as

      (521)

      showing that the polarization decreased to zero at T = T0 as shown in figure 58

      Dielectric susceptibility at T lt T0 can be estimated as

      (522)

      Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

      will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

      values near T0

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      Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

      This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

      (523)

      Now substituting in (523) yields

      (524)

      Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      536 Case ndash II First Order Transition

      Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

      now more than T0 This gives rise to the following free energy vs polarization plot

      Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

      The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

      is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

      Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

      In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

      free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

      (525)

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      On the other hand field E must also be zero for the polarization to be spontaneous ie

      (526)

      The polarization and susceptibility at Tc are obtained by solving two equations and are given as

      (527)

      and

      (528)

      The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

      heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

      temperature higher than Tc the sample will be in paraelectric state This results in thermal

      hysteresis when these materials are thermally cycled across Tc

      If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

      Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

      Solid State Physics AJ Dekker Macmillan Publishing

      Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      537 Ferroelectric Domains

      In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

      Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

      The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

      directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

      or 90deg domain walls

      Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

      Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

      depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

      Now the question is Why is there a domain wall

      The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

      associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

      splitting of the material into oppositely oriented domains or

      compensation of the electrical charge via electrical conduction through the crystal

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      Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

      by transmission electron microscopy

      Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      538 Analytical treatment of domain wall energy

      Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

      (529)

      where Uc effect of applied field on the domain energy

      Up and Ux bulk electrical and elastic energies

      Ud depolarization energy and

      Uw domain energy

      Ud is the energy related to the internal field set up in the crystal by the polarization and not

      compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

      (530)

      Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

      is the polarization at the center of the domain

      Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

      width (d) and crystal volume (V) and is given as

      (531)

      To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

      in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

      wrt domain wall thickness d ie dΔGdd = 0 resulting in

      (532)

      Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      539 Ferroelectric Switching and Domains

      Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

      At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

      Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

      If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

      microCcm2and E is electric field across the sample in Vcm The process is something like this

      Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

      Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

      reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

      polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

      Further increase of electric field in the opposite direction will cause complete reversal of orientation

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      of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

      Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

      Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

      >

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      5310 Measurement of Hysteresis Loop

      Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

      The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

      crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

      This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

      and coercive field Ec

      A ferroelectric materials shows polarization of the order of 50-100 microCcm2

      Figure 5 15 Schematic representation of sawyer-tower circuit

      Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

      Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

      atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

      Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

      Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

      a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

      Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

      becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

      positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

      The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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      Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

      Because the distorted octahedra are coupled together in ferroelectric form there is a very large

      spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

      BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

      orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

      5312 Applications of Ferroelectrics

      In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

      Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

      (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

      Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

      where their dielectric constant increases linearly with temperature they can be used for cameraflashes

      53121 Nonvolatile Memories

      Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

      two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

      Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

      53122 Camera Flashes

      In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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      Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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      Module 5 Nonlinear Dielectrics

      Summary

      Summary

      In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

      can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

      and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

      binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

      One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

      5474 Actuators

      In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

      In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

      You can have it in two forms

      Direct Piezo Actuators with strokes lower than 100 microns or so and

      Amplified Piezoelectric Actuators which can yield millimeter long strokes

      Some of the examples of applications are

      Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

      Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

      Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

      Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

      In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

      As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

      5475 Frequency Standards

      Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

      Quartz clocks

      Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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      Module 5 Nonlinear Dielectrics

      Summary

      Summary

      Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

      54 Piezoelectric Ceramics

      Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

      Pb(ZrTi)O3)

      An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

      For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

      541 Direct Piezoelectric Effect

      Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

      (533)

      where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

      542 Reverse or Converse Piezoelectric Effect

      The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

      (534)

      where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

      Figure 520 Direct and Converse PiezoelectricEffects

      The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

      543 Poling of Piezoelectric Materials

      As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

      The values of piezoelectric coefficient of some materials are given below

      Material Piezoelectric Constant d(pmV)

      Quartz 23

      Barium Titanate 100-149

      Lead Niobate 80-85

      Lead zirconate titanate 250-365

      So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

      Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

      field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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      Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

      544 Depolarization of Piezoelectrics

      Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

      polarization or rather result in alignment of dipoles gets lost

      Figure 522 Animation on depolarization offerroelectrics

      (Courtesy copy DoITPoMS University of Cambridge)

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      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

      545 Common PIezoelectric Materials

      5451 Barium Titanate (BaTiO3)

      This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

      used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

      Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

      1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

      must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

      5452 Pb(ZrTi)O3 or PZT

      PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

      The phase diagram of PZT is shown below

      Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

      The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

      lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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      few poling directions available making it a useful piezoelectric

      Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

      546 Measurement of Piezoelectric Properties

      Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

      In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

      Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

      The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

      (535)

      Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

      (536)

      Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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      One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

      547 Applications of Piezoelectric Ceramics

      Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

      5471 Power Generation

      Gas Lighter

      Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

      Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

      One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

      Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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      Power Transformer

      A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

      An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

      Figure 526 Schematic of a piezoelectrictransformer

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      Module 5 Special Dielectrics Piezoelectric Ceramics

      5472 Piezoelectric Sensors

      Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

      Other sensor applications are

      Detection and generation of sonar waves

      To detect detonation in automotive engine by sampling the vibrations of the engine block

      To detect the precise moment of fuel injection in an automotive engine

      Detection of acoustic emissions in acoustic emission testing

      Microbalances as very sensitive chemical and biological sensors

      Strain gauges

      Medical applications using ultrasound waves

      Kidney stone treatment

      In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

      Figure 527 Ultrasonic waves creation and

      >

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      kidney stone treatment and ultrasound imagingof the fetus

      (Courtesy copy DoITPoMS University of Cambridge)

      5473 Ultrasound Imaging Using Transduction Effect

      Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

      55 Pyroelectric Ceramics

      Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

      Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

      Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

      551 Difference between Pyroelectric and Ferroelectric Material

      Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

      Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

      552 Theory of Piezoelectric Materials

      From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

      (537)

      Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

      Assuming electric field E as constant differentiating the above equation with temperature leads to

      (538)

      Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

      we write

      Δ OR

      Δ (539)

      Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

      Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

      (540)

      The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

      As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

      553 Measurement of Pyroelectric Coefficient

      One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

      (541)

      Where Ip is the pyrocurrent and is given as

      (542)

      where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

      respectively

      Figure 530 Circuit for measuring pyroelectriccoefficient

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      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

      554 Direct and Indirect Effect

      Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

      Since change in the polarization can also be expressed as depending

      upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

      Figure 531 Direct-Indirect effect animation

      (Courtesy copy DoITPoMS University of Cambridge)

      >

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      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

      555 Common Pyroelectric Materials

      Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

      The most common materials are tabulated below

      Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

      LiTaO3 single crystal Hexagonal 665 -230

      075Pb(Mg13-Nb23)O3-025PbTiO3

      (PMN-PT) Ceramic

      Perovskite 150 -1300

      Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

      Triglycine sulphate

      (NH2CH2COOH)3H2SO4

      Sulphate 49 -280

      Polyvinylidene fluoride (PVDF) film Polymer 80 -27

      5551 Triglycine Sulphate (TGS)

      High pyroelectric coefficient

      Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

      Can be modified to withstand temperatures above Curie point without depoling

      Used in thermal imaging cameras

      5552 Polyvinylidene Fluoride (PVDF)

      Poor pyroelectric coefficient

      Readily available in large areas of thin film

      More stable to heat vacuum and moisture than TGS mechanically robust

      Low heat conductivity and low permittivity

      High loss tangent

      Commonly used for burglar alarms

      5553 Perovskite Ferroelectric Ceramics

      Generally robust and insensitive to moisture and vacuum

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      High pyroelectric coefficient and low loss

      Better operation near TC

      Strong dependence on composition

      As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

      RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

      556 Common Applications

      5561 Burglar Alarms

      Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

      Figure 532 Working of an IR intruder alarm

      (Courtesy copy DoITPoMS University ofCambridge)

      5562 Infrared or Thermal Imaging

      Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

      The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

      >

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      A typical photograph generated from IR imaging looks like this

      Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

      Here is a simple explanation of how IT imaging using pyroelectrics works

      A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

      This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

      Figure 534 Process of imagecreation

      5563 Pollutant Control

      The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

      Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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      Figure 535 Gas detection using a pyroelectricdetector

      (Courtesy copy DoITPoMS University of Cambridge)

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      Module 5 Nonlinear Dielectrics

      Summary

      Summary

      Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        53 Ferroelectric Ceramics

        Ferroelectric effect was first observed in Rochelle salt KNaC4H4O64H2O by Czech scientist Roger

        Valasek in 1921 Afterwards for years the discovery did not raise much excitement possibly due tothe world war However after a few decades renewed technological interest led to much moreextensive studies and a better understanding

        In the subsequent years many materials were discovered and were of technological interest as theywere employed into a variety of applications Among various categories of ferroelectric materialsfollowing stand out either due to interest in the structure or in the properties

        Tri-glycine sulfate and isomorphous materials

        Pottasium dihyrogen phosphates and isomorphous materials

        Barium titanate and other perovskite structured compounds such as KNbO3 PbTiO3 etc

        Complex oxides such as Aurrivillious compounds

        Rochelle Salt and similar compounds

        Ferroelectric Sulfates

        Among the above perovskite related compounds have been studied most primarily due to theirexciting properties and reasonably high transition temperatures making them attractive for variousapplications

        In the following section we will look some of the structural and thermodynamic features of thesematerials with main emphasis on perovskite compounds for the sake of illustration

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        531 Permanent Dipole Moment and Polarization

        These materials consist of net permanent dipole moment ie finite vector sum of dipole momenteven in the absence of electric field This requires the material to be non-centrosymmetric whereasdipole moment would be forced to be zero in a centrosymmteric material due to symmetryconsiderations

        On top of this there must be a spontaneous polarization as well which means the centers of positiveand negative charges in a crystal would never be the same

        The following is the figure showing the crystal structure of a perovskite structured material such asBaTiO3 Here in cubic structure (A) the dipole is zero while in tetragonal form (B) the dipole

        moment is finite This displaced position of the central atom is the energetically stable position iethe free energy is minimum

        Figure 52 Cubic and tetragonal perovskite structures with dipolemoment in latter represented by an arrow due to movement ofcentral B ion up or down along c-axis

        When this kind of ferroelectric material is switched ie subjected to a bipolar electric field it exhibitsa polarization vs electric field plot as shown below You can see that there is finite polarization in theabsence of electric field ie two equal and opposite values +Pr or -Pr also called remnant

        polarization These two values can be connected with the position of a central atom in the octahedra in the figureabove So when you apply field in the direction the central atom moves up with respect to oxygenoctahedral and when you change the polarity it comes down in the opposite direction the extent ofdisplacement being similar

        The plot shows a hysteresis which is important for applications such as memory devices We willexplain the details of this phenomenon in the subsequent sections

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        Figure 53 A typical ferroelectric hysteresisloop

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        532 Principle of Ferroelectricity Energetics

        The movement of central atom in the above structure can explained in terms of a potential energydiagram

        Figure 54 Potential energy well and crystal structure for an ABO3structured ferroelectric

        This situation can be explained in terms of a potential energy between two adjacent low energysites There are two equilibrium positions in which a B ion can stay but to change from one state toanother energy must be provided to overcome an energy barrier ΔE These energy wells further tiltto the left or right depending upon the polarity of the electric field ie in the non-zero field statemaking on configuration more stable than another However a coercive field which is the fieldrequired to bring the polarization back to zero is needed when you switch to other direction of thefield

        Ferroelectric materials follow Curie-Weiss law which is expressed as

        (51)

        Here N is the number of dipoles per unit volume of the material a is dipolar polarizability and Tc is

        defined as the Ferroelectric transition temperature or the Curie temperature

        Ferroelectric behaviour is observed below the Curie Temperature above which the ferroelectricphase converts into a paraelectric phase which always has higher symmetry than the ferroelectricphase (for example transformation of low symmetry tetragonal BaTiO3 to higher symmetry cubic

        BaTiO3 at about 120oC while heating) and ferroelectricity disappears A paraelectric state is

        essentially a centrosymmetric higher symmetry state where dipoles are randomly oriented in acrystal giving rise to zero polarization

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        Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        533 Proof of Curie-Weiss Law

        We can now say that in a ferroelectric material reversible spontaneous alignment of electric dipolestakes place by mutual interaction This happens due to a local field E which is increased by dipolealignment in the direction of field Interestingly this phenomenon happens below a criticaltemperature Tc when crystal enters into nonsymetric state where thermal energy cannot randomize

        the electric dipoles presumably due to dipole-dipole interactions and local field

        Following the basic principles we developed in module 4 polarization P can be expressed as

        (52)

        Where local field E = E + P3e0 as given by Clausius-Mossotti relationship and er is the relative

        dielectric permittivity and a is total polarizability Substitution for E in (52) results in

        ie

        or

        (53)

        Since we know that susceptibility we get

        (54)

        Equation (54) shows that both χ and er must approach 8 when Na3e0 approaches 1

        This can be assumed to be a right condition for ferroelectrics as near the ferroelectric transition theyexhibit very large susceptibilities and dielectric constant At this point we can also ignore theelectronic ionic and interface polarizations assuming that dipolar polarizability is too high such thatad gtgt ae + ai + aint at a critical temperature Tc Here define a = ad = CkT where C is Curiersquos

        constant This is the right sort of relation as we have already seen the temperature dependence ofdipolar polarization in section (453)

        Hence we can further write

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        OR

        (55)

        Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

        we get

        OR

        (56)

        Thus by now modifying equation (54) Curie-Weiss law can be expressed as

        (57)

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        534 Thermodyanamic Basis of Ferroelectric Phase Transitions

        Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

        These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

        Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

        (58)

        where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

        is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

        Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

        (59)

        where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

        Converse piezoelectric effect is expressed as

        (510)

        Where dijkt is in mV

        Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

        (511)

        where Pi is the vector of pyroelectric coefficient in cm-2K-1

        Displacement is expressed as

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        (512)

        So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

        From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

        For a ferroelectric system the free energy G can be expressed in terms of ten variables as

        (513)

        where Px Py Pz are the components of the polarization are the stress

        components and T is the temperature

        We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

        (514)

        Note that only even powers are taken because energy is same for plusmnPS states

        Here a b c are the temperature dependent constants and E is the electric field

        The equilibrium is found by establishing ie

        (515)

        ie

        E = (516)

        If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

        If we ignore higher power terms then

        (517)

        leading to

        (518)

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        which is the same expression that we encountered for linear dielectrics

        According to Landau-Devonshire theory near the Curie point (T~T0) we assume

        a = a0 (T - T0) (519)

        As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

        (520)

        In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

        Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

        paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

        nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

        Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        535 Case I Second order Transition

        When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

        second order transition (do not get confused between T0 and Tc as the distiction will become clear

        in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

        Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

        Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

        The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

        retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

        polarization can be expressed as

        (521)

        showing that the polarization decreased to zero at T = T0 as shown in figure 58

        Dielectric susceptibility at T lt T0 can be estimated as

        (522)

        Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

        will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

        values near T0

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        Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

        This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

        (523)

        Now substituting in (523) yields

        (524)

        Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        536 Case ndash II First Order Transition

        Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

        now more than T0 This gives rise to the following free energy vs polarization plot

        Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

        The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

        is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

        Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

        In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

        free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

        (525)

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        On the other hand field E must also be zero for the polarization to be spontaneous ie

        (526)

        The polarization and susceptibility at Tc are obtained by solving two equations and are given as

        (527)

        and

        (528)

        The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

        heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

        temperature higher than Tc the sample will be in paraelectric state This results in thermal

        hysteresis when these materials are thermally cycled across Tc

        If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

        Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

        Solid State Physics AJ Dekker Macmillan Publishing

        Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        537 Ferroelectric Domains

        In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

        Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

        The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

        directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

        or 90deg domain walls

        Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

        Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

        depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

        Now the question is Why is there a domain wall

        The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

        associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

        splitting of the material into oppositely oriented domains or

        compensation of the electrical charge via electrical conduction through the crystal

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        Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

        by transmission electron microscopy

        Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        538 Analytical treatment of domain wall energy

        Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

        (529)

        where Uc effect of applied field on the domain energy

        Up and Ux bulk electrical and elastic energies

        Ud depolarization energy and

        Uw domain energy

        Ud is the energy related to the internal field set up in the crystal by the polarization and not

        compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

        (530)

        Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

        is the polarization at the center of the domain

        Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

        width (d) and crystal volume (V) and is given as

        (531)

        To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

        in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

        wrt domain wall thickness d ie dΔGdd = 0 resulting in

        (532)

        Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        539 Ferroelectric Switching and Domains

        Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

        At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

        Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

        If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

        microCcm2and E is electric field across the sample in Vcm The process is something like this

        Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

        Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

        reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

        polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

        Further increase of electric field in the opposite direction will cause complete reversal of orientation

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        of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

        Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

        Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

        >

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        5310 Measurement of Hysteresis Loop

        Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

        The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

        crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

        This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

        and coercive field Ec

        A ferroelectric materials shows polarization of the order of 50-100 microCcm2

        Figure 5 15 Schematic representation of sawyer-tower circuit

        Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

        Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

        atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

        Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

        Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

        a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

        Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

        becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

        positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

        The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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        Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

        Because the distorted octahedra are coupled together in ferroelectric form there is a very large

        spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

        BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

        orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

        5312 Applications of Ferroelectrics

        In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

        Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

        (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

        Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

        where their dielectric constant increases linearly with temperature they can be used for cameraflashes

        53121 Nonvolatile Memories

        Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

        two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

        Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

        53122 Camera Flashes

        In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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        Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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        Module 5 Nonlinear Dielectrics

        Summary

        Summary

        In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

        can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

        and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

        binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

        One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

        5474 Actuators

        In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

        In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

        You can have it in two forms

        Direct Piezo Actuators with strokes lower than 100 microns or so and

        Amplified Piezoelectric Actuators which can yield millimeter long strokes

        Some of the examples of applications are

        Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

        Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

        Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

        Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

        In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

        As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

        5475 Frequency Standards

        Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

        Quartz clocks

        Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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        Module 5 Nonlinear Dielectrics

        Summary

        Summary

        Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

        54 Piezoelectric Ceramics

        Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

        Pb(ZrTi)O3)

        An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

        For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

        541 Direct Piezoelectric Effect

        Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

        (533)

        where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

        542 Reverse or Converse Piezoelectric Effect

        The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

        (534)

        where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

        Figure 520 Direct and Converse PiezoelectricEffects

        The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

        543 Poling of Piezoelectric Materials

        As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

        The values of piezoelectric coefficient of some materials are given below

        Material Piezoelectric Constant d(pmV)

        Quartz 23

        Barium Titanate 100-149

        Lead Niobate 80-85

        Lead zirconate titanate 250-365

        So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

        Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

        field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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        Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

        544 Depolarization of Piezoelectrics

        Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

        polarization or rather result in alignment of dipoles gets lost

        Figure 522 Animation on depolarization offerroelectrics

        (Courtesy copy DoITPoMS University of Cambridge)

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        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

        545 Common PIezoelectric Materials

        5451 Barium Titanate (BaTiO3)

        This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

        used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

        Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

        1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

        must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

        5452 Pb(ZrTi)O3 or PZT

        PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

        The phase diagram of PZT is shown below

        Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

        The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

        lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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        few poling directions available making it a useful piezoelectric

        Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

        546 Measurement of Piezoelectric Properties

        Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

        In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

        Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

        The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

        (535)

        Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

        (536)

        Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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        One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

        547 Applications of Piezoelectric Ceramics

        Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

        5471 Power Generation

        Gas Lighter

        Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

        Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

        One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

        Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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        Power Transformer

        A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

        An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

        Figure 526 Schematic of a piezoelectrictransformer

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        Module 5 Special Dielectrics Piezoelectric Ceramics

        5472 Piezoelectric Sensors

        Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

        Other sensor applications are

        Detection and generation of sonar waves

        To detect detonation in automotive engine by sampling the vibrations of the engine block

        To detect the precise moment of fuel injection in an automotive engine

        Detection of acoustic emissions in acoustic emission testing

        Microbalances as very sensitive chemical and biological sensors

        Strain gauges

        Medical applications using ultrasound waves

        Kidney stone treatment

        In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

        Figure 527 Ultrasonic waves creation and

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        kidney stone treatment and ultrasound imagingof the fetus

        (Courtesy copy DoITPoMS University of Cambridge)

        5473 Ultrasound Imaging Using Transduction Effect

        Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

        55 Pyroelectric Ceramics

        Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

        Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

        Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

        551 Difference between Pyroelectric and Ferroelectric Material

        Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

        Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

        552 Theory of Piezoelectric Materials

        From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

        (537)

        Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

        Assuming electric field E as constant differentiating the above equation with temperature leads to

        (538)

        Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

        we write

        Δ OR

        Δ (539)

        Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

        Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

        (540)

        The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

        As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

        553 Measurement of Pyroelectric Coefficient

        One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

        (541)

        Where Ip is the pyrocurrent and is given as

        (542)

        where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

        respectively

        Figure 530 Circuit for measuring pyroelectriccoefficient

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        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

        554 Direct and Indirect Effect

        Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

        Since change in the polarization can also be expressed as depending

        upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

        Figure 531 Direct-Indirect effect animation

        (Courtesy copy DoITPoMS University of Cambridge)

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        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

        555 Common Pyroelectric Materials

        Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

        The most common materials are tabulated below

        Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

        LiTaO3 single crystal Hexagonal 665 -230

        075Pb(Mg13-Nb23)O3-025PbTiO3

        (PMN-PT) Ceramic

        Perovskite 150 -1300

        Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

        Triglycine sulphate

        (NH2CH2COOH)3H2SO4

        Sulphate 49 -280

        Polyvinylidene fluoride (PVDF) film Polymer 80 -27

        5551 Triglycine Sulphate (TGS)

        High pyroelectric coefficient

        Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

        Can be modified to withstand temperatures above Curie point without depoling

        Used in thermal imaging cameras

        5552 Polyvinylidene Fluoride (PVDF)

        Poor pyroelectric coefficient

        Readily available in large areas of thin film

        More stable to heat vacuum and moisture than TGS mechanically robust

        Low heat conductivity and low permittivity

        High loss tangent

        Commonly used for burglar alarms

        5553 Perovskite Ferroelectric Ceramics

        Generally robust and insensitive to moisture and vacuum

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        High pyroelectric coefficient and low loss

        Better operation near TC

        Strong dependence on composition

        As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

        RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

        556 Common Applications

        5561 Burglar Alarms

        Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

        Figure 532 Working of an IR intruder alarm

        (Courtesy copy DoITPoMS University ofCambridge)

        5562 Infrared or Thermal Imaging

        Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

        The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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        A typical photograph generated from IR imaging looks like this

        Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

        Here is a simple explanation of how IT imaging using pyroelectrics works

        A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

        This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

        Figure 534 Process of imagecreation

        5563 Pollutant Control

        The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

        Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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        Figure 535 Gas detection using a pyroelectricdetector

        (Courtesy copy DoITPoMS University of Cambridge)

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        Module 5 Nonlinear Dielectrics

        Summary

        Summary

        Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          531 Permanent Dipole Moment and Polarization

          These materials consist of net permanent dipole moment ie finite vector sum of dipole momenteven in the absence of electric field This requires the material to be non-centrosymmetric whereasdipole moment would be forced to be zero in a centrosymmteric material due to symmetryconsiderations

          On top of this there must be a spontaneous polarization as well which means the centers of positiveand negative charges in a crystal would never be the same

          The following is the figure showing the crystal structure of a perovskite structured material such asBaTiO3 Here in cubic structure (A) the dipole is zero while in tetragonal form (B) the dipole

          moment is finite This displaced position of the central atom is the energetically stable position iethe free energy is minimum

          Figure 52 Cubic and tetragonal perovskite structures with dipolemoment in latter represented by an arrow due to movement ofcentral B ion up or down along c-axis

          When this kind of ferroelectric material is switched ie subjected to a bipolar electric field it exhibitsa polarization vs electric field plot as shown below You can see that there is finite polarization in theabsence of electric field ie two equal and opposite values +Pr or -Pr also called remnant

          polarization These two values can be connected with the position of a central atom in the octahedra in the figureabove So when you apply field in the direction the central atom moves up with respect to oxygenoctahedral and when you change the polarity it comes down in the opposite direction the extent ofdisplacement being similar

          The plot shows a hysteresis which is important for applications such as memory devices We willexplain the details of this phenomenon in the subsequent sections

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          Figure 53 A typical ferroelectric hysteresisloop

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          532 Principle of Ferroelectricity Energetics

          The movement of central atom in the above structure can explained in terms of a potential energydiagram

          Figure 54 Potential energy well and crystal structure for an ABO3structured ferroelectric

          This situation can be explained in terms of a potential energy between two adjacent low energysites There are two equilibrium positions in which a B ion can stay but to change from one state toanother energy must be provided to overcome an energy barrier ΔE These energy wells further tiltto the left or right depending upon the polarity of the electric field ie in the non-zero field statemaking on configuration more stable than another However a coercive field which is the fieldrequired to bring the polarization back to zero is needed when you switch to other direction of thefield

          Ferroelectric materials follow Curie-Weiss law which is expressed as

          (51)

          Here N is the number of dipoles per unit volume of the material a is dipolar polarizability and Tc is

          defined as the Ferroelectric transition temperature or the Curie temperature

          Ferroelectric behaviour is observed below the Curie Temperature above which the ferroelectricphase converts into a paraelectric phase which always has higher symmetry than the ferroelectricphase (for example transformation of low symmetry tetragonal BaTiO3 to higher symmetry cubic

          BaTiO3 at about 120oC while heating) and ferroelectricity disappears A paraelectric state is

          essentially a centrosymmetric higher symmetry state where dipoles are randomly oriented in acrystal giving rise to zero polarization

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          Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          533 Proof of Curie-Weiss Law

          We can now say that in a ferroelectric material reversible spontaneous alignment of electric dipolestakes place by mutual interaction This happens due to a local field E which is increased by dipolealignment in the direction of field Interestingly this phenomenon happens below a criticaltemperature Tc when crystal enters into nonsymetric state where thermal energy cannot randomize

          the electric dipoles presumably due to dipole-dipole interactions and local field

          Following the basic principles we developed in module 4 polarization P can be expressed as

          (52)

          Where local field E = E + P3e0 as given by Clausius-Mossotti relationship and er is the relative

          dielectric permittivity and a is total polarizability Substitution for E in (52) results in

          ie

          or

          (53)

          Since we know that susceptibility we get

          (54)

          Equation (54) shows that both χ and er must approach 8 when Na3e0 approaches 1

          This can be assumed to be a right condition for ferroelectrics as near the ferroelectric transition theyexhibit very large susceptibilities and dielectric constant At this point we can also ignore theelectronic ionic and interface polarizations assuming that dipolar polarizability is too high such thatad gtgt ae + ai + aint at a critical temperature Tc Here define a = ad = CkT where C is Curiersquos

          constant This is the right sort of relation as we have already seen the temperature dependence ofdipolar polarization in section (453)

          Hence we can further write

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          OR

          (55)

          Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

          we get

          OR

          (56)

          Thus by now modifying equation (54) Curie-Weiss law can be expressed as

          (57)

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          534 Thermodyanamic Basis of Ferroelectric Phase Transitions

          Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

          These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

          Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

          (58)

          where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

          is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

          Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

          (59)

          where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

          Converse piezoelectric effect is expressed as

          (510)

          Where dijkt is in mV

          Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

          (511)

          where Pi is the vector of pyroelectric coefficient in cm-2K-1

          Displacement is expressed as

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          (512)

          So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

          From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

          For a ferroelectric system the free energy G can be expressed in terms of ten variables as

          (513)

          where Px Py Pz are the components of the polarization are the stress

          components and T is the temperature

          We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

          (514)

          Note that only even powers are taken because energy is same for plusmnPS states

          Here a b c are the temperature dependent constants and E is the electric field

          The equilibrium is found by establishing ie

          (515)

          ie

          E = (516)

          If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

          If we ignore higher power terms then

          (517)

          leading to

          (518)

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          which is the same expression that we encountered for linear dielectrics

          According to Landau-Devonshire theory near the Curie point (T~T0) we assume

          a = a0 (T - T0) (519)

          As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

          (520)

          In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

          Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

          paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

          nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

          Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          535 Case I Second order Transition

          When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

          second order transition (do not get confused between T0 and Tc as the distiction will become clear

          in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

          Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

          Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

          The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

          retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

          polarization can be expressed as

          (521)

          showing that the polarization decreased to zero at T = T0 as shown in figure 58

          Dielectric susceptibility at T lt T0 can be estimated as

          (522)

          Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

          will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

          values near T0

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          Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

          This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

          (523)

          Now substituting in (523) yields

          (524)

          Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          536 Case ndash II First Order Transition

          Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

          now more than T0 This gives rise to the following free energy vs polarization plot

          Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

          The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

          is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

          Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

          In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

          free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

          (525)

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          On the other hand field E must also be zero for the polarization to be spontaneous ie

          (526)

          The polarization and susceptibility at Tc are obtained by solving two equations and are given as

          (527)

          and

          (528)

          The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

          heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

          temperature higher than Tc the sample will be in paraelectric state This results in thermal

          hysteresis when these materials are thermally cycled across Tc

          If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

          Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

          Solid State Physics AJ Dekker Macmillan Publishing

          Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          537 Ferroelectric Domains

          In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

          Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

          The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

          directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

          or 90deg domain walls

          Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

          Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

          depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

          Now the question is Why is there a domain wall

          The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

          associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

          splitting of the material into oppositely oriented domains or

          compensation of the electrical charge via electrical conduction through the crystal

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          Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

          by transmission electron microscopy

          Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          538 Analytical treatment of domain wall energy

          Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

          (529)

          where Uc effect of applied field on the domain energy

          Up and Ux bulk electrical and elastic energies

          Ud depolarization energy and

          Uw domain energy

          Ud is the energy related to the internal field set up in the crystal by the polarization and not

          compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

          (530)

          Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

          is the polarization at the center of the domain

          Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

          width (d) and crystal volume (V) and is given as

          (531)

          To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

          in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

          wrt domain wall thickness d ie dΔGdd = 0 resulting in

          (532)

          Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          539 Ferroelectric Switching and Domains

          Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

          At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

          Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

          If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

          microCcm2and E is electric field across the sample in Vcm The process is something like this

          Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

          Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

          reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

          polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

          Further increase of electric field in the opposite direction will cause complete reversal of orientation

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          of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

          Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

          Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

          >

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          5310 Measurement of Hysteresis Loop

          Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

          The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

          crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

          This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

          and coercive field Ec

          A ferroelectric materials shows polarization of the order of 50-100 microCcm2

          Figure 5 15 Schematic representation of sawyer-tower circuit

          Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

          Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

          atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

          Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

          Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

          a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

          Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

          becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

          positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

          The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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          Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

          Because the distorted octahedra are coupled together in ferroelectric form there is a very large

          spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

          BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

          orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

          5312 Applications of Ferroelectrics

          In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

          Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

          (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

          Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

          where their dielectric constant increases linearly with temperature they can be used for cameraflashes

          53121 Nonvolatile Memories

          Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

          two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

          Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

          53122 Camera Flashes

          In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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          Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

          >

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          Module 5 Nonlinear Dielectrics

          Summary

          Summary

          In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

          can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

          and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

          binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

          One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

          5474 Actuators

          In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

          In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

          You can have it in two forms

          Direct Piezo Actuators with strokes lower than 100 microns or so and

          Amplified Piezoelectric Actuators which can yield millimeter long strokes

          Some of the examples of applications are

          Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

          Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

          Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

          Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

          In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

          As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

          5475 Frequency Standards

          Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

          Quartz clocks

          Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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          Module 5 Nonlinear Dielectrics

          Summary

          Summary

          Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

          54 Piezoelectric Ceramics

          Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

          Pb(ZrTi)O3)

          An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

          For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

          541 Direct Piezoelectric Effect

          Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

          (533)

          where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

          542 Reverse or Converse Piezoelectric Effect

          The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

          (534)

          where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

          Figure 520 Direct and Converse PiezoelectricEffects

          The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

          543 Poling of Piezoelectric Materials

          As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

          The values of piezoelectric coefficient of some materials are given below

          Material Piezoelectric Constant d(pmV)

          Quartz 23

          Barium Titanate 100-149

          Lead Niobate 80-85

          Lead zirconate titanate 250-365

          So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

          Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

          field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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          Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

          544 Depolarization of Piezoelectrics

          Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

          polarization or rather result in alignment of dipoles gets lost

          Figure 522 Animation on depolarization offerroelectrics

          (Courtesy copy DoITPoMS University of Cambridge)

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          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

          545 Common PIezoelectric Materials

          5451 Barium Titanate (BaTiO3)

          This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

          used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

          Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

          1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

          must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

          5452 Pb(ZrTi)O3 or PZT

          PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

          The phase diagram of PZT is shown below

          Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

          The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

          lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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          few poling directions available making it a useful piezoelectric

          Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

          546 Measurement of Piezoelectric Properties

          Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

          In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

          Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

          The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

          (535)

          Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

          (536)

          Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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          One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

          547 Applications of Piezoelectric Ceramics

          Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

          5471 Power Generation

          Gas Lighter

          Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

          Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

          One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

          Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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          Power Transformer

          A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

          An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

          Figure 526 Schematic of a piezoelectrictransformer

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          Module 5 Special Dielectrics Piezoelectric Ceramics

          5472 Piezoelectric Sensors

          Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

          Other sensor applications are

          Detection and generation of sonar waves

          To detect detonation in automotive engine by sampling the vibrations of the engine block

          To detect the precise moment of fuel injection in an automotive engine

          Detection of acoustic emissions in acoustic emission testing

          Microbalances as very sensitive chemical and biological sensors

          Strain gauges

          Medical applications using ultrasound waves

          Kidney stone treatment

          In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

          Figure 527 Ultrasonic waves creation and

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          kidney stone treatment and ultrasound imagingof the fetus

          (Courtesy copy DoITPoMS University of Cambridge)

          5473 Ultrasound Imaging Using Transduction Effect

          Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

          55 Pyroelectric Ceramics

          Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

          Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

          Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

          551 Difference between Pyroelectric and Ferroelectric Material

          Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

          Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

          552 Theory of Piezoelectric Materials

          From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

          (537)

          Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

          Assuming electric field E as constant differentiating the above equation with temperature leads to

          (538)

          Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

          we write

          Δ OR

          Δ (539)

          Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

          Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

          (540)

          The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

          As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

          553 Measurement of Pyroelectric Coefficient

          One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

          (541)

          Where Ip is the pyrocurrent and is given as

          (542)

          where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

          respectively

          Figure 530 Circuit for measuring pyroelectriccoefficient

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          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

          554 Direct and Indirect Effect

          Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

          Since change in the polarization can also be expressed as depending

          upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

          Figure 531 Direct-Indirect effect animation

          (Courtesy copy DoITPoMS University of Cambridge)

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          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

          555 Common Pyroelectric Materials

          Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

          The most common materials are tabulated below

          Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

          LiTaO3 single crystal Hexagonal 665 -230

          075Pb(Mg13-Nb23)O3-025PbTiO3

          (PMN-PT) Ceramic

          Perovskite 150 -1300

          Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

          Triglycine sulphate

          (NH2CH2COOH)3H2SO4

          Sulphate 49 -280

          Polyvinylidene fluoride (PVDF) film Polymer 80 -27

          5551 Triglycine Sulphate (TGS)

          High pyroelectric coefficient

          Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

          Can be modified to withstand temperatures above Curie point without depoling

          Used in thermal imaging cameras

          5552 Polyvinylidene Fluoride (PVDF)

          Poor pyroelectric coefficient

          Readily available in large areas of thin film

          More stable to heat vacuum and moisture than TGS mechanically robust

          Low heat conductivity and low permittivity

          High loss tangent

          Commonly used for burglar alarms

          5553 Perovskite Ferroelectric Ceramics

          Generally robust and insensitive to moisture and vacuum

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          High pyroelectric coefficient and low loss

          Better operation near TC

          Strong dependence on composition

          As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

          RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

          556 Common Applications

          5561 Burglar Alarms

          Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

          Figure 532 Working of an IR intruder alarm

          (Courtesy copy DoITPoMS University ofCambridge)

          5562 Infrared or Thermal Imaging

          Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

          The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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          A typical photograph generated from IR imaging looks like this

          Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

          Here is a simple explanation of how IT imaging using pyroelectrics works

          A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

          This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

          Figure 534 Process of imagecreation

          5563 Pollutant Control

          The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

          Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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          Figure 535 Gas detection using a pyroelectricdetector

          (Courtesy copy DoITPoMS University of Cambridge)

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          Module 5 Nonlinear Dielectrics

          Summary

          Summary

          Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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            Figure 53 A typical ferroelectric hysteresisloop

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            532 Principle of Ferroelectricity Energetics

            The movement of central atom in the above structure can explained in terms of a potential energydiagram

            Figure 54 Potential energy well and crystal structure for an ABO3structured ferroelectric

            This situation can be explained in terms of a potential energy between two adjacent low energysites There are two equilibrium positions in which a B ion can stay but to change from one state toanother energy must be provided to overcome an energy barrier ΔE These energy wells further tiltto the left or right depending upon the polarity of the electric field ie in the non-zero field statemaking on configuration more stable than another However a coercive field which is the fieldrequired to bring the polarization back to zero is needed when you switch to other direction of thefield

            Ferroelectric materials follow Curie-Weiss law which is expressed as

            (51)

            Here N is the number of dipoles per unit volume of the material a is dipolar polarizability and Tc is

            defined as the Ferroelectric transition temperature or the Curie temperature

            Ferroelectric behaviour is observed below the Curie Temperature above which the ferroelectricphase converts into a paraelectric phase which always has higher symmetry than the ferroelectricphase (for example transformation of low symmetry tetragonal BaTiO3 to higher symmetry cubic

            BaTiO3 at about 120oC while heating) and ferroelectricity disappears A paraelectric state is

            essentially a centrosymmetric higher symmetry state where dipoles are randomly oriented in acrystal giving rise to zero polarization

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            Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            533 Proof of Curie-Weiss Law

            We can now say that in a ferroelectric material reversible spontaneous alignment of electric dipolestakes place by mutual interaction This happens due to a local field E which is increased by dipolealignment in the direction of field Interestingly this phenomenon happens below a criticaltemperature Tc when crystal enters into nonsymetric state where thermal energy cannot randomize

            the electric dipoles presumably due to dipole-dipole interactions and local field

            Following the basic principles we developed in module 4 polarization P can be expressed as

            (52)

            Where local field E = E + P3e0 as given by Clausius-Mossotti relationship and er is the relative

            dielectric permittivity and a is total polarizability Substitution for E in (52) results in

            ie

            or

            (53)

            Since we know that susceptibility we get

            (54)

            Equation (54) shows that both χ and er must approach 8 when Na3e0 approaches 1

            This can be assumed to be a right condition for ferroelectrics as near the ferroelectric transition theyexhibit very large susceptibilities and dielectric constant At this point we can also ignore theelectronic ionic and interface polarizations assuming that dipolar polarizability is too high such thatad gtgt ae + ai + aint at a critical temperature Tc Here define a = ad = CkT where C is Curiersquos

            constant This is the right sort of relation as we have already seen the temperature dependence ofdipolar polarization in section (453)

            Hence we can further write

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            OR

            (55)

            Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

            we get

            OR

            (56)

            Thus by now modifying equation (54) Curie-Weiss law can be expressed as

            (57)

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            534 Thermodyanamic Basis of Ferroelectric Phase Transitions

            Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

            These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

            Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

            (58)

            where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

            is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

            Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

            (59)

            where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

            Converse piezoelectric effect is expressed as

            (510)

            Where dijkt is in mV

            Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

            (511)

            where Pi is the vector of pyroelectric coefficient in cm-2K-1

            Displacement is expressed as

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            (512)

            So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

            From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

            For a ferroelectric system the free energy G can be expressed in terms of ten variables as

            (513)

            where Px Py Pz are the components of the polarization are the stress

            components and T is the temperature

            We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

            (514)

            Note that only even powers are taken because energy is same for plusmnPS states

            Here a b c are the temperature dependent constants and E is the electric field

            The equilibrium is found by establishing ie

            (515)

            ie

            E = (516)

            If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

            If we ignore higher power terms then

            (517)

            leading to

            (518)

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            which is the same expression that we encountered for linear dielectrics

            According to Landau-Devonshire theory near the Curie point (T~T0) we assume

            a = a0 (T - T0) (519)

            As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

            (520)

            In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

            Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

            paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

            nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

            Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            535 Case I Second order Transition

            When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

            second order transition (do not get confused between T0 and Tc as the distiction will become clear

            in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

            Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

            Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

            The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

            retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

            polarization can be expressed as

            (521)

            showing that the polarization decreased to zero at T = T0 as shown in figure 58

            Dielectric susceptibility at T lt T0 can be estimated as

            (522)

            Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

            will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

            values near T0

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            Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

            This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

            (523)

            Now substituting in (523) yields

            (524)

            Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            536 Case ndash II First Order Transition

            Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

            now more than T0 This gives rise to the following free energy vs polarization plot

            Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

            The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

            is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

            Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

            In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

            free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

            (525)

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            On the other hand field E must also be zero for the polarization to be spontaneous ie

            (526)

            The polarization and susceptibility at Tc are obtained by solving two equations and are given as

            (527)

            and

            (528)

            The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

            heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

            temperature higher than Tc the sample will be in paraelectric state This results in thermal

            hysteresis when these materials are thermally cycled across Tc

            If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

            Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

            Solid State Physics AJ Dekker Macmillan Publishing

            Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            537 Ferroelectric Domains

            In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

            Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

            The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

            directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

            or 90deg domain walls

            Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

            Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

            depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

            Now the question is Why is there a domain wall

            The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

            associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

            splitting of the material into oppositely oriented domains or

            compensation of the electrical charge via electrical conduction through the crystal

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            Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

            by transmission electron microscopy

            Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            538 Analytical treatment of domain wall energy

            Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

            (529)

            where Uc effect of applied field on the domain energy

            Up and Ux bulk electrical and elastic energies

            Ud depolarization energy and

            Uw domain energy

            Ud is the energy related to the internal field set up in the crystal by the polarization and not

            compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

            (530)

            Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

            is the polarization at the center of the domain

            Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

            width (d) and crystal volume (V) and is given as

            (531)

            To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

            in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

            wrt domain wall thickness d ie dΔGdd = 0 resulting in

            (532)

            Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            539 Ferroelectric Switching and Domains

            Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

            At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

            Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

            If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

            microCcm2and E is electric field across the sample in Vcm The process is something like this

            Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

            Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

            reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

            polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

            Further increase of electric field in the opposite direction will cause complete reversal of orientation

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            of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

            Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

            Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

            >

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            5310 Measurement of Hysteresis Loop

            Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

            The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

            crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

            This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

            and coercive field Ec

            A ferroelectric materials shows polarization of the order of 50-100 microCcm2

            Figure 5 15 Schematic representation of sawyer-tower circuit

            Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

            Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

            atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

            Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

            Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

            a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

            Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

            becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

            positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

            The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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            Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

            Because the distorted octahedra are coupled together in ferroelectric form there is a very large

            spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

            BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

            orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

            5312 Applications of Ferroelectrics

            In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

            Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

            (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

            Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

            where their dielectric constant increases linearly with temperature they can be used for cameraflashes

            53121 Nonvolatile Memories

            Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

            two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

            Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

            53122 Camera Flashes

            In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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            Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

            >

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            Module 5 Nonlinear Dielectrics

            Summary

            Summary

            In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

            can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

            and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

            binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

            One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

            5474 Actuators

            In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

            In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

            You can have it in two forms

            Direct Piezo Actuators with strokes lower than 100 microns or so and

            Amplified Piezoelectric Actuators which can yield millimeter long strokes

            Some of the examples of applications are

            Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

            Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

            Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

            Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

            In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

            As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

            5475 Frequency Standards

            Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

            Quartz clocks

            Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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            Module 5 Nonlinear Dielectrics

            Summary

            Summary

            Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

            54 Piezoelectric Ceramics

            Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

            Pb(ZrTi)O3)

            An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

            For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

            541 Direct Piezoelectric Effect

            Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

            (533)

            where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

            542 Reverse or Converse Piezoelectric Effect

            The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

            (534)

            where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

            Figure 520 Direct and Converse PiezoelectricEffects

            The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

            543 Poling of Piezoelectric Materials

            As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

            The values of piezoelectric coefficient of some materials are given below

            Material Piezoelectric Constant d(pmV)

            Quartz 23

            Barium Titanate 100-149

            Lead Niobate 80-85

            Lead zirconate titanate 250-365

            So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

            Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

            field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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            Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

            544 Depolarization of Piezoelectrics

            Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

            polarization or rather result in alignment of dipoles gets lost

            Figure 522 Animation on depolarization offerroelectrics

            (Courtesy copy DoITPoMS University of Cambridge)

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            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

            545 Common PIezoelectric Materials

            5451 Barium Titanate (BaTiO3)

            This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

            used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

            Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

            1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

            must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

            5452 Pb(ZrTi)O3 or PZT

            PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

            The phase diagram of PZT is shown below

            Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

            The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

            lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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            few poling directions available making it a useful piezoelectric

            Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

            546 Measurement of Piezoelectric Properties

            Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

            In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

            Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

            The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

            (535)

            Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

            (536)

            Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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            One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

            547 Applications of Piezoelectric Ceramics

            Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

            5471 Power Generation

            Gas Lighter

            Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

            Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

            One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

            Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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            Power Transformer

            A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

            An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

            Figure 526 Schematic of a piezoelectrictransformer

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            Module 5 Special Dielectrics Piezoelectric Ceramics

            5472 Piezoelectric Sensors

            Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

            Other sensor applications are

            Detection and generation of sonar waves

            To detect detonation in automotive engine by sampling the vibrations of the engine block

            To detect the precise moment of fuel injection in an automotive engine

            Detection of acoustic emissions in acoustic emission testing

            Microbalances as very sensitive chemical and biological sensors

            Strain gauges

            Medical applications using ultrasound waves

            Kidney stone treatment

            In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

            Figure 527 Ultrasonic waves creation and

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            kidney stone treatment and ultrasound imagingof the fetus

            (Courtesy copy DoITPoMS University of Cambridge)

            5473 Ultrasound Imaging Using Transduction Effect

            Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

            55 Pyroelectric Ceramics

            Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

            Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

            Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

            551 Difference between Pyroelectric and Ferroelectric Material

            Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

            Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

            552 Theory of Piezoelectric Materials

            From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

            (537)

            Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

            Assuming electric field E as constant differentiating the above equation with temperature leads to

            (538)

            Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

            we write

            Δ OR

            Δ (539)

            Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

            Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

            (540)

            The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

            As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

            553 Measurement of Pyroelectric Coefficient

            One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

            (541)

            Where Ip is the pyrocurrent and is given as

            (542)

            where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

            respectively

            Figure 530 Circuit for measuring pyroelectriccoefficient

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            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

            554 Direct and Indirect Effect

            Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

            Since change in the polarization can also be expressed as depending

            upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

            Figure 531 Direct-Indirect effect animation

            (Courtesy copy DoITPoMS University of Cambridge)

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            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

            555 Common Pyroelectric Materials

            Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

            The most common materials are tabulated below

            Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

            LiTaO3 single crystal Hexagonal 665 -230

            075Pb(Mg13-Nb23)O3-025PbTiO3

            (PMN-PT) Ceramic

            Perovskite 150 -1300

            Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

            Triglycine sulphate

            (NH2CH2COOH)3H2SO4

            Sulphate 49 -280

            Polyvinylidene fluoride (PVDF) film Polymer 80 -27

            5551 Triglycine Sulphate (TGS)

            High pyroelectric coefficient

            Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

            Can be modified to withstand temperatures above Curie point without depoling

            Used in thermal imaging cameras

            5552 Polyvinylidene Fluoride (PVDF)

            Poor pyroelectric coefficient

            Readily available in large areas of thin film

            More stable to heat vacuum and moisture than TGS mechanically robust

            Low heat conductivity and low permittivity

            High loss tangent

            Commonly used for burglar alarms

            5553 Perovskite Ferroelectric Ceramics

            Generally robust and insensitive to moisture and vacuum

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            High pyroelectric coefficient and low loss

            Better operation near TC

            Strong dependence on composition

            As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

            RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

            556 Common Applications

            5561 Burglar Alarms

            Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

            Figure 532 Working of an IR intruder alarm

            (Courtesy copy DoITPoMS University ofCambridge)

            5562 Infrared or Thermal Imaging

            Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

            The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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            A typical photograph generated from IR imaging looks like this

            Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

            Here is a simple explanation of how IT imaging using pyroelectrics works

            A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

            This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

            Figure 534 Process of imagecreation

            5563 Pollutant Control

            The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

            Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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            Figure 535 Gas detection using a pyroelectricdetector

            (Courtesy copy DoITPoMS University of Cambridge)

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            Module 5 Nonlinear Dielectrics

            Summary

            Summary

            Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              532 Principle of Ferroelectricity Energetics

              The movement of central atom in the above structure can explained in terms of a potential energydiagram

              Figure 54 Potential energy well and crystal structure for an ABO3structured ferroelectric

              This situation can be explained in terms of a potential energy between two adjacent low energysites There are two equilibrium positions in which a B ion can stay but to change from one state toanother energy must be provided to overcome an energy barrier ΔE These energy wells further tiltto the left or right depending upon the polarity of the electric field ie in the non-zero field statemaking on configuration more stable than another However a coercive field which is the fieldrequired to bring the polarization back to zero is needed when you switch to other direction of thefield

              Ferroelectric materials follow Curie-Weiss law which is expressed as

              (51)

              Here N is the number of dipoles per unit volume of the material a is dipolar polarizability and Tc is

              defined as the Ferroelectric transition temperature or the Curie temperature

              Ferroelectric behaviour is observed below the Curie Temperature above which the ferroelectricphase converts into a paraelectric phase which always has higher symmetry than the ferroelectricphase (for example transformation of low symmetry tetragonal BaTiO3 to higher symmetry cubic

              BaTiO3 at about 120oC while heating) and ferroelectricity disappears A paraelectric state is

              essentially a centrosymmetric higher symmetry state where dipoles are randomly oriented in acrystal giving rise to zero polarization

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              Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              533 Proof of Curie-Weiss Law

              We can now say that in a ferroelectric material reversible spontaneous alignment of electric dipolestakes place by mutual interaction This happens due to a local field E which is increased by dipolealignment in the direction of field Interestingly this phenomenon happens below a criticaltemperature Tc when crystal enters into nonsymetric state where thermal energy cannot randomize

              the electric dipoles presumably due to dipole-dipole interactions and local field

              Following the basic principles we developed in module 4 polarization P can be expressed as

              (52)

              Where local field E = E + P3e0 as given by Clausius-Mossotti relationship and er is the relative

              dielectric permittivity and a is total polarizability Substitution for E in (52) results in

              ie

              or

              (53)

              Since we know that susceptibility we get

              (54)

              Equation (54) shows that both χ and er must approach 8 when Na3e0 approaches 1

              This can be assumed to be a right condition for ferroelectrics as near the ferroelectric transition theyexhibit very large susceptibilities and dielectric constant At this point we can also ignore theelectronic ionic and interface polarizations assuming that dipolar polarizability is too high such thatad gtgt ae + ai + aint at a critical temperature Tc Here define a = ad = CkT where C is Curiersquos

              constant This is the right sort of relation as we have already seen the temperature dependence ofdipolar polarization in section (453)

              Hence we can further write

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              OR

              (55)

              Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

              we get

              OR

              (56)

              Thus by now modifying equation (54) Curie-Weiss law can be expressed as

              (57)

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              534 Thermodyanamic Basis of Ferroelectric Phase Transitions

              Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

              These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

              Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

              (58)

              where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

              is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

              Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

              (59)

              where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

              Converse piezoelectric effect is expressed as

              (510)

              Where dijkt is in mV

              Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

              (511)

              where Pi is the vector of pyroelectric coefficient in cm-2K-1

              Displacement is expressed as

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              (512)

              So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

              From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

              For a ferroelectric system the free energy G can be expressed in terms of ten variables as

              (513)

              where Px Py Pz are the components of the polarization are the stress

              components and T is the temperature

              We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

              (514)

              Note that only even powers are taken because energy is same for plusmnPS states

              Here a b c are the temperature dependent constants and E is the electric field

              The equilibrium is found by establishing ie

              (515)

              ie

              E = (516)

              If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

              If we ignore higher power terms then

              (517)

              leading to

              (518)

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              which is the same expression that we encountered for linear dielectrics

              According to Landau-Devonshire theory near the Curie point (T~T0) we assume

              a = a0 (T - T0) (519)

              As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

              (520)

              In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

              Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

              paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

              nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

              Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              535 Case I Second order Transition

              When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

              second order transition (do not get confused between T0 and Tc as the distiction will become clear

              in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

              Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

              Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

              The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

              retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

              polarization can be expressed as

              (521)

              showing that the polarization decreased to zero at T = T0 as shown in figure 58

              Dielectric susceptibility at T lt T0 can be estimated as

              (522)

              Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

              will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

              values near T0

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              Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

              This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

              (523)

              Now substituting in (523) yields

              (524)

              Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              536 Case ndash II First Order Transition

              Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

              now more than T0 This gives rise to the following free energy vs polarization plot

              Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

              The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

              is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

              Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

              In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

              free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

              (525)

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              On the other hand field E must also be zero for the polarization to be spontaneous ie

              (526)

              The polarization and susceptibility at Tc are obtained by solving two equations and are given as

              (527)

              and

              (528)

              The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

              heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

              temperature higher than Tc the sample will be in paraelectric state This results in thermal

              hysteresis when these materials are thermally cycled across Tc

              If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

              Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

              Solid State Physics AJ Dekker Macmillan Publishing

              Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              537 Ferroelectric Domains

              In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

              Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

              The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

              directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

              or 90deg domain walls

              Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

              Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

              depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

              Now the question is Why is there a domain wall

              The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

              associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

              splitting of the material into oppositely oriented domains or

              compensation of the electrical charge via electrical conduction through the crystal

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              Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

              by transmission electron microscopy

              Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              538 Analytical treatment of domain wall energy

              Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

              (529)

              where Uc effect of applied field on the domain energy

              Up and Ux bulk electrical and elastic energies

              Ud depolarization energy and

              Uw domain energy

              Ud is the energy related to the internal field set up in the crystal by the polarization and not

              compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

              (530)

              Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

              is the polarization at the center of the domain

              Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

              width (d) and crystal volume (V) and is given as

              (531)

              To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

              in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

              wrt domain wall thickness d ie dΔGdd = 0 resulting in

              (532)

              Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              539 Ferroelectric Switching and Domains

              Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

              At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

              Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

              If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

              microCcm2and E is electric field across the sample in Vcm The process is something like this

              Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

              Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

              reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

              polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

              Further increase of electric field in the opposite direction will cause complete reversal of orientation

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              of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

              Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

              Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              5310 Measurement of Hysteresis Loop

              Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

              The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

              crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

              This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

              and coercive field Ec

              A ferroelectric materials shows polarization of the order of 50-100 microCcm2

              Figure 5 15 Schematic representation of sawyer-tower circuit

              Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

              Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

              atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

              Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

              Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

              a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

              Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

              becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

              positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

              The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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              Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

              Because the distorted octahedra are coupled together in ferroelectric form there is a very large

              spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

              BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

              orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

              5312 Applications of Ferroelectrics

              In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

              Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

              (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

              Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

              where their dielectric constant increases linearly with temperature they can be used for cameraflashes

              53121 Nonvolatile Memories

              Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

              two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

              Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

              53122 Camera Flashes

              In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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              Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

              >

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              Module 5 Nonlinear Dielectrics

              Summary

              Summary

              In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

              can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

              and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

              binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

              One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

              5474 Actuators

              In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

              In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

              You can have it in two forms

              Direct Piezo Actuators with strokes lower than 100 microns or so and

              Amplified Piezoelectric Actuators which can yield millimeter long strokes

              Some of the examples of applications are

              Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

              Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

              Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

              Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

              In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

              As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

              5475 Frequency Standards

              Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

              Quartz clocks

              Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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              Module 5 Nonlinear Dielectrics

              Summary

              Summary

              Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

              54 Piezoelectric Ceramics

              Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

              Pb(ZrTi)O3)

              An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

              For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

              541 Direct Piezoelectric Effect

              Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

              (533)

              where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

              542 Reverse or Converse Piezoelectric Effect

              The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

              (534)

              where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

              Figure 520 Direct and Converse PiezoelectricEffects

              The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

              543 Poling of Piezoelectric Materials

              As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

              The values of piezoelectric coefficient of some materials are given below

              Material Piezoelectric Constant d(pmV)

              Quartz 23

              Barium Titanate 100-149

              Lead Niobate 80-85

              Lead zirconate titanate 250-365

              So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

              Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

              field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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              Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

              544 Depolarization of Piezoelectrics

              Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

              polarization or rather result in alignment of dipoles gets lost

              Figure 522 Animation on depolarization offerroelectrics

              (Courtesy copy DoITPoMS University of Cambridge)

              >

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              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

              545 Common PIezoelectric Materials

              5451 Barium Titanate (BaTiO3)

              This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

              used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

              Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

              1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

              must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

              5452 Pb(ZrTi)O3 or PZT

              PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

              The phase diagram of PZT is shown below

              Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

              The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

              lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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              few poling directions available making it a useful piezoelectric

              Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

              546 Measurement of Piezoelectric Properties

              Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

              In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

              Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

              The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

              (535)

              Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

              (536)

              Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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              One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

              547 Applications of Piezoelectric Ceramics

              Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

              5471 Power Generation

              Gas Lighter

              Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

              Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

              One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

              Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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              Power Transformer

              A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

              An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

              Figure 526 Schematic of a piezoelectrictransformer

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              Module 5 Special Dielectrics Piezoelectric Ceramics

              5472 Piezoelectric Sensors

              Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

              Other sensor applications are

              Detection and generation of sonar waves

              To detect detonation in automotive engine by sampling the vibrations of the engine block

              To detect the precise moment of fuel injection in an automotive engine

              Detection of acoustic emissions in acoustic emission testing

              Microbalances as very sensitive chemical and biological sensors

              Strain gauges

              Medical applications using ultrasound waves

              Kidney stone treatment

              In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

              Figure 527 Ultrasonic waves creation and

              >

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              kidney stone treatment and ultrasound imagingof the fetus

              (Courtesy copy DoITPoMS University of Cambridge)

              5473 Ultrasound Imaging Using Transduction Effect

              Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

              55 Pyroelectric Ceramics

              Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

              Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

              Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

              551 Difference between Pyroelectric and Ferroelectric Material

              Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

              Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

              552 Theory of Piezoelectric Materials

              From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

              (537)

              Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

              Assuming electric field E as constant differentiating the above equation with temperature leads to

              (538)

              Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

              we write

              Δ OR

              Δ (539)

              Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

              Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

              (540)

              The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

              As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

              553 Measurement of Pyroelectric Coefficient

              One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

              (541)

              Where Ip is the pyrocurrent and is given as

              (542)

              where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

              respectively

              Figure 530 Circuit for measuring pyroelectriccoefficient

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              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

              554 Direct and Indirect Effect

              Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

              Since change in the polarization can also be expressed as depending

              upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

              Figure 531 Direct-Indirect effect animation

              (Courtesy copy DoITPoMS University of Cambridge)

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              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

              555 Common Pyroelectric Materials

              Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

              The most common materials are tabulated below

              Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

              LiTaO3 single crystal Hexagonal 665 -230

              075Pb(Mg13-Nb23)O3-025PbTiO3

              (PMN-PT) Ceramic

              Perovskite 150 -1300

              Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

              Triglycine sulphate

              (NH2CH2COOH)3H2SO4

              Sulphate 49 -280

              Polyvinylidene fluoride (PVDF) film Polymer 80 -27

              5551 Triglycine Sulphate (TGS)

              High pyroelectric coefficient

              Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

              Can be modified to withstand temperatures above Curie point without depoling

              Used in thermal imaging cameras

              5552 Polyvinylidene Fluoride (PVDF)

              Poor pyroelectric coefficient

              Readily available in large areas of thin film

              More stable to heat vacuum and moisture than TGS mechanically robust

              Low heat conductivity and low permittivity

              High loss tangent

              Commonly used for burglar alarms

              5553 Perovskite Ferroelectric Ceramics

              Generally robust and insensitive to moisture and vacuum

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              High pyroelectric coefficient and low loss

              Better operation near TC

              Strong dependence on composition

              As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

              RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

              556 Common Applications

              5561 Burglar Alarms

              Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

              Figure 532 Working of an IR intruder alarm

              (Courtesy copy DoITPoMS University ofCambridge)

              5562 Infrared or Thermal Imaging

              Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

              The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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              A typical photograph generated from IR imaging looks like this

              Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

              Here is a simple explanation of how IT imaging using pyroelectrics works

              A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

              This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

              Figure 534 Process of imagecreation

              5563 Pollutant Control

              The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

              Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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              Figure 535 Gas detection using a pyroelectricdetector

              (Courtesy copy DoITPoMS University of Cambridge)

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              Module 5 Nonlinear Dielectrics

              Summary

              Summary

              Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                533 Proof of Curie-Weiss Law

                We can now say that in a ferroelectric material reversible spontaneous alignment of electric dipolestakes place by mutual interaction This happens due to a local field E which is increased by dipolealignment in the direction of field Interestingly this phenomenon happens below a criticaltemperature Tc when crystal enters into nonsymetric state where thermal energy cannot randomize

                the electric dipoles presumably due to dipole-dipole interactions and local field

                Following the basic principles we developed in module 4 polarization P can be expressed as

                (52)

                Where local field E = E + P3e0 as given by Clausius-Mossotti relationship and er is the relative

                dielectric permittivity and a is total polarizability Substitution for E in (52) results in

                ie

                or

                (53)

                Since we know that susceptibility we get

                (54)

                Equation (54) shows that both χ and er must approach 8 when Na3e0 approaches 1

                This can be assumed to be a right condition for ferroelectrics as near the ferroelectric transition theyexhibit very large susceptibilities and dielectric constant At this point we can also ignore theelectronic ionic and interface polarizations assuming that dipolar polarizability is too high such thatad gtgt ae + ai + aint at a critical temperature Tc Here define a = ad = CkT where C is Curiersquos

                constant This is the right sort of relation as we have already seen the temperature dependence ofdipolar polarization in section (453)

                Hence we can further write

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                OR

                (55)

                Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

                we get

                OR

                (56)

                Thus by now modifying equation (54) Curie-Weiss law can be expressed as

                (57)

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                534 Thermodyanamic Basis of Ferroelectric Phase Transitions

                Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

                These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

                Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

                (58)

                where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

                is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

                Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

                (59)

                where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

                Converse piezoelectric effect is expressed as

                (510)

                Where dijkt is in mV

                Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

                (511)

                where Pi is the vector of pyroelectric coefficient in cm-2K-1

                Displacement is expressed as

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                (512)

                So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

                From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

                For a ferroelectric system the free energy G can be expressed in terms of ten variables as

                (513)

                where Px Py Pz are the components of the polarization are the stress

                components and T is the temperature

                We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

                (514)

                Note that only even powers are taken because energy is same for plusmnPS states

                Here a b c are the temperature dependent constants and E is the electric field

                The equilibrium is found by establishing ie

                (515)

                ie

                E = (516)

                If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

                If we ignore higher power terms then

                (517)

                leading to

                (518)

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                which is the same expression that we encountered for linear dielectrics

                According to Landau-Devonshire theory near the Curie point (T~T0) we assume

                a = a0 (T - T0) (519)

                As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

                (520)

                In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

                Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

                paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

                nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

                Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                535 Case I Second order Transition

                When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

                second order transition (do not get confused between T0 and Tc as the distiction will become clear

                in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

                Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

                Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

                The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

                retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

                polarization can be expressed as

                (521)

                showing that the polarization decreased to zero at T = T0 as shown in figure 58

                Dielectric susceptibility at T lt T0 can be estimated as

                (522)

                Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

                will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

                values near T0

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                Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

                This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

                (523)

                Now substituting in (523) yields

                (524)

                Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                536 Case ndash II First Order Transition

                Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

                now more than T0 This gives rise to the following free energy vs polarization plot

                Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

                The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

                is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

                Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

                In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

                free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

                (525)

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                On the other hand field E must also be zero for the polarization to be spontaneous ie

                (526)

                The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                (527)

                and

                (528)

                The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                temperature higher than Tc the sample will be in paraelectric state This results in thermal

                hysteresis when these materials are thermally cycled across Tc

                If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                Solid State Physics AJ Dekker Macmillan Publishing

                Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                537 Ferroelectric Domains

                In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                or 90deg domain walls

                Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                Now the question is Why is there a domain wall

                The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                splitting of the material into oppositely oriented domains or

                compensation of the electrical charge via electrical conduction through the crystal

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                Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                by transmission electron microscopy

                Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                538 Analytical treatment of domain wall energy

                Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                (529)

                where Uc effect of applied field on the domain energy

                Up and Ux bulk electrical and elastic energies

                Ud depolarization energy and

                Uw domain energy

                Ud is the energy related to the internal field set up in the crystal by the polarization and not

                compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                (530)

                Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                is the polarization at the center of the domain

                Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                width (d) and crystal volume (V) and is given as

                (531)

                To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                wrt domain wall thickness d ie dΔGdd = 0 resulting in

                (532)

                Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                539 Ferroelectric Switching and Domains

                Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                microCcm2and E is electric field across the sample in Vcm The process is something like this

                Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                5310 Measurement of Hysteresis Loop

                Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                and coercive field Ec

                A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                Figure 5 15 Schematic representation of sawyer-tower circuit

                Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                5312 Applications of Ferroelectrics

                In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                53121 Nonvolatile Memories

                Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                53122 Camera Flashes

                In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                Module 5 Nonlinear Dielectrics

                Summary

                Summary

                In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                5474 Actuators

                In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                You can have it in two forms

                Direct Piezo Actuators with strokes lower than 100 microns or so and

                Amplified Piezoelectric Actuators which can yield millimeter long strokes

                Some of the examples of applications are

                Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                5475 Frequency Standards

                Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                Quartz clocks

                Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                Module 5 Nonlinear Dielectrics

                Summary

                Summary

                Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                54 Piezoelectric Ceramics

                Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                Pb(ZrTi)O3)

                An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                541 Direct Piezoelectric Effect

                Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                (533)

                where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                542 Reverse or Converse Piezoelectric Effect

                The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                (534)

                where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                Figure 520 Direct and Converse PiezoelectricEffects

                The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                543 Poling of Piezoelectric Materials

                As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                The values of piezoelectric coefficient of some materials are given below

                Material Piezoelectric Constant d(pmV)

                Quartz 23

                Barium Titanate 100-149

                Lead Niobate 80-85

                Lead zirconate titanate 250-365

                So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                544 Depolarization of Piezoelectrics

                Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                polarization or rather result in alignment of dipoles gets lost

                Figure 522 Animation on depolarization offerroelectrics

                (Courtesy copy DoITPoMS University of Cambridge)

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                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                545 Common PIezoelectric Materials

                5451 Barium Titanate (BaTiO3)

                This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                5452 Pb(ZrTi)O3 or PZT

                PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                The phase diagram of PZT is shown below

                Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                few poling directions available making it a useful piezoelectric

                Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                546 Measurement of Piezoelectric Properties

                Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                (535)

                Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                (536)

                Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                547 Applications of Piezoelectric Ceramics

                Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                5471 Power Generation

                Gas Lighter

                Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                Power Transformer

                A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                Figure 526 Schematic of a piezoelectrictransformer

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                Module 5 Special Dielectrics Piezoelectric Ceramics

                5472 Piezoelectric Sensors

                Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                Other sensor applications are

                Detection and generation of sonar waves

                To detect detonation in automotive engine by sampling the vibrations of the engine block

                To detect the precise moment of fuel injection in an automotive engine

                Detection of acoustic emissions in acoustic emission testing

                Microbalances as very sensitive chemical and biological sensors

                Strain gauges

                Medical applications using ultrasound waves

                Kidney stone treatment

                In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                Figure 527 Ultrasonic waves creation and

                >

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                kidney stone treatment and ultrasound imagingof the fetus

                (Courtesy copy DoITPoMS University of Cambridge)

                5473 Ultrasound Imaging Using Transduction Effect

                Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                55 Pyroelectric Ceramics

                Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                551 Difference between Pyroelectric and Ferroelectric Material

                Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                552 Theory of Piezoelectric Materials

                From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                (537)

                Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                Assuming electric field E as constant differentiating the above equation with temperature leads to

                (538)

                Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                we write

                Δ OR

                Δ (539)

                Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                (540)

                The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                553 Measurement of Pyroelectric Coefficient

                One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                (541)

                Where Ip is the pyrocurrent and is given as

                (542)

                where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                respectively

                Figure 530 Circuit for measuring pyroelectriccoefficient

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                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                554 Direct and Indirect Effect

                Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                Since change in the polarization can also be expressed as depending

                upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                Figure 531 Direct-Indirect effect animation

                (Courtesy copy DoITPoMS University of Cambridge)

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                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                555 Common Pyroelectric Materials

                Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                The most common materials are tabulated below

                Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                LiTaO3 single crystal Hexagonal 665 -230

                075Pb(Mg13-Nb23)O3-025PbTiO3

                (PMN-PT) Ceramic

                Perovskite 150 -1300

                Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                Triglycine sulphate

                (NH2CH2COOH)3H2SO4

                Sulphate 49 -280

                Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                5551 Triglycine Sulphate (TGS)

                High pyroelectric coefficient

                Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                Can be modified to withstand temperatures above Curie point without depoling

                Used in thermal imaging cameras

                5552 Polyvinylidene Fluoride (PVDF)

                Poor pyroelectric coefficient

                Readily available in large areas of thin film

                More stable to heat vacuum and moisture than TGS mechanically robust

                Low heat conductivity and low permittivity

                High loss tangent

                Commonly used for burglar alarms

                5553 Perovskite Ferroelectric Ceramics

                Generally robust and insensitive to moisture and vacuum

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                High pyroelectric coefficient and low loss

                Better operation near TC

                Strong dependence on composition

                As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                556 Common Applications

                5561 Burglar Alarms

                Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                Figure 532 Working of an IR intruder alarm

                (Courtesy copy DoITPoMS University ofCambridge)

                5562 Infrared or Thermal Imaging

                Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                >

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                A typical photograph generated from IR imaging looks like this

                Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                Here is a simple explanation of how IT imaging using pyroelectrics works

                A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                Figure 534 Process of imagecreation

                5563 Pollutant Control

                The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                Figure 535 Gas detection using a pyroelectricdetector

                (Courtesy copy DoITPoMS University of Cambridge)

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                Module 5 Nonlinear Dielectrics

                Summary

                Summary

                Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  533 Proof of Curie-Weiss Law

                  We can now say that in a ferroelectric material reversible spontaneous alignment of electric dipolestakes place by mutual interaction This happens due to a local field E which is increased by dipolealignment in the direction of field Interestingly this phenomenon happens below a criticaltemperature Tc when crystal enters into nonsymetric state where thermal energy cannot randomize

                  the electric dipoles presumably due to dipole-dipole interactions and local field

                  Following the basic principles we developed in module 4 polarization P can be expressed as

                  (52)

                  Where local field E = E + P3e0 as given by Clausius-Mossotti relationship and er is the relative

                  dielectric permittivity and a is total polarizability Substitution for E in (52) results in

                  ie

                  or

                  (53)

                  Since we know that susceptibility we get

                  (54)

                  Equation (54) shows that both χ and er must approach 8 when Na3e0 approaches 1

                  This can be assumed to be a right condition for ferroelectrics as near the ferroelectric transition theyexhibit very large susceptibilities and dielectric constant At this point we can also ignore theelectronic ionic and interface polarizations assuming that dipolar polarizability is too high such thatad gtgt ae + ai + aint at a critical temperature Tc Here define a = ad = CkT where C is Curiersquos

                  constant This is the right sort of relation as we have already seen the temperature dependence ofdipolar polarization in section (453)

                  Hence we can further write

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                  OR

                  (55)

                  Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

                  we get

                  OR

                  (56)

                  Thus by now modifying equation (54) Curie-Weiss law can be expressed as

                  (57)

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  534 Thermodyanamic Basis of Ferroelectric Phase Transitions

                  Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

                  These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

                  Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

                  (58)

                  where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

                  is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

                  Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

                  (59)

                  where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

                  Converse piezoelectric effect is expressed as

                  (510)

                  Where dijkt is in mV

                  Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

                  (511)

                  where Pi is the vector of pyroelectric coefficient in cm-2K-1

                  Displacement is expressed as

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                  (512)

                  So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

                  From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

                  For a ferroelectric system the free energy G can be expressed in terms of ten variables as

                  (513)

                  where Px Py Pz are the components of the polarization are the stress

                  components and T is the temperature

                  We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

                  (514)

                  Note that only even powers are taken because energy is same for plusmnPS states

                  Here a b c are the temperature dependent constants and E is the electric field

                  The equilibrium is found by establishing ie

                  (515)

                  ie

                  E = (516)

                  If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

                  If we ignore higher power terms then

                  (517)

                  leading to

                  (518)

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                  which is the same expression that we encountered for linear dielectrics

                  According to Landau-Devonshire theory near the Curie point (T~T0) we assume

                  a = a0 (T - T0) (519)

                  As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

                  (520)

                  In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

                  Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

                  paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

                  nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

                  Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  535 Case I Second order Transition

                  When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

                  second order transition (do not get confused between T0 and Tc as the distiction will become clear

                  in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

                  Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

                  Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

                  The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

                  retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

                  polarization can be expressed as

                  (521)

                  showing that the polarization decreased to zero at T = T0 as shown in figure 58

                  Dielectric susceptibility at T lt T0 can be estimated as

                  (522)

                  Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

                  will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

                  values near T0

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                  Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

                  This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

                  (523)

                  Now substituting in (523) yields

                  (524)

                  Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  536 Case ndash II First Order Transition

                  Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

                  now more than T0 This gives rise to the following free energy vs polarization plot

                  Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

                  The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

                  is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

                  Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

                  In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

                  free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

                  (525)

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                  On the other hand field E must also be zero for the polarization to be spontaneous ie

                  (526)

                  The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                  (527)

                  and

                  (528)

                  The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                  heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                  temperature higher than Tc the sample will be in paraelectric state This results in thermal

                  hysteresis when these materials are thermally cycled across Tc

                  If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                  Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                  Solid State Physics AJ Dekker Macmillan Publishing

                  Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  537 Ferroelectric Domains

                  In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                  Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                  The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                  directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                  or 90deg domain walls

                  Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                  Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                  depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                  Now the question is Why is there a domain wall

                  The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                  associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                  splitting of the material into oppositely oriented domains or

                  compensation of the electrical charge via electrical conduction through the crystal

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                  Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                  by transmission electron microscopy

                  Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  538 Analytical treatment of domain wall energy

                  Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                  (529)

                  where Uc effect of applied field on the domain energy

                  Up and Ux bulk electrical and elastic energies

                  Ud depolarization energy and

                  Uw domain energy

                  Ud is the energy related to the internal field set up in the crystal by the polarization and not

                  compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                  (530)

                  Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                  is the polarization at the center of the domain

                  Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                  width (d) and crystal volume (V) and is given as

                  (531)

                  To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                  in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                  wrt domain wall thickness d ie dΔGdd = 0 resulting in

                  (532)

                  Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  539 Ferroelectric Switching and Domains

                  Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                  At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                  Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                  If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                  microCcm2and E is electric field across the sample in Vcm The process is something like this

                  Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                  Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                  reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                  polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                  Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                  of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                  Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                  Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  5310 Measurement of Hysteresis Loop

                  Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                  The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                  crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                  This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                  and coercive field Ec

                  A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                  Figure 5 15 Schematic representation of sawyer-tower circuit

                  Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                  Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                  atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                  Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                  Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                  a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                  Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                  becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                  positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                  The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                  Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                  Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                  spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                  BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                  orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                  5312 Applications of Ferroelectrics

                  In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                  Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                  (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                  Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                  where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                  53121 Nonvolatile Memories

                  Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                  two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                  Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                  53122 Camera Flashes

                  In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                  Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                  Module 5 Nonlinear Dielectrics

                  Summary

                  Summary

                  In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                  can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                  and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                  binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                  One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                  5474 Actuators

                  In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                  In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                  You can have it in two forms

                  Direct Piezo Actuators with strokes lower than 100 microns or so and

                  Amplified Piezoelectric Actuators which can yield millimeter long strokes

                  Some of the examples of applications are

                  Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                  Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                  Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                  Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                  In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                  As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                  5475 Frequency Standards

                  Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                  Quartz clocks

                  Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                  Module 5 Nonlinear Dielectrics

                  Summary

                  Summary

                  Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                  54 Piezoelectric Ceramics

                  Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                  Pb(ZrTi)O3)

                  An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                  For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                  541 Direct Piezoelectric Effect

                  Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                  (533)

                  where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                  542 Reverse or Converse Piezoelectric Effect

                  The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                  (534)

                  where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                  Figure 520 Direct and Converse PiezoelectricEffects

                  The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                  543 Poling of Piezoelectric Materials

                  As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                  The values of piezoelectric coefficient of some materials are given below

                  Material Piezoelectric Constant d(pmV)

                  Quartz 23

                  Barium Titanate 100-149

                  Lead Niobate 80-85

                  Lead zirconate titanate 250-365

                  So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                  Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                  field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                  Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                  544 Depolarization of Piezoelectrics

                  Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                  polarization or rather result in alignment of dipoles gets lost

                  Figure 522 Animation on depolarization offerroelectrics

                  (Courtesy copy DoITPoMS University of Cambridge)

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                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                  545 Common PIezoelectric Materials

                  5451 Barium Titanate (BaTiO3)

                  This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                  used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                  Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                  1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                  must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                  5452 Pb(ZrTi)O3 or PZT

                  PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                  The phase diagram of PZT is shown below

                  Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                  The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                  lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                  few poling directions available making it a useful piezoelectric

                  Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                  546 Measurement of Piezoelectric Properties

                  Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                  In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                  Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                  The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                  (535)

                  Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                  (536)

                  Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                  One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                  547 Applications of Piezoelectric Ceramics

                  Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                  5471 Power Generation

                  Gas Lighter

                  Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                  Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                  One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                  Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                  Power Transformer

                  A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                  An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                  Figure 526 Schematic of a piezoelectrictransformer

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                  Module 5 Special Dielectrics Piezoelectric Ceramics

                  5472 Piezoelectric Sensors

                  Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                  Other sensor applications are

                  Detection and generation of sonar waves

                  To detect detonation in automotive engine by sampling the vibrations of the engine block

                  To detect the precise moment of fuel injection in an automotive engine

                  Detection of acoustic emissions in acoustic emission testing

                  Microbalances as very sensitive chemical and biological sensors

                  Strain gauges

                  Medical applications using ultrasound waves

                  Kidney stone treatment

                  In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                  Figure 527 Ultrasonic waves creation and

                  >

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                  kidney stone treatment and ultrasound imagingof the fetus

                  (Courtesy copy DoITPoMS University of Cambridge)

                  5473 Ultrasound Imaging Using Transduction Effect

                  Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                  55 Pyroelectric Ceramics

                  Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                  Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                  Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                  551 Difference between Pyroelectric and Ferroelectric Material

                  Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                  Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                  552 Theory of Piezoelectric Materials

                  From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                  (537)

                  Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                  Assuming electric field E as constant differentiating the above equation with temperature leads to

                  (538)

                  Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                  we write

                  Δ OR

                  Δ (539)

                  Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                  Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                  (540)

                  The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                  As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                  553 Measurement of Pyroelectric Coefficient

                  One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                  (541)

                  Where Ip is the pyrocurrent and is given as

                  (542)

                  where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                  respectively

                  Figure 530 Circuit for measuring pyroelectriccoefficient

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                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                  554 Direct and Indirect Effect

                  Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                  Since change in the polarization can also be expressed as depending

                  upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                  Figure 531 Direct-Indirect effect animation

                  (Courtesy copy DoITPoMS University of Cambridge)

                  >

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                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                  555 Common Pyroelectric Materials

                  Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                  The most common materials are tabulated below

                  Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                  LiTaO3 single crystal Hexagonal 665 -230

                  075Pb(Mg13-Nb23)O3-025PbTiO3

                  (PMN-PT) Ceramic

                  Perovskite 150 -1300

                  Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                  Triglycine sulphate

                  (NH2CH2COOH)3H2SO4

                  Sulphate 49 -280

                  Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                  5551 Triglycine Sulphate (TGS)

                  High pyroelectric coefficient

                  Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                  Can be modified to withstand temperatures above Curie point without depoling

                  Used in thermal imaging cameras

                  5552 Polyvinylidene Fluoride (PVDF)

                  Poor pyroelectric coefficient

                  Readily available in large areas of thin film

                  More stable to heat vacuum and moisture than TGS mechanically robust

                  Low heat conductivity and low permittivity

                  High loss tangent

                  Commonly used for burglar alarms

                  5553 Perovskite Ferroelectric Ceramics

                  Generally robust and insensitive to moisture and vacuum

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                  High pyroelectric coefficient and low loss

                  Better operation near TC

                  Strong dependence on composition

                  As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                  RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                  556 Common Applications

                  5561 Burglar Alarms

                  Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                  Figure 532 Working of an IR intruder alarm

                  (Courtesy copy DoITPoMS University ofCambridge)

                  5562 Infrared or Thermal Imaging

                  Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                  The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                  >

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                  A typical photograph generated from IR imaging looks like this

                  Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                  Here is a simple explanation of how IT imaging using pyroelectrics works

                  A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                  This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                  Figure 534 Process of imagecreation

                  5563 Pollutant Control

                  The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                  Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                  Figure 535 Gas detection using a pyroelectricdetector

                  (Courtesy copy DoITPoMS University of Cambridge)

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                  Module 5 Nonlinear Dielectrics

                  Summary

                  Summary

                  Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                    OR

                    (55)

                    Below this Tc spontaneous polarization is prevalent and dipoles tend to align So since C = adkT

                    we get

                    OR

                    (56)

                    Thus by now modifying equation (54) Curie-Weiss law can be expressed as

                    (57)

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                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                    534 Thermodyanamic Basis of Ferroelectric Phase Transitions

                    Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

                    These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

                    Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

                    (58)

                    where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

                    is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

                    Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

                    (59)

                    where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

                    Converse piezoelectric effect is expressed as

                    (510)

                    Where dijkt is in mV

                    Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

                    (511)

                    where Pi is the vector of pyroelectric coefficient in cm-2K-1

                    Displacement is expressed as

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                    (512)

                    So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

                    From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

                    For a ferroelectric system the free energy G can be expressed in terms of ten variables as

                    (513)

                    where Px Py Pz are the components of the polarization are the stress

                    components and T is the temperature

                    We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

                    (514)

                    Note that only even powers are taken because energy is same for plusmnPS states

                    Here a b c are the temperature dependent constants and E is the electric field

                    The equilibrium is found by establishing ie

                    (515)

                    ie

                    E = (516)

                    If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

                    If we ignore higher power terms then

                    (517)

                    leading to

                    (518)

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                    which is the same expression that we encountered for linear dielectrics

                    According to Landau-Devonshire theory near the Curie point (T~T0) we assume

                    a = a0 (T - T0) (519)

                    As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

                    (520)

                    In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

                    Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

                    paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

                    nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

                    Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                    535 Case I Second order Transition

                    When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

                    second order transition (do not get confused between T0 and Tc as the distiction will become clear

                    in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

                    Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

                    Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

                    The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

                    retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

                    polarization can be expressed as

                    (521)

                    showing that the polarization decreased to zero at T = T0 as shown in figure 58

                    Dielectric susceptibility at T lt T0 can be estimated as

                    (522)

                    Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

                    will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

                    values near T0

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                    Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

                    This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

                    (523)

                    Now substituting in (523) yields

                    (524)

                    Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                    536 Case ndash II First Order Transition

                    Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

                    now more than T0 This gives rise to the following free energy vs polarization plot

                    Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

                    The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

                    is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

                    Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

                    In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

                    free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

                    (525)

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                    On the other hand field E must also be zero for the polarization to be spontaneous ie

                    (526)

                    The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                    (527)

                    and

                    (528)

                    The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                    heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                    temperature higher than Tc the sample will be in paraelectric state This results in thermal

                    hysteresis when these materials are thermally cycled across Tc

                    If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                    Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                    Solid State Physics AJ Dekker Macmillan Publishing

                    Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                    537 Ferroelectric Domains

                    In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                    Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                    The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                    directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                    or 90deg domain walls

                    Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                    Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                    depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                    Now the question is Why is there a domain wall

                    The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                    associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                    splitting of the material into oppositely oriented domains or

                    compensation of the electrical charge via electrical conduction through the crystal

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                    Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                    by transmission electron microscopy

                    Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                    538 Analytical treatment of domain wall energy

                    Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                    (529)

                    where Uc effect of applied field on the domain energy

                    Up and Ux bulk electrical and elastic energies

                    Ud depolarization energy and

                    Uw domain energy

                    Ud is the energy related to the internal field set up in the crystal by the polarization and not

                    compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                    (530)

                    Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                    is the polarization at the center of the domain

                    Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                    width (d) and crystal volume (V) and is given as

                    (531)

                    To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                    in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                    wrt domain wall thickness d ie dΔGdd = 0 resulting in

                    (532)

                    Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                    539 Ferroelectric Switching and Domains

                    Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                    At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                    Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                    If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                    microCcm2and E is electric field across the sample in Vcm The process is something like this

                    Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                    Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                    reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                    polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                    Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                    of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                    Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                    Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                    5310 Measurement of Hysteresis Loop

                    Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                    The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                    crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                    This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                    and coercive field Ec

                    A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                    Figure 5 15 Schematic representation of sawyer-tower circuit

                    Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                    5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                    Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                    atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                    Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                    Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                    a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                    Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                    becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                    positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                    The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                    Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                    Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                    spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                    BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                    orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                    5312 Applications of Ferroelectrics

                    In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                    Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                    (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                    Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                    where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                    53121 Nonvolatile Memories

                    Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                    two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                    Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                    53122 Camera Flashes

                    In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                    Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                    Module 5 Nonlinear Dielectrics

                    Summary

                    Summary

                    In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                    can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                    and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                    binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                    One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                    5474 Actuators

                    In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                    In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                    You can have it in two forms

                    Direct Piezo Actuators with strokes lower than 100 microns or so and

                    Amplified Piezoelectric Actuators which can yield millimeter long strokes

                    Some of the examples of applications are

                    Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                    Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                    Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                    Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                    In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                    As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                    5475 Frequency Standards

                    Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                    Quartz clocks

                    Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                    Module 5 Nonlinear Dielectrics

                    Summary

                    Summary

                    Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                    54 Piezoelectric Ceramics

                    Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                    Pb(ZrTi)O3)

                    An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                    For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                    541 Direct Piezoelectric Effect

                    Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                    (533)

                    where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                    542 Reverse or Converse Piezoelectric Effect

                    The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                    (534)

                    where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                    Figure 520 Direct and Converse PiezoelectricEffects

                    The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                    543 Poling of Piezoelectric Materials

                    As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                    The values of piezoelectric coefficient of some materials are given below

                    Material Piezoelectric Constant d(pmV)

                    Quartz 23

                    Barium Titanate 100-149

                    Lead Niobate 80-85

                    Lead zirconate titanate 250-365

                    So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                    Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                    field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                    Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                    544 Depolarization of Piezoelectrics

                    Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                    polarization or rather result in alignment of dipoles gets lost

                    Figure 522 Animation on depolarization offerroelectrics

                    (Courtesy copy DoITPoMS University of Cambridge)

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                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                    545 Common PIezoelectric Materials

                    5451 Barium Titanate (BaTiO3)

                    This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                    used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                    Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                    1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                    must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                    5452 Pb(ZrTi)O3 or PZT

                    PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                    The phase diagram of PZT is shown below

                    Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                    The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                    lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                    few poling directions available making it a useful piezoelectric

                    Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                    546 Measurement of Piezoelectric Properties

                    Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                    In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                    Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                    The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                    (535)

                    Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                    (536)

                    Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                    One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                    547 Applications of Piezoelectric Ceramics

                    Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                    5471 Power Generation

                    Gas Lighter

                    Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                    Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                    One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                    Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                    Power Transformer

                    A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                    An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                    Figure 526 Schematic of a piezoelectrictransformer

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                    Module 5 Special Dielectrics Piezoelectric Ceramics

                    5472 Piezoelectric Sensors

                    Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                    Other sensor applications are

                    Detection and generation of sonar waves

                    To detect detonation in automotive engine by sampling the vibrations of the engine block

                    To detect the precise moment of fuel injection in an automotive engine

                    Detection of acoustic emissions in acoustic emission testing

                    Microbalances as very sensitive chemical and biological sensors

                    Strain gauges

                    Medical applications using ultrasound waves

                    Kidney stone treatment

                    In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                    Figure 527 Ultrasonic waves creation and

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                    kidney stone treatment and ultrasound imagingof the fetus

                    (Courtesy copy DoITPoMS University of Cambridge)

                    5473 Ultrasound Imaging Using Transduction Effect

                    Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                    55 Pyroelectric Ceramics

                    Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                    Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                    Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                    551 Difference between Pyroelectric and Ferroelectric Material

                    Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                    Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                    552 Theory of Piezoelectric Materials

                    From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                    (537)

                    Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                    Assuming electric field E as constant differentiating the above equation with temperature leads to

                    (538)

                    Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                    we write

                    Δ OR

                    Δ (539)

                    Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                    Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                    (540)

                    The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                    As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                    553 Measurement of Pyroelectric Coefficient

                    One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                    (541)

                    Where Ip is the pyrocurrent and is given as

                    (542)

                    where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                    respectively

                    Figure 530 Circuit for measuring pyroelectriccoefficient

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                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                    554 Direct and Indirect Effect

                    Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                    Since change in the polarization can also be expressed as depending

                    upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                    Figure 531 Direct-Indirect effect animation

                    (Courtesy copy DoITPoMS University of Cambridge)

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                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                    555 Common Pyroelectric Materials

                    Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                    The most common materials are tabulated below

                    Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                    LiTaO3 single crystal Hexagonal 665 -230

                    075Pb(Mg13-Nb23)O3-025PbTiO3

                    (PMN-PT) Ceramic

                    Perovskite 150 -1300

                    Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                    Triglycine sulphate

                    (NH2CH2COOH)3H2SO4

                    Sulphate 49 -280

                    Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                    5551 Triglycine Sulphate (TGS)

                    High pyroelectric coefficient

                    Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                    Can be modified to withstand temperatures above Curie point without depoling

                    Used in thermal imaging cameras

                    5552 Polyvinylidene Fluoride (PVDF)

                    Poor pyroelectric coefficient

                    Readily available in large areas of thin film

                    More stable to heat vacuum and moisture than TGS mechanically robust

                    Low heat conductivity and low permittivity

                    High loss tangent

                    Commonly used for burglar alarms

                    5553 Perovskite Ferroelectric Ceramics

                    Generally robust and insensitive to moisture and vacuum

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                    High pyroelectric coefficient and low loss

                    Better operation near TC

                    Strong dependence on composition

                    As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                    RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                    556 Common Applications

                    5561 Burglar Alarms

                    Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                    Figure 532 Working of an IR intruder alarm

                    (Courtesy copy DoITPoMS University ofCambridge)

                    5562 Infrared or Thermal Imaging

                    Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                    The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                    A typical photograph generated from IR imaging looks like this

                    Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                    Here is a simple explanation of how IT imaging using pyroelectrics works

                    A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                    This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                    Figure 534 Process of imagecreation

                    5563 Pollutant Control

                    The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                    Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                    Figure 535 Gas detection using a pyroelectricdetector

                    (Courtesy copy DoITPoMS University of Cambridge)

                    >

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                    Module 5 Nonlinear Dielectrics

                    Summary

                    Summary

                    Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                      534 Thermodyanamic Basis of Ferroelectric Phase Transitions

                      Thermodynamic theory to understand the ferroelectric phase transitions was developed aftercontributions from Lev Landau and VL Ginzburg both Soviet physicists and AF Devonshire BritishPhysicist The approach is based around calculating the free energy of system and working aroundother thermodynamic parameters to predict the nature of phase transition Here before we go intodetails of this theory we will look at the some of the basic definitions

                      These non-linear dielectrics exhibit various kinds of couplings between physical properties and canbe expressed mathematically For instance below are the expressions for ferroelectric piezoelectricand pyroelectric couplings

                      Ferroelectric Effect Electric charge in a polar material can be induced by application of an external electric field and canbe expressed as

                      (58)

                      where χij is the susceptibility in Fm (actually dimensionless but here eo ie permittivity of free space

                      is also included which has dimension of Fm) and is second rank tensor Note that the equation isvalid only for the linear region of the hysteresis curve

                      Piezoelectric effectSimilarly the charge induced by application of external stress ie piezoelectric effect can beexpressed by

                      (59)

                      where is the piezoelectric coefficient and is third rank tensor with units CN is the stressapplied

                      Converse piezoelectric effect is expressed as

                      (510)

                      Where dijkt is in mV

                      Pyroelectric EffectInduced charge by temperature change ie pyroelectric effect is expressed by

                      (511)

                      where Pi is the vector of pyroelectric coefficient in cm-2K-1

                      Displacement is expressed as

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                      (512)

                      So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

                      From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

                      For a ferroelectric system the free energy G can be expressed in terms of ten variables as

                      (513)

                      where Px Py Pz are the components of the polarization are the stress

                      components and T is the temperature

                      We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

                      (514)

                      Note that only even powers are taken because energy is same for plusmnPS states

                      Here a b c are the temperature dependent constants and E is the electric field

                      The equilibrium is found by establishing ie

                      (515)

                      ie

                      E = (516)

                      If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

                      If we ignore higher power terms then

                      (517)

                      leading to

                      (518)

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                      which is the same expression that we encountered for linear dielectrics

                      According to Landau-Devonshire theory near the Curie point (T~T0) we assume

                      a = a0 (T - T0) (519)

                      As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

                      (520)

                      In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

                      Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

                      paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

                      nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

                      Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                      535 Case I Second order Transition

                      When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

                      second order transition (do not get confused between T0 and Tc as the distiction will become clear

                      in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

                      Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

                      Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

                      The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

                      retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

                      polarization can be expressed as

                      (521)

                      showing that the polarization decreased to zero at T = T0 as shown in figure 58

                      Dielectric susceptibility at T lt T0 can be estimated as

                      (522)

                      Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

                      will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

                      values near T0

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                      Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

                      This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

                      (523)

                      Now substituting in (523) yields

                      (524)

                      Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                      536 Case ndash II First Order Transition

                      Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

                      now more than T0 This gives rise to the following free energy vs polarization plot

                      Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

                      The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

                      is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

                      Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

                      In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

                      free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

                      (525)

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                      On the other hand field E must also be zero for the polarization to be spontaneous ie

                      (526)

                      The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                      (527)

                      and

                      (528)

                      The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                      heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                      temperature higher than Tc the sample will be in paraelectric state This results in thermal

                      hysteresis when these materials are thermally cycled across Tc

                      If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                      Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                      Solid State Physics AJ Dekker Macmillan Publishing

                      Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                      537 Ferroelectric Domains

                      In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                      Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                      The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                      directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                      or 90deg domain walls

                      Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                      Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                      depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                      Now the question is Why is there a domain wall

                      The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                      associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                      splitting of the material into oppositely oriented domains or

                      compensation of the electrical charge via electrical conduction through the crystal

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                      Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                      by transmission electron microscopy

                      Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                      538 Analytical treatment of domain wall energy

                      Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                      (529)

                      where Uc effect of applied field on the domain energy

                      Up and Ux bulk electrical and elastic energies

                      Ud depolarization energy and

                      Uw domain energy

                      Ud is the energy related to the internal field set up in the crystal by the polarization and not

                      compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                      (530)

                      Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                      is the polarization at the center of the domain

                      Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                      width (d) and crystal volume (V) and is given as

                      (531)

                      To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                      in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                      wrt domain wall thickness d ie dΔGdd = 0 resulting in

                      (532)

                      Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                      539 Ferroelectric Switching and Domains

                      Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                      At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                      Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                      If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                      microCcm2and E is electric field across the sample in Vcm The process is something like this

                      Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                      Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                      reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                      polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                      Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                      of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                      Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                      Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                      5310 Measurement of Hysteresis Loop

                      Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                      The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                      crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                      This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                      and coercive field Ec

                      A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                      Figure 5 15 Schematic representation of sawyer-tower circuit

                      Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                      5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                      Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                      atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                      Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                      Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                      a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                      Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                      becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                      positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                      The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                      Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                      Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                      spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                      BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                      orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                      5312 Applications of Ferroelectrics

                      In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                      Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                      (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                      Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                      where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                      53121 Nonvolatile Memories

                      Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                      two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                      Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                      53122 Camera Flashes

                      In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                      Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

                      >

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                      Module 5 Nonlinear Dielectrics

                      Summary

                      Summary

                      In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                      can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                      and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                      binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                      One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                      5474 Actuators

                      In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                      In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                      You can have it in two forms

                      Direct Piezo Actuators with strokes lower than 100 microns or so and

                      Amplified Piezoelectric Actuators which can yield millimeter long strokes

                      Some of the examples of applications are

                      Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                      Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                      Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                      Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                      In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                      As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                      5475 Frequency Standards

                      Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                      Quartz clocks

                      Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                      Module 5 Nonlinear Dielectrics

                      Summary

                      Summary

                      Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                      54 Piezoelectric Ceramics

                      Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                      Pb(ZrTi)O3)

                      An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                      For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                      541 Direct Piezoelectric Effect

                      Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                      (533)

                      where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                      542 Reverse or Converse Piezoelectric Effect

                      The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                      (534)

                      where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                      Figure 520 Direct and Converse PiezoelectricEffects

                      The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                      543 Poling of Piezoelectric Materials

                      As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                      The values of piezoelectric coefficient of some materials are given below

                      Material Piezoelectric Constant d(pmV)

                      Quartz 23

                      Barium Titanate 100-149

                      Lead Niobate 80-85

                      Lead zirconate titanate 250-365

                      So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                      Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                      field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                      Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                      544 Depolarization of Piezoelectrics

                      Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                      polarization or rather result in alignment of dipoles gets lost

                      Figure 522 Animation on depolarization offerroelectrics

                      (Courtesy copy DoITPoMS University of Cambridge)

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                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                      545 Common PIezoelectric Materials

                      5451 Barium Titanate (BaTiO3)

                      This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                      used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                      Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                      1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                      must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                      5452 Pb(ZrTi)O3 or PZT

                      PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                      The phase diagram of PZT is shown below

                      Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                      The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                      lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                      few poling directions available making it a useful piezoelectric

                      Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                      546 Measurement of Piezoelectric Properties

                      Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                      In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                      Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                      The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                      (535)

                      Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                      (536)

                      Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                      One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                      547 Applications of Piezoelectric Ceramics

                      Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                      5471 Power Generation

                      Gas Lighter

                      Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                      Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                      One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                      Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                      Power Transformer

                      A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                      An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                      Figure 526 Schematic of a piezoelectrictransformer

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                      Module 5 Special Dielectrics Piezoelectric Ceramics

                      5472 Piezoelectric Sensors

                      Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                      Other sensor applications are

                      Detection and generation of sonar waves

                      To detect detonation in automotive engine by sampling the vibrations of the engine block

                      To detect the precise moment of fuel injection in an automotive engine

                      Detection of acoustic emissions in acoustic emission testing

                      Microbalances as very sensitive chemical and biological sensors

                      Strain gauges

                      Medical applications using ultrasound waves

                      Kidney stone treatment

                      In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                      Figure 527 Ultrasonic waves creation and

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                      kidney stone treatment and ultrasound imagingof the fetus

                      (Courtesy copy DoITPoMS University of Cambridge)

                      5473 Ultrasound Imaging Using Transduction Effect

                      Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                      55 Pyroelectric Ceramics

                      Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                      Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                      Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                      551 Difference between Pyroelectric and Ferroelectric Material

                      Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                      Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                      552 Theory of Piezoelectric Materials

                      From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                      (537)

                      Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                      Assuming electric field E as constant differentiating the above equation with temperature leads to

                      (538)

                      Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                      we write

                      Δ OR

                      Δ (539)

                      Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                      Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                      (540)

                      The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                      As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                      553 Measurement of Pyroelectric Coefficient

                      One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                      (541)

                      Where Ip is the pyrocurrent and is given as

                      (542)

                      where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                      respectively

                      Figure 530 Circuit for measuring pyroelectriccoefficient

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                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                      554 Direct and Indirect Effect

                      Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                      Since change in the polarization can also be expressed as depending

                      upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                      Figure 531 Direct-Indirect effect animation

                      (Courtesy copy DoITPoMS University of Cambridge)

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                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                      555 Common Pyroelectric Materials

                      Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                      The most common materials are tabulated below

                      Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                      LiTaO3 single crystal Hexagonal 665 -230

                      075Pb(Mg13-Nb23)O3-025PbTiO3

                      (PMN-PT) Ceramic

                      Perovskite 150 -1300

                      Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                      Triglycine sulphate

                      (NH2CH2COOH)3H2SO4

                      Sulphate 49 -280

                      Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                      5551 Triglycine Sulphate (TGS)

                      High pyroelectric coefficient

                      Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                      Can be modified to withstand temperatures above Curie point without depoling

                      Used in thermal imaging cameras

                      5552 Polyvinylidene Fluoride (PVDF)

                      Poor pyroelectric coefficient

                      Readily available in large areas of thin film

                      More stable to heat vacuum and moisture than TGS mechanically robust

                      Low heat conductivity and low permittivity

                      High loss tangent

                      Commonly used for burglar alarms

                      5553 Perovskite Ferroelectric Ceramics

                      Generally robust and insensitive to moisture and vacuum

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                      High pyroelectric coefficient and low loss

                      Better operation near TC

                      Strong dependence on composition

                      As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                      RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                      556 Common Applications

                      5561 Burglar Alarms

                      Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                      Figure 532 Working of an IR intruder alarm

                      (Courtesy copy DoITPoMS University ofCambridge)

                      5562 Infrared or Thermal Imaging

                      Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                      The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                      A typical photograph generated from IR imaging looks like this

                      Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                      Here is a simple explanation of how IT imaging using pyroelectrics works

                      A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                      This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                      Figure 534 Process of imagecreation

                      5563 Pollutant Control

                      The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                      Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                      Figure 535 Gas detection using a pyroelectricdetector

                      (Courtesy copy DoITPoMS University of Cambridge)

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                      Module 5 Nonlinear Dielectrics

                      Summary

                      Summary

                      Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                        (512)

                        So depending upon the state of material many such effects may be present together Thesecouplings between thermal elastic or electric properties can be understood formally by adopting athermodynamic approach The results of such an approach yield equations of state which relate thematerial parameters with different experimental conditions which assist in modeling of the parametersand in understanding the response of various devices

                        From the laws of thermodynamics the thermodynamic state of any crystal in a state of equilibriumcan be completely established by the value of number of variables which in case of ferroelectricsinclude temperature T entropy S electric field E polarization P stress s and strain e Usuallyparameters like electric field E and stress s can be treated as external or independent variables whilepolarization and strain can be treated as internal or dependent variables

                        For a ferroelectric system the free energy G can be expressed in terms of ten variables as

                        (513)

                        where Px Py Pz are the components of the polarization are the stress

                        components and T is the temperature

                        We can get the value of the independent variables in thermal equilibrium at the free energyminimum For an uniaxial ferroelectric free energy can be expanded in terms of polarization ignoringthe stress field Here we select the origin of free energy for a free unpolarized and unstrained crystalto be zero Hence

                        (514)

                        Note that only even powers are taken because energy is same for plusmnPS states

                        Here a b c are the temperature dependent constants and E is the electric field

                        The equilibrium is found by establishing ie

                        (515)

                        ie

                        E = (516)

                        If all of a b and c are positive then P = 0 is the only root of the equation as shown below in thefigure This is situation for a paraelectric material where polarization is zero when field is zero

                        If we ignore higher power terms then

                        (517)

                        leading to

                        (518)

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                        which is the same expression that we encountered for linear dielectrics

                        According to Landau-Devonshire theory near the Curie point (T~T0) we assume

                        a = a0 (T - T0) (519)

                        As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

                        (520)

                        In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

                        Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

                        paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

                        nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

                        Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                        535 Case I Second order Transition

                        When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

                        second order transition (do not get confused between T0 and Tc as the distiction will become clear

                        in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

                        Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

                        Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

                        The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

                        retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

                        polarization can be expressed as

                        (521)

                        showing that the polarization decreased to zero at T = T0 as shown in figure 58

                        Dielectric susceptibility at T lt T0 can be estimated as

                        (522)

                        Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

                        will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

                        values near T0

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                        Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

                        This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

                        (523)

                        Now substituting in (523) yields

                        (524)

                        Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                        536 Case ndash II First Order Transition

                        Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

                        now more than T0 This gives rise to the following free energy vs polarization plot

                        Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

                        The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

                        is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

                        Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

                        In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

                        free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

                        (525)

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                        On the other hand field E must also be zero for the polarization to be spontaneous ie

                        (526)

                        The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                        (527)

                        and

                        (528)

                        The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                        heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                        temperature higher than Tc the sample will be in paraelectric state This results in thermal

                        hysteresis when these materials are thermally cycled across Tc

                        If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                        Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                        Solid State Physics AJ Dekker Macmillan Publishing

                        Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                        537 Ferroelectric Domains

                        In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                        Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                        The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                        directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                        or 90deg domain walls

                        Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                        Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                        depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                        Now the question is Why is there a domain wall

                        The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                        associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                        splitting of the material into oppositely oriented domains or

                        compensation of the electrical charge via electrical conduction through the crystal

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                        Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                        by transmission electron microscopy

                        Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                        538 Analytical treatment of domain wall energy

                        Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                        (529)

                        where Uc effect of applied field on the domain energy

                        Up and Ux bulk electrical and elastic energies

                        Ud depolarization energy and

                        Uw domain energy

                        Ud is the energy related to the internal field set up in the crystal by the polarization and not

                        compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                        (530)

                        Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                        is the polarization at the center of the domain

                        Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                        width (d) and crystal volume (V) and is given as

                        (531)

                        To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                        in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                        wrt domain wall thickness d ie dΔGdd = 0 resulting in

                        (532)

                        Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                        539 Ferroelectric Switching and Domains

                        Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                        At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                        Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                        If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                        microCcm2and E is electric field across the sample in Vcm The process is something like this

                        Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                        Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                        reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                        polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                        Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                        of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                        Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                        Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                        5310 Measurement of Hysteresis Loop

                        Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                        The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                        crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                        This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                        and coercive field Ec

                        A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                        Figure 5 15 Schematic representation of sawyer-tower circuit

                        Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                        5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                        Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                        atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                        Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                        Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                        a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                        Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                        becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                        positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                        The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                        Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                        Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                        spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                        BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                        orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                        5312 Applications of Ferroelectrics

                        In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                        Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                        (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                        Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                        where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                        53121 Nonvolatile Memories

                        Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                        two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                        Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                        53122 Camera Flashes

                        In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                        Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                        Module 5 Nonlinear Dielectrics

                        Summary

                        Summary

                        In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                        can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                        and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                        binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                        One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                        5474 Actuators

                        In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                        In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                        You can have it in two forms

                        Direct Piezo Actuators with strokes lower than 100 microns or so and

                        Amplified Piezoelectric Actuators which can yield millimeter long strokes

                        Some of the examples of applications are

                        Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                        Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                        Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                        Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                        In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                        As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                        5475 Frequency Standards

                        Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                        Quartz clocks

                        Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                        Module 5 Nonlinear Dielectrics

                        Summary

                        Summary

                        Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                        54 Piezoelectric Ceramics

                        Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                        Pb(ZrTi)O3)

                        An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                        For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                        541 Direct Piezoelectric Effect

                        Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                        (533)

                        where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                        542 Reverse or Converse Piezoelectric Effect

                        The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                        (534)

                        where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                        Figure 520 Direct and Converse PiezoelectricEffects

                        The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                        543 Poling of Piezoelectric Materials

                        As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                        The values of piezoelectric coefficient of some materials are given below

                        Material Piezoelectric Constant d(pmV)

                        Quartz 23

                        Barium Titanate 100-149

                        Lead Niobate 80-85

                        Lead zirconate titanate 250-365

                        So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                        Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                        field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                        Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                        544 Depolarization of Piezoelectrics

                        Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                        polarization or rather result in alignment of dipoles gets lost

                        Figure 522 Animation on depolarization offerroelectrics

                        (Courtesy copy DoITPoMS University of Cambridge)

                        >

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                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                        545 Common PIezoelectric Materials

                        5451 Barium Titanate (BaTiO3)

                        This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                        used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                        Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                        1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                        must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                        5452 Pb(ZrTi)O3 or PZT

                        PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                        The phase diagram of PZT is shown below

                        Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                        The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                        lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                        few poling directions available making it a useful piezoelectric

                        Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                        546 Measurement of Piezoelectric Properties

                        Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                        In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                        Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                        The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                        (535)

                        Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                        (536)

                        Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                        One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                        547 Applications of Piezoelectric Ceramics

                        Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                        5471 Power Generation

                        Gas Lighter

                        Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                        Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                        One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                        Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                        Power Transformer

                        A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                        An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                        Figure 526 Schematic of a piezoelectrictransformer

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                        Module 5 Special Dielectrics Piezoelectric Ceramics

                        5472 Piezoelectric Sensors

                        Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                        Other sensor applications are

                        Detection and generation of sonar waves

                        To detect detonation in automotive engine by sampling the vibrations of the engine block

                        To detect the precise moment of fuel injection in an automotive engine

                        Detection of acoustic emissions in acoustic emission testing

                        Microbalances as very sensitive chemical and biological sensors

                        Strain gauges

                        Medical applications using ultrasound waves

                        Kidney stone treatment

                        In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                        Figure 527 Ultrasonic waves creation and

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                        kidney stone treatment and ultrasound imagingof the fetus

                        (Courtesy copy DoITPoMS University of Cambridge)

                        5473 Ultrasound Imaging Using Transduction Effect

                        Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                        55 Pyroelectric Ceramics

                        Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                        Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                        Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                        551 Difference between Pyroelectric and Ferroelectric Material

                        Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                        Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                        552 Theory of Piezoelectric Materials

                        From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                        (537)

                        Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                        Assuming electric field E as constant differentiating the above equation with temperature leads to

                        (538)

                        Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                        we write

                        Δ OR

                        Δ (539)

                        Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                        Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                        (540)

                        The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                        As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                        553 Measurement of Pyroelectric Coefficient

                        One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                        (541)

                        Where Ip is the pyrocurrent and is given as

                        (542)

                        where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                        respectively

                        Figure 530 Circuit for measuring pyroelectriccoefficient

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                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                        554 Direct and Indirect Effect

                        Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                        Since change in the polarization can also be expressed as depending

                        upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                        Figure 531 Direct-Indirect effect animation

                        (Courtesy copy DoITPoMS University of Cambridge)

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                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                        555 Common Pyroelectric Materials

                        Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                        The most common materials are tabulated below

                        Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                        LiTaO3 single crystal Hexagonal 665 -230

                        075Pb(Mg13-Nb23)O3-025PbTiO3

                        (PMN-PT) Ceramic

                        Perovskite 150 -1300

                        Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                        Triglycine sulphate

                        (NH2CH2COOH)3H2SO4

                        Sulphate 49 -280

                        Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                        5551 Triglycine Sulphate (TGS)

                        High pyroelectric coefficient

                        Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                        Can be modified to withstand temperatures above Curie point without depoling

                        Used in thermal imaging cameras

                        5552 Polyvinylidene Fluoride (PVDF)

                        Poor pyroelectric coefficient

                        Readily available in large areas of thin film

                        More stable to heat vacuum and moisture than TGS mechanically robust

                        Low heat conductivity and low permittivity

                        High loss tangent

                        Commonly used for burglar alarms

                        5553 Perovskite Ferroelectric Ceramics

                        Generally robust and insensitive to moisture and vacuum

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                        High pyroelectric coefficient and low loss

                        Better operation near TC

                        Strong dependence on composition

                        As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                        RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                        556 Common Applications

                        5561 Burglar Alarms

                        Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                        Figure 532 Working of an IR intruder alarm

                        (Courtesy copy DoITPoMS University ofCambridge)

                        5562 Infrared or Thermal Imaging

                        Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                        The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                        A typical photograph generated from IR imaging looks like this

                        Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                        Here is a simple explanation of how IT imaging using pyroelectrics works

                        A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                        This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                        Figure 534 Process of imagecreation

                        5563 Pollutant Control

                        The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                        Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                        Figure 535 Gas detection using a pyroelectricdetector

                        (Courtesy copy DoITPoMS University of Cambridge)

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                        Module 5 Nonlinear Dielectrics

                        Summary

                        Summary

                        Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                          which is the same expression that we encountered for linear dielectrics

                          According to Landau-Devonshire theory near the Curie point (T~T0) we assume

                          a = a0 (T - T0) (519)

                          As a result the free energy expansion (513) only lsquoarsquo is dependent on temperature while otherconstants are temperature independent Incorporating (518) into (513) yields

                          (520)

                          In this expression for all known ferroelectrics both ao and c are positive while depending upon thesign of b the phase transition nature changes

                          Figure 56 (a) show the free energy vs polarization plot when T gtgt T0 ie when the crystal is in

                          paraelectric state On the other hand if a lt 0 when T ltlt T0 and b and c are positive there will be a

                          nonzero root of P in addition P = 0 as shown below in figure 56 (b) representing the ferroelectricstate with non-zero polarization at zero field

                          Figure 56 Free energy vs polarization for (a)paraelectric (above T0) and (b) ferroelectric crystal(below T0)

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                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                          535 Case I Second order Transition

                          When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

                          second order transition (do not get confused between T0 and Tc as the distiction will become clear

                          in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

                          Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

                          Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

                          The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

                          retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

                          polarization can be expressed as

                          (521)

                          showing that the polarization decreased to zero at T = T0 as shown in figure 58

                          Dielectric susceptibility at T lt T0 can be estimated as

                          (522)

                          Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

                          will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

                          values near T0

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                          Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

                          This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

                          (523)

                          Now substituting in (523) yields

                          (524)

                          Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                          536 Case ndash II First Order Transition

                          Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

                          now more than T0 This gives rise to the following free energy vs polarization plot

                          Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

                          The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

                          is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

                          Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

                          In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

                          free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

                          (525)

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                          On the other hand field E must also be zero for the polarization to be spontaneous ie

                          (526)

                          The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                          (527)

                          and

                          (528)

                          The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                          heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                          temperature higher than Tc the sample will be in paraelectric state This results in thermal

                          hysteresis when these materials are thermally cycled across Tc

                          If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                          Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                          Solid State Physics AJ Dekker Macmillan Publishing

                          Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                          537 Ferroelectric Domains

                          In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                          Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                          The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                          directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                          or 90deg domain walls

                          Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                          Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                          depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                          Now the question is Why is there a domain wall

                          The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                          associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                          splitting of the material into oppositely oriented domains or

                          compensation of the electrical charge via electrical conduction through the crystal

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                          Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                          by transmission electron microscopy

                          Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                          538 Analytical treatment of domain wall energy

                          Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                          (529)

                          where Uc effect of applied field on the domain energy

                          Up and Ux bulk electrical and elastic energies

                          Ud depolarization energy and

                          Uw domain energy

                          Ud is the energy related to the internal field set up in the crystal by the polarization and not

                          compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                          (530)

                          Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                          is the polarization at the center of the domain

                          Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                          width (d) and crystal volume (V) and is given as

                          (531)

                          To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                          in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                          wrt domain wall thickness d ie dΔGdd = 0 resulting in

                          (532)

                          Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                          539 Ferroelectric Switching and Domains

                          Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                          At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                          Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                          If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                          microCcm2and E is electric field across the sample in Vcm The process is something like this

                          Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                          Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                          reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                          polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                          Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                          of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                          Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                          Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                          5310 Measurement of Hysteresis Loop

                          Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                          The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                          crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                          This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                          and coercive field Ec

                          A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                          Figure 5 15 Schematic representation of sawyer-tower circuit

                          Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                          5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                          Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                          atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                          Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                          Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                          a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                          Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                          becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                          positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                          The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                          Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                          Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                          spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                          BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                          orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                          5312 Applications of Ferroelectrics

                          In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                          Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                          (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                          Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                          where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                          53121 Nonvolatile Memories

                          Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                          two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                          Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                          53122 Camera Flashes

                          In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                          Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                          Module 5 Nonlinear Dielectrics

                          Summary

                          Summary

                          In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                          can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                          and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                          binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                          One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                          5474 Actuators

                          In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                          In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                          You can have it in two forms

                          Direct Piezo Actuators with strokes lower than 100 microns or so and

                          Amplified Piezoelectric Actuators which can yield millimeter long strokes

                          Some of the examples of applications are

                          Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                          Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                          Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                          Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                          In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                          As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                          5475 Frequency Standards

                          Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                          Quartz clocks

                          Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                          Module 5 Nonlinear Dielectrics

                          Summary

                          Summary

                          Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                          54 Piezoelectric Ceramics

                          Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                          Pb(ZrTi)O3)

                          An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                          For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                          541 Direct Piezoelectric Effect

                          Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                          (533)

                          where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                          542 Reverse or Converse Piezoelectric Effect

                          The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                          (534)

                          where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                          Figure 520 Direct and Converse PiezoelectricEffects

                          The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                          543 Poling of Piezoelectric Materials

                          As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                          The values of piezoelectric coefficient of some materials are given below

                          Material Piezoelectric Constant d(pmV)

                          Quartz 23

                          Barium Titanate 100-149

                          Lead Niobate 80-85

                          Lead zirconate titanate 250-365

                          So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                          Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                          field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                          Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                          544 Depolarization of Piezoelectrics

                          Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                          polarization or rather result in alignment of dipoles gets lost

                          Figure 522 Animation on depolarization offerroelectrics

                          (Courtesy copy DoITPoMS University of Cambridge)

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                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                          545 Common PIezoelectric Materials

                          5451 Barium Titanate (BaTiO3)

                          This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                          used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                          Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                          1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                          must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                          5452 Pb(ZrTi)O3 or PZT

                          PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                          The phase diagram of PZT is shown below

                          Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                          The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                          lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                          few poling directions available making it a useful piezoelectric

                          Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                          546 Measurement of Piezoelectric Properties

                          Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                          In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                          Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                          The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                          (535)

                          Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                          (536)

                          Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                          One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                          547 Applications of Piezoelectric Ceramics

                          Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                          5471 Power Generation

                          Gas Lighter

                          Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                          Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                          One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                          Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                          Power Transformer

                          A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                          An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                          Figure 526 Schematic of a piezoelectrictransformer

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                          Module 5 Special Dielectrics Piezoelectric Ceramics

                          5472 Piezoelectric Sensors

                          Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                          Other sensor applications are

                          Detection and generation of sonar waves

                          To detect detonation in automotive engine by sampling the vibrations of the engine block

                          To detect the precise moment of fuel injection in an automotive engine

                          Detection of acoustic emissions in acoustic emission testing

                          Microbalances as very sensitive chemical and biological sensors

                          Strain gauges

                          Medical applications using ultrasound waves

                          Kidney stone treatment

                          In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                          Figure 527 Ultrasonic waves creation and

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                          kidney stone treatment and ultrasound imagingof the fetus

                          (Courtesy copy DoITPoMS University of Cambridge)

                          5473 Ultrasound Imaging Using Transduction Effect

                          Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                          55 Pyroelectric Ceramics

                          Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                          Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                          Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                          551 Difference between Pyroelectric and Ferroelectric Material

                          Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                          Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                          552 Theory of Piezoelectric Materials

                          From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                          (537)

                          Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                          Assuming electric field E as constant differentiating the above equation with temperature leads to

                          (538)

                          Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                          we write

                          Δ OR

                          Δ (539)

                          Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                          Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                          (540)

                          The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                          As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                          553 Measurement of Pyroelectric Coefficient

                          One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                          (541)

                          Where Ip is the pyrocurrent and is given as

                          (542)

                          where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                          respectively

                          Figure 530 Circuit for measuring pyroelectriccoefficient

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                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                          554 Direct and Indirect Effect

                          Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                          Since change in the polarization can also be expressed as depending

                          upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                          Figure 531 Direct-Indirect effect animation

                          (Courtesy copy DoITPoMS University of Cambridge)

                          >

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                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                          555 Common Pyroelectric Materials

                          Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                          The most common materials are tabulated below

                          Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                          LiTaO3 single crystal Hexagonal 665 -230

                          075Pb(Mg13-Nb23)O3-025PbTiO3

                          (PMN-PT) Ceramic

                          Perovskite 150 -1300

                          Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                          Triglycine sulphate

                          (NH2CH2COOH)3H2SO4

                          Sulphate 49 -280

                          Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                          5551 Triglycine Sulphate (TGS)

                          High pyroelectric coefficient

                          Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                          Can be modified to withstand temperatures above Curie point without depoling

                          Used in thermal imaging cameras

                          5552 Polyvinylidene Fluoride (PVDF)

                          Poor pyroelectric coefficient

                          Readily available in large areas of thin film

                          More stable to heat vacuum and moisture than TGS mechanically robust

                          Low heat conductivity and low permittivity

                          High loss tangent

                          Commonly used for burglar alarms

                          5553 Perovskite Ferroelectric Ceramics

                          Generally robust and insensitive to moisture and vacuum

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                          High pyroelectric coefficient and low loss

                          Better operation near TC

                          Strong dependence on composition

                          As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                          RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                          556 Common Applications

                          5561 Burglar Alarms

                          Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                          Figure 532 Working of an IR intruder alarm

                          (Courtesy copy DoITPoMS University ofCambridge)

                          5562 Infrared or Thermal Imaging

                          Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                          The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                          >

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                          A typical photograph generated from IR imaging looks like this

                          Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                          Here is a simple explanation of how IT imaging using pyroelectrics works

                          A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                          This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                          Figure 534 Process of imagecreation

                          5563 Pollutant Control

                          The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                          Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                          Figure 535 Gas detection using a pyroelectricdetector

                          (Courtesy copy DoITPoMS University of Cambridge)

                          >

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                          Module 5 Nonlinear Dielectrics

                          Summary

                          Summary

                          Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                            535 Case I Second order Transition

                            When b is positive the ferroelectric transition occurs at a temperature T = T0 and is called as

                            second order transition (do not get confused between T0 and Tc as the distiction will become clear

                            in the next section when we learn first order phase transition) Under such a situation free energyas function of polarization evolves continuously when temperature is changes ie from a curve withsingle minima at P = 0 when T lt T0 to a plot with two minima at P = +P0 and ndashP0 when T gt T0

                            Two curves become closely related if lsquoarsquo changes continuously with temperature and changes signat Tc and can be shown together as in figure 57 (a) below

                            Figure 57 Effect of temperature on the free energy vs polarizationplot Note how the sign of a changes with temperature and its effecton the curve

                            The spontaneous polarization P0 can be estimated by substituting E = 0 in equation (520) and

                            retaining only two lowest order terms since all the coefficients ie a0 b and c are positive The

                            polarization can be expressed as

                            (521)

                            showing that the polarization decreased to zero at T = T0 as shown in figure 58

                            Dielectric susceptibility at T lt T0 can be estimated as

                            (522)

                            Showing that susceptibility will have a divergence at T = T0 or its reciprocal (ie dielectric stiffness)

                            will vanish at T = T0 as shown in figure 58 In real materials susceptibility reaches very large

                            values near T0

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                            Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

                            This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

                            (523)

                            Now substituting in (523) yields

                            (524)

                            Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                            536 Case ndash II First Order Transition

                            Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

                            now more than T0 This gives rise to the following free energy vs polarization plot

                            Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

                            The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

                            is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

                            Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

                            In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

                            free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

                            (525)

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                            On the other hand field E must also be zero for the polarization to be spontaneous ie

                            (526)

                            The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                            (527)

                            and

                            (528)

                            The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                            heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                            temperature higher than Tc the sample will be in paraelectric state This results in thermal

                            hysteresis when these materials are thermally cycled across Tc

                            If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                            Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                            Solid State Physics AJ Dekker Macmillan Publishing

                            Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                            537 Ferroelectric Domains

                            In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                            Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                            The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                            directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                            or 90deg domain walls

                            Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                            Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                            depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                            Now the question is Why is there a domain wall

                            The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                            associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                            splitting of the material into oppositely oriented domains or

                            compensation of the electrical charge via electrical conduction through the crystal

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                            Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                            by transmission electron microscopy

                            Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                            538 Analytical treatment of domain wall energy

                            Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                            (529)

                            where Uc effect of applied field on the domain energy

                            Up and Ux bulk electrical and elastic energies

                            Ud depolarization energy and

                            Uw domain energy

                            Ud is the energy related to the internal field set up in the crystal by the polarization and not

                            compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                            (530)

                            Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                            is the polarization at the center of the domain

                            Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                            width (d) and crystal volume (V) and is given as

                            (531)

                            To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                            in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                            wrt domain wall thickness d ie dΔGdd = 0 resulting in

                            (532)

                            Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                            539 Ferroelectric Switching and Domains

                            Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                            At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                            Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                            If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                            microCcm2and E is electric field across the sample in Vcm The process is something like this

                            Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                            Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                            reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                            polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                            Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                            of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                            Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                            Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                            5310 Measurement of Hysteresis Loop

                            Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                            The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                            crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                            This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                            and coercive field Ec

                            A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                            Figure 5 15 Schematic representation of sawyer-tower circuit

                            Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                            5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                            Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                            atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                            Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                            Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                            a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                            Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                            becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                            positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                            The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                            Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                            Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                            spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                            BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                            orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                            5312 Applications of Ferroelectrics

                            In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                            Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                            (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                            Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                            where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                            53121 Nonvolatile Memories

                            Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                            two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                            Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                            53122 Camera Flashes

                            In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                            Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

                            >

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                            Module 5 Nonlinear Dielectrics

                            Summary

                            Summary

                            In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                            can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                            and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                            binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                            One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                            5474 Actuators

                            In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                            In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                            You can have it in two forms

                            Direct Piezo Actuators with strokes lower than 100 microns or so and

                            Amplified Piezoelectric Actuators which can yield millimeter long strokes

                            Some of the examples of applications are

                            Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                            Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                            Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                            Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                            In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                            As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                            5475 Frequency Standards

                            Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                            Quartz clocks

                            Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                            Module 5 Nonlinear Dielectrics

                            Summary

                            Summary

                            Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                            54 Piezoelectric Ceramics

                            Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                            Pb(ZrTi)O3)

                            An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                            For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                            541 Direct Piezoelectric Effect

                            Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                            (533)

                            where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                            542 Reverse or Converse Piezoelectric Effect

                            The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                            (534)

                            where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                            Figure 520 Direct and Converse PiezoelectricEffects

                            The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                            543 Poling of Piezoelectric Materials

                            As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                            The values of piezoelectric coefficient of some materials are given below

                            Material Piezoelectric Constant d(pmV)

                            Quartz 23

                            Barium Titanate 100-149

                            Lead Niobate 80-85

                            Lead zirconate titanate 250-365

                            So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                            Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                            field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                            Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                            544 Depolarization of Piezoelectrics

                            Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                            polarization or rather result in alignment of dipoles gets lost

                            Figure 522 Animation on depolarization offerroelectrics

                            (Courtesy copy DoITPoMS University of Cambridge)

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                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                            545 Common PIezoelectric Materials

                            5451 Barium Titanate (BaTiO3)

                            This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                            used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                            Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                            1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                            must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                            5452 Pb(ZrTi)O3 or PZT

                            PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                            The phase diagram of PZT is shown below

                            Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                            The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                            lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                            few poling directions available making it a useful piezoelectric

                            Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                            546 Measurement of Piezoelectric Properties

                            Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                            In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                            Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                            The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                            (535)

                            Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                            (536)

                            Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                            One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                            547 Applications of Piezoelectric Ceramics

                            Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                            5471 Power Generation

                            Gas Lighter

                            Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                            Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                            One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                            Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                            Power Transformer

                            A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                            An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                            Figure 526 Schematic of a piezoelectrictransformer

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                            Module 5 Special Dielectrics Piezoelectric Ceramics

                            5472 Piezoelectric Sensors

                            Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                            Other sensor applications are

                            Detection and generation of sonar waves

                            To detect detonation in automotive engine by sampling the vibrations of the engine block

                            To detect the precise moment of fuel injection in an automotive engine

                            Detection of acoustic emissions in acoustic emission testing

                            Microbalances as very sensitive chemical and biological sensors

                            Strain gauges

                            Medical applications using ultrasound waves

                            Kidney stone treatment

                            In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                            Figure 527 Ultrasonic waves creation and

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                            kidney stone treatment and ultrasound imagingof the fetus

                            (Courtesy copy DoITPoMS University of Cambridge)

                            5473 Ultrasound Imaging Using Transduction Effect

                            Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                            55 Pyroelectric Ceramics

                            Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                            Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                            Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                            551 Difference between Pyroelectric and Ferroelectric Material

                            Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                            Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                            552 Theory of Piezoelectric Materials

                            From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                            (537)

                            Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                            Assuming electric field E as constant differentiating the above equation with temperature leads to

                            (538)

                            Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                            we write

                            Δ OR

                            Δ (539)

                            Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                            Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                            (540)

                            The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                            As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                            553 Measurement of Pyroelectric Coefficient

                            One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                            (541)

                            Where Ip is the pyrocurrent and is given as

                            (542)

                            where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                            respectively

                            Figure 530 Circuit for measuring pyroelectriccoefficient

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                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                            554 Direct and Indirect Effect

                            Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                            Since change in the polarization can also be expressed as depending

                            upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                            Figure 531 Direct-Indirect effect animation

                            (Courtesy copy DoITPoMS University of Cambridge)

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                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                            555 Common Pyroelectric Materials

                            Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                            The most common materials are tabulated below

                            Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                            LiTaO3 single crystal Hexagonal 665 -230

                            075Pb(Mg13-Nb23)O3-025PbTiO3

                            (PMN-PT) Ceramic

                            Perovskite 150 -1300

                            Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                            Triglycine sulphate

                            (NH2CH2COOH)3H2SO4

                            Sulphate 49 -280

                            Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                            5551 Triglycine Sulphate (TGS)

                            High pyroelectric coefficient

                            Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                            Can be modified to withstand temperatures above Curie point without depoling

                            Used in thermal imaging cameras

                            5552 Polyvinylidene Fluoride (PVDF)

                            Poor pyroelectric coefficient

                            Readily available in large areas of thin film

                            More stable to heat vacuum and moisture than TGS mechanically robust

                            Low heat conductivity and low permittivity

                            High loss tangent

                            Commonly used for burglar alarms

                            5553 Perovskite Ferroelectric Ceramics

                            Generally robust and insensitive to moisture and vacuum

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                            High pyroelectric coefficient and low loss

                            Better operation near TC

                            Strong dependence on composition

                            As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                            RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                            556 Common Applications

                            5561 Burglar Alarms

                            Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                            Figure 532 Working of an IR intruder alarm

                            (Courtesy copy DoITPoMS University ofCambridge)

                            5562 Infrared or Thermal Imaging

                            Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                            The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                            A typical photograph generated from IR imaging looks like this

                            Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                            Here is a simple explanation of how IT imaging using pyroelectrics works

                            A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                            This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                            Figure 534 Process of imagecreation

                            5563 Pollutant Control

                            The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                            Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                            Figure 535 Gas detection using a pyroelectricdetector

                            (Courtesy copy DoITPoMS University of Cambridge)

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                            Module 5 Nonlinear Dielectrics

                            Summary

                            Summary

                            Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                              Figure 58 Effect of temperature on polarization andreciprocal susceptibility for a second order phasetransformation

                              This transition is also depicted by a discontinuity in specific heat at transition which is estimated byusing P = 0 at T gt T0 while using value given by (515) for T lt T0

                              (523)

                              Now substituting in (523) yields

                              (524)

                              Examples of ferroelectric materials showing a second order transition are materials like Rochelle saltand KH2PO4

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                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                              536 Case ndash II First Order Transition

                              Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

                              now more than T0 This gives rise to the following free energy vs polarization plot

                              Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

                              The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

                              is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

                              Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

                              In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

                              free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

                              (525)

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                              On the other hand field E must also be zero for the polarization to be spontaneous ie

                              (526)

                              The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                              (527)

                              and

                              (528)

                              The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                              heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                              temperature higher than Tc the sample will be in paraelectric state This results in thermal

                              hysteresis when these materials are thermally cycled across Tc

                              If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                              Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                              Solid State Physics AJ Dekker Macmillan Publishing

                              Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                              537 Ferroelectric Domains

                              In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                              Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                              The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                              directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                              or 90deg domain walls

                              Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                              Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                              depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                              Now the question is Why is there a domain wall

                              The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                              associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                              splitting of the material into oppositely oriented domains or

                              compensation of the electrical charge via electrical conduction through the crystal

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                              Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                              by transmission electron microscopy

                              Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                              538 Analytical treatment of domain wall energy

                              Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                              (529)

                              where Uc effect of applied field on the domain energy

                              Up and Ux bulk electrical and elastic energies

                              Ud depolarization energy and

                              Uw domain energy

                              Ud is the energy related to the internal field set up in the crystal by the polarization and not

                              compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                              (530)

                              Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                              is the polarization at the center of the domain

                              Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                              width (d) and crystal volume (V) and is given as

                              (531)

                              To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                              in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                              wrt domain wall thickness d ie dΔGdd = 0 resulting in

                              (532)

                              Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                              539 Ferroelectric Switching and Domains

                              Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                              At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                              Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                              If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                              microCcm2and E is electric field across the sample in Vcm The process is something like this

                              Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                              Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                              reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                              polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                              Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                              of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                              Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                              Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

                              >

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                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                              5310 Measurement of Hysteresis Loop

                              Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                              The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                              crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                              This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                              and coercive field Ec

                              A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                              Figure 5 15 Schematic representation of sawyer-tower circuit

                              Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                              5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                              Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                              atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                              Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                              Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                              a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                              Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                              becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                              positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                              The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                              Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                              Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                              spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                              BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                              orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                              5312 Applications of Ferroelectrics

                              In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                              Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                              (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                              Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                              where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                              53121 Nonvolatile Memories

                              Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                              two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                              Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                              53122 Camera Flashes

                              In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                              Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                              Module 5 Nonlinear Dielectrics

                              Summary

                              Summary

                              In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                              can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                              and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                              binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                              One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                              5474 Actuators

                              In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                              In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                              You can have it in two forms

                              Direct Piezo Actuators with strokes lower than 100 microns or so and

                              Amplified Piezoelectric Actuators which can yield millimeter long strokes

                              Some of the examples of applications are

                              Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                              Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                              Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                              Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                              In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                              As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                              5475 Frequency Standards

                              Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                              Quartz clocks

                              Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                              Module 5 Nonlinear Dielectrics

                              Summary

                              Summary

                              Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                              54 Piezoelectric Ceramics

                              Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                              Pb(ZrTi)O3)

                              An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                              For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                              541 Direct Piezoelectric Effect

                              Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                              (533)

                              where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                              542 Reverse or Converse Piezoelectric Effect

                              The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                              (534)

                              where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                              Figure 520 Direct and Converse PiezoelectricEffects

                              The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                              543 Poling of Piezoelectric Materials

                              As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                              The values of piezoelectric coefficient of some materials are given below

                              Material Piezoelectric Constant d(pmV)

                              Quartz 23

                              Barium Titanate 100-149

                              Lead Niobate 80-85

                              Lead zirconate titanate 250-365

                              So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                              Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                              field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                              Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                              544 Depolarization of Piezoelectrics

                              Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                              polarization or rather result in alignment of dipoles gets lost

                              Figure 522 Animation on depolarization offerroelectrics

                              (Courtesy copy DoITPoMS University of Cambridge)

                              >

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                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                              545 Common PIezoelectric Materials

                              5451 Barium Titanate (BaTiO3)

                              This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                              used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                              Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                              1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                              must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                              5452 Pb(ZrTi)O3 or PZT

                              PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                              The phase diagram of PZT is shown below

                              Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                              The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                              lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                              few poling directions available making it a useful piezoelectric

                              Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                              546 Measurement of Piezoelectric Properties

                              Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                              In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                              Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                              The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                              (535)

                              Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                              (536)

                              Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                              One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                              547 Applications of Piezoelectric Ceramics

                              Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                              5471 Power Generation

                              Gas Lighter

                              Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                              Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                              One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                              Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                              Power Transformer

                              A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                              An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                              Figure 526 Schematic of a piezoelectrictransformer

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                              Module 5 Special Dielectrics Piezoelectric Ceramics

                              5472 Piezoelectric Sensors

                              Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                              Other sensor applications are

                              Detection and generation of sonar waves

                              To detect detonation in automotive engine by sampling the vibrations of the engine block

                              To detect the precise moment of fuel injection in an automotive engine

                              Detection of acoustic emissions in acoustic emission testing

                              Microbalances as very sensitive chemical and biological sensors

                              Strain gauges

                              Medical applications using ultrasound waves

                              Kidney stone treatment

                              In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                              Figure 527 Ultrasonic waves creation and

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                              kidney stone treatment and ultrasound imagingof the fetus

                              (Courtesy copy DoITPoMS University of Cambridge)

                              5473 Ultrasound Imaging Using Transduction Effect

                              Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                              55 Pyroelectric Ceramics

                              Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                              Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                              Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                              551 Difference between Pyroelectric and Ferroelectric Material

                              Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                              Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                              552 Theory of Piezoelectric Materials

                              From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                              (537)

                              Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                              Assuming electric field E as constant differentiating the above equation with temperature leads to

                              (538)

                              Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                              we write

                              Δ OR

                              Δ (539)

                              Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                              Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                              (540)

                              The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                              As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                              553 Measurement of Pyroelectric Coefficient

                              One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                              (541)

                              Where Ip is the pyrocurrent and is given as

                              (542)

                              where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                              respectively

                              Figure 530 Circuit for measuring pyroelectriccoefficient

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                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                              554 Direct and Indirect Effect

                              Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                              Since change in the polarization can also be expressed as depending

                              upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                              Figure 531 Direct-Indirect effect animation

                              (Courtesy copy DoITPoMS University of Cambridge)

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                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                              555 Common Pyroelectric Materials

                              Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                              The most common materials are tabulated below

                              Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                              LiTaO3 single crystal Hexagonal 665 -230

                              075Pb(Mg13-Nb23)O3-025PbTiO3

                              (PMN-PT) Ceramic

                              Perovskite 150 -1300

                              Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                              Triglycine sulphate

                              (NH2CH2COOH)3H2SO4

                              Sulphate 49 -280

                              Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                              5551 Triglycine Sulphate (TGS)

                              High pyroelectric coefficient

                              Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                              Can be modified to withstand temperatures above Curie point without depoling

                              Used in thermal imaging cameras

                              5552 Polyvinylidene Fluoride (PVDF)

                              Poor pyroelectric coefficient

                              Readily available in large areas of thin film

                              More stable to heat vacuum and moisture than TGS mechanically robust

                              Low heat conductivity and low permittivity

                              High loss tangent

                              Commonly used for burglar alarms

                              5553 Perovskite Ferroelectric Ceramics

                              Generally robust and insensitive to moisture and vacuum

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                              High pyroelectric coefficient and low loss

                              Better operation near TC

                              Strong dependence on composition

                              As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                              RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                              556 Common Applications

                              5561 Burglar Alarms

                              Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                              Figure 532 Working of an IR intruder alarm

                              (Courtesy copy DoITPoMS University ofCambridge)

                              5562 Infrared or Thermal Imaging

                              Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                              The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                              A typical photograph generated from IR imaging looks like this

                              Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                              Here is a simple explanation of how IT imaging using pyroelectrics works

                              A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                              This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                              Figure 534 Process of imagecreation

                              5563 Pollutant Control

                              The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                              Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                              Figure 535 Gas detection using a pyroelectricdetector

                              (Courtesy copy DoITPoMS University of Cambridge)

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                              Module 5 Nonlinear Dielectrics

                              Summary

                              Summary

                              Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                536 Case ndash II First Order Transition

                                Another situation to consider is that when a lt 0 b lt 0 but c gt 0 What this means is that freeenergy vs polarization plot has three equal minima one for P = 0 and the other two for P ne 0 at thesame temperature ie at the same value of lsquoarsquo at a temperature T = T0 Curie temperature which is

                                now more than T0 This gives rise to the following free energy vs polarization plot

                                Figure 59 Free energy vs polarizationschematic plot for a first order phasetransition

                                The most important feature of this phase transition is that polarization ie the order parameterdrops from P ne 0 to zero discontinuously at T = Tc and is called as first order phase transition This

                                is also very clearly demonstrated by a discontinuity in the reciprocal of dielectric susceptibility asseen below For example solid-liquid phase transition is a first order phase transition while amongvarious ferroelectrics barium titanate is a fine example of first order transition amongferroelectrics

                                Figure 510 Polarization and reciprocalsusceptibility plot for a first order phasetransition

                                In order to compute the non-zero polarization (P0) and susceptibility at the transition the value of

                                free energy (513) for P = 0 and P = P0 must be equal at T = Tc ie

                                (525)

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                                On the other hand field E must also be zero for the polarization to be spontaneous ie

                                (526)

                                The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                                (527)

                                and

                                (528)

                                The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                                heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                                temperature higher than Tc the sample will be in paraelectric state This results in thermal

                                hysteresis when these materials are thermally cycled across Tc

                                If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                                Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                                Solid State Physics AJ Dekker Macmillan Publishing

                                Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                537 Ferroelectric Domains

                                In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                                Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                                The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                                directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                                or 90deg domain walls

                                Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                                Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                                depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                                Now the question is Why is there a domain wall

                                The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                                associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                                splitting of the material into oppositely oriented domains or

                                compensation of the electrical charge via electrical conduction through the crystal

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                                Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                                by transmission electron microscopy

                                Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                538 Analytical treatment of domain wall energy

                                Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                                (529)

                                where Uc effect of applied field on the domain energy

                                Up and Ux bulk electrical and elastic energies

                                Ud depolarization energy and

                                Uw domain energy

                                Ud is the energy related to the internal field set up in the crystal by the polarization and not

                                compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                                (530)

                                Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                                is the polarization at the center of the domain

                                Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                                width (d) and crystal volume (V) and is given as

                                (531)

                                To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                                in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                                wrt domain wall thickness d ie dΔGdd = 0 resulting in

                                (532)

                                Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                539 Ferroelectric Switching and Domains

                                Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                                At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                                Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                                If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                                microCcm2and E is electric field across the sample in Vcm The process is something like this

                                Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                                Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                                reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                                polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                                Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                                of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                                Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                                Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                5310 Measurement of Hysteresis Loop

                                Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                                The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                                crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                                This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                                and coercive field Ec

                                A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                                Figure 5 15 Schematic representation of sawyer-tower circuit

                                Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                                Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                                atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                                Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                                Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                                a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                                Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                                becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                                positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                                The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                                Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                5312 Applications of Ferroelectrics

                                In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                53121 Nonvolatile Memories

                                Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                53122 Camera Flashes

                                In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                Module 5 Nonlinear Dielectrics

                                Summary

                                Summary

                                In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                5474 Actuators

                                In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                You can have it in two forms

                                Direct Piezo Actuators with strokes lower than 100 microns or so and

                                Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                Some of the examples of applications are

                                Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                5475 Frequency Standards

                                Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                Quartz clocks

                                Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                Module 5 Nonlinear Dielectrics

                                Summary

                                Summary

                                Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                54 Piezoelectric Ceramics

                                Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                Pb(ZrTi)O3)

                                An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                541 Direct Piezoelectric Effect

                                Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                (533)

                                where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                542 Reverse or Converse Piezoelectric Effect

                                The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                (534)

                                where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                Figure 520 Direct and Converse PiezoelectricEffects

                                The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                543 Poling of Piezoelectric Materials

                                As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                The values of piezoelectric coefficient of some materials are given below

                                Material Piezoelectric Constant d(pmV)

                                Quartz 23

                                Barium Titanate 100-149

                                Lead Niobate 80-85

                                Lead zirconate titanate 250-365

                                So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                544 Depolarization of Piezoelectrics

                                Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                polarization or rather result in alignment of dipoles gets lost

                                Figure 522 Animation on depolarization offerroelectrics

                                (Courtesy copy DoITPoMS University of Cambridge)

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                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                545 Common PIezoelectric Materials

                                5451 Barium Titanate (BaTiO3)

                                This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                5452 Pb(ZrTi)O3 or PZT

                                PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                The phase diagram of PZT is shown below

                                Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                few poling directions available making it a useful piezoelectric

                                Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                546 Measurement of Piezoelectric Properties

                                Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                (535)

                                Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                (536)

                                Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                547 Applications of Piezoelectric Ceramics

                                Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                5471 Power Generation

                                Gas Lighter

                                Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                Power Transformer

                                A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                Figure 526 Schematic of a piezoelectrictransformer

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                                Module 5 Special Dielectrics Piezoelectric Ceramics

                                5472 Piezoelectric Sensors

                                Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                Other sensor applications are

                                Detection and generation of sonar waves

                                To detect detonation in automotive engine by sampling the vibrations of the engine block

                                To detect the precise moment of fuel injection in an automotive engine

                                Detection of acoustic emissions in acoustic emission testing

                                Microbalances as very sensitive chemical and biological sensors

                                Strain gauges

                                Medical applications using ultrasound waves

                                Kidney stone treatment

                                In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                Figure 527 Ultrasonic waves creation and

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                                kidney stone treatment and ultrasound imagingof the fetus

                                (Courtesy copy DoITPoMS University of Cambridge)

                                5473 Ultrasound Imaging Using Transduction Effect

                                Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                55 Pyroelectric Ceramics

                                Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                551 Difference between Pyroelectric and Ferroelectric Material

                                Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                552 Theory of Piezoelectric Materials

                                From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                (537)

                                Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                Assuming electric field E as constant differentiating the above equation with temperature leads to

                                (538)

                                Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                we write

                                Δ OR

                                Δ (539)

                                Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                (540)

                                The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                553 Measurement of Pyroelectric Coefficient

                                One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                (541)

                                Where Ip is the pyrocurrent and is given as

                                (542)

                                where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                respectively

                                Figure 530 Circuit for measuring pyroelectriccoefficient

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                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                554 Direct and Indirect Effect

                                Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                Since change in the polarization can also be expressed as depending

                                upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                Figure 531 Direct-Indirect effect animation

                                (Courtesy copy DoITPoMS University of Cambridge)

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                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                555 Common Pyroelectric Materials

                                Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                The most common materials are tabulated below

                                Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                LiTaO3 single crystal Hexagonal 665 -230

                                075Pb(Mg13-Nb23)O3-025PbTiO3

                                (PMN-PT) Ceramic

                                Perovskite 150 -1300

                                Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                Triglycine sulphate

                                (NH2CH2COOH)3H2SO4

                                Sulphate 49 -280

                                Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                5551 Triglycine Sulphate (TGS)

                                High pyroelectric coefficient

                                Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                Can be modified to withstand temperatures above Curie point without depoling

                                Used in thermal imaging cameras

                                5552 Polyvinylidene Fluoride (PVDF)

                                Poor pyroelectric coefficient

                                Readily available in large areas of thin film

                                More stable to heat vacuum and moisture than TGS mechanically robust

                                Low heat conductivity and low permittivity

                                High loss tangent

                                Commonly used for burglar alarms

                                5553 Perovskite Ferroelectric Ceramics

                                Generally robust and insensitive to moisture and vacuum

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                                High pyroelectric coefficient and low loss

                                Better operation near TC

                                Strong dependence on composition

                                As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                556 Common Applications

                                5561 Burglar Alarms

                                Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                Figure 532 Working of an IR intruder alarm

                                (Courtesy copy DoITPoMS University ofCambridge)

                                5562 Infrared or Thermal Imaging

                                Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                >

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                                A typical photograph generated from IR imaging looks like this

                                Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                Here is a simple explanation of how IT imaging using pyroelectrics works

                                A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                Figure 534 Process of imagecreation

                                5563 Pollutant Control

                                The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                Figure 535 Gas detection using a pyroelectricdetector

                                (Courtesy copy DoITPoMS University of Cambridge)

                                >

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                                Module 5 Nonlinear Dielectrics

                                Summary

                                Summary

                                Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                  On the other hand field E must also be zero for the polarization to be spontaneous ie

                                  (526)

                                  The polarization and susceptibility at Tc are obtained by solving two equations and are given as

                                  (527)

                                  and

                                  (528)

                                  The fact that there are three minima at T=Tc is reflected in whether the Tc is approached while

                                  heating or cooling More specifically the material will be in other of the two non-zero polarizationstates if is heated from an initial temperature that is lower than Tc whereas if it is cooled from a

                                  temperature higher than Tc the sample will be in paraelectric state This results in thermal

                                  hysteresis when these materials are thermally cycled across Tc

                                  If you are interested in further reading about the phase transitions in ferroelectrics refer to thefollowing texts

                                  Principles and Applications of Ferroelectrics and Related Materials M Linesand A Glass Clarendon Press Oxford

                                  Solid State Physics AJ Dekker Macmillan Publishing

                                  Ferroelectric Crystals F Jona and G Shirane Dover Publishing

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                                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                  537 Ferroelectric Domains

                                  In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                                  Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                                  The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                                  directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                                  or 90deg domain walls

                                  Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                                  Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                                  depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                                  Now the question is Why is there a domain wall

                                  The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                                  associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                                  splitting of the material into oppositely oriented domains or

                                  compensation of the electrical charge via electrical conduction through the crystal

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                                  Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                                  by transmission electron microscopy

                                  Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                  538 Analytical treatment of domain wall energy

                                  Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                                  (529)

                                  where Uc effect of applied field on the domain energy

                                  Up and Ux bulk electrical and elastic energies

                                  Ud depolarization energy and

                                  Uw domain energy

                                  Ud is the energy related to the internal field set up in the crystal by the polarization and not

                                  compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                                  (530)

                                  Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                                  is the polarization at the center of the domain

                                  Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                                  width (d) and crystal volume (V) and is given as

                                  (531)

                                  To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                                  in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                                  wrt domain wall thickness d ie dΔGdd = 0 resulting in

                                  (532)

                                  Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                  539 Ferroelectric Switching and Domains

                                  Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                                  At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                                  Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                                  If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                                  microCcm2and E is electric field across the sample in Vcm The process is something like this

                                  Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                                  Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                                  reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                                  polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                                  Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                                  of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                                  Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                                  Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                  5310 Measurement of Hysteresis Loop

                                  Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                                  The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                                  crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                                  This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                                  and coercive field Ec

                                  A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                                  Figure 5 15 Schematic representation of sawyer-tower circuit

                                  Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                  5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                                  Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                                  atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                                  Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                                  Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                                  a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                                  Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                                  becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                                  positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                                  The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                                  Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                  Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                  spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                  BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                  orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                  5312 Applications of Ferroelectrics

                                  In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                  Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                  (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                  Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                  where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                  53121 Nonvolatile Memories

                                  Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                  two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                  Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                  53122 Camera Flashes

                                  In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                  Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                  Module 5 Nonlinear Dielectrics

                                  Summary

                                  Summary

                                  In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                  can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                  and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                  binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                  One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                  5474 Actuators

                                  In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                  In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                  You can have it in two forms

                                  Direct Piezo Actuators with strokes lower than 100 microns or so and

                                  Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                  Some of the examples of applications are

                                  Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                  Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                  Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                  Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                  In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                  As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                  5475 Frequency Standards

                                  Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                  Quartz clocks

                                  Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                  Module 5 Nonlinear Dielectrics

                                  Summary

                                  Summary

                                  Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                  54 Piezoelectric Ceramics

                                  Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                  Pb(ZrTi)O3)

                                  An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                  For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                  541 Direct Piezoelectric Effect

                                  Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                  (533)

                                  where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                  542 Reverse or Converse Piezoelectric Effect

                                  The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                  (534)

                                  where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                  Figure 520 Direct and Converse PiezoelectricEffects

                                  The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                  543 Poling of Piezoelectric Materials

                                  As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                  The values of piezoelectric coefficient of some materials are given below

                                  Material Piezoelectric Constant d(pmV)

                                  Quartz 23

                                  Barium Titanate 100-149

                                  Lead Niobate 80-85

                                  Lead zirconate titanate 250-365

                                  So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                  Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                  field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                  Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                  544 Depolarization of Piezoelectrics

                                  Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                  polarization or rather result in alignment of dipoles gets lost

                                  Figure 522 Animation on depolarization offerroelectrics

                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                  545 Common PIezoelectric Materials

                                  5451 Barium Titanate (BaTiO3)

                                  This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                  used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                  Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                  1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                  must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                  5452 Pb(ZrTi)O3 or PZT

                                  PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                  The phase diagram of PZT is shown below

                                  Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                  The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                  lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                  few poling directions available making it a useful piezoelectric

                                  Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                  546 Measurement of Piezoelectric Properties

                                  Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                  In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                  Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                  The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                  (535)

                                  Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                  (536)

                                  Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                  One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                  547 Applications of Piezoelectric Ceramics

                                  Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                  5471 Power Generation

                                  Gas Lighter

                                  Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                  Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                  One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                  Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                  Power Transformer

                                  A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                  An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                  Figure 526 Schematic of a piezoelectrictransformer

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                                  Module 5 Special Dielectrics Piezoelectric Ceramics

                                  5472 Piezoelectric Sensors

                                  Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                  Other sensor applications are

                                  Detection and generation of sonar waves

                                  To detect detonation in automotive engine by sampling the vibrations of the engine block

                                  To detect the precise moment of fuel injection in an automotive engine

                                  Detection of acoustic emissions in acoustic emission testing

                                  Microbalances as very sensitive chemical and biological sensors

                                  Strain gauges

                                  Medical applications using ultrasound waves

                                  Kidney stone treatment

                                  In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                  Figure 527 Ultrasonic waves creation and

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                                  kidney stone treatment and ultrasound imagingof the fetus

                                  (Courtesy copy DoITPoMS University of Cambridge)

                                  5473 Ultrasound Imaging Using Transduction Effect

                                  Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                  55 Pyroelectric Ceramics

                                  Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                  Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                  Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                  551 Difference between Pyroelectric and Ferroelectric Material

                                  Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                  Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                  552 Theory of Piezoelectric Materials

                                  From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                  (537)

                                  Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                  Assuming electric field E as constant differentiating the above equation with temperature leads to

                                  (538)

                                  Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                  we write

                                  Δ OR

                                  Δ (539)

                                  Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                  Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                  (540)

                                  The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                  As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                  553 Measurement of Pyroelectric Coefficient

                                  One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                  (541)

                                  Where Ip is the pyrocurrent and is given as

                                  (542)

                                  where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                  respectively

                                  Figure 530 Circuit for measuring pyroelectriccoefficient

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                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                  554 Direct and Indirect Effect

                                  Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                  Since change in the polarization can also be expressed as depending

                                  upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                  Figure 531 Direct-Indirect effect animation

                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                  555 Common Pyroelectric Materials

                                  Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                  The most common materials are tabulated below

                                  Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                  LiTaO3 single crystal Hexagonal 665 -230

                                  075Pb(Mg13-Nb23)O3-025PbTiO3

                                  (PMN-PT) Ceramic

                                  Perovskite 150 -1300

                                  Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                  Triglycine sulphate

                                  (NH2CH2COOH)3H2SO4

                                  Sulphate 49 -280

                                  Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                  5551 Triglycine Sulphate (TGS)

                                  High pyroelectric coefficient

                                  Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                  Can be modified to withstand temperatures above Curie point without depoling

                                  Used in thermal imaging cameras

                                  5552 Polyvinylidene Fluoride (PVDF)

                                  Poor pyroelectric coefficient

                                  Readily available in large areas of thin film

                                  More stable to heat vacuum and moisture than TGS mechanically robust

                                  Low heat conductivity and low permittivity

                                  High loss tangent

                                  Commonly used for burglar alarms

                                  5553 Perovskite Ferroelectric Ceramics

                                  Generally robust and insensitive to moisture and vacuum

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                                  High pyroelectric coefficient and low loss

                                  Better operation near TC

                                  Strong dependence on composition

                                  As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                  RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                  556 Common Applications

                                  5561 Burglar Alarms

                                  Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                  Figure 532 Working of an IR intruder alarm

                                  (Courtesy copy DoITPoMS University ofCambridge)

                                  5562 Infrared or Thermal Imaging

                                  Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                  The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                  A typical photograph generated from IR imaging looks like this

                                  Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                  Here is a simple explanation of how IT imaging using pyroelectrics works

                                  A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                  This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                  Figure 534 Process of imagecreation

                                  5563 Pollutant Control

                                  The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                  Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                  Figure 535 Gas detection using a pyroelectricdetector

                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                  Module 5 Nonlinear Dielectrics

                                  Summary

                                  Summary

                                  Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                    537 Ferroelectric Domains

                                    In a ferroelectric crystal it is likely that the alignment of dipoles in one of the polar directionsextends only over a region of the crystal and there can be different regions in the crystal withaligned dipoles which are oriented in many different directions with respect to one another

                                    Regions of uniform polarization are called domains separated by a boundary called domain wall You should not confuse ferroelectric domain walls with the grain boundaries Depending upon thegrain size one grain can have more than one or more domains

                                    The types of domain walls that can occur in a ferroelectric crystal depend upon the crystal structureand symmetry of both paraelectric and ferroelectric phases For instance rhombohedral phase oflead zirconate titanate Pb(ZrTi)O3 has Ps vector along [111]-direction which gives eight possible

                                    directions of spontaneous polarization with 180o 71o and 109o domain walls On the other hand atetragonal perovskite like PbTiO3 has Ps along the [001]-axis and here domain walls are either 180deg

                                    or 90deg domain walls

                                    Figure 5 11 Schematic representation of a 180deg and 90degdomain walls in a tetragonal perovskite crystal such as BaTiO3

                                    Formation of the domains may also be the result of mechanical constraints associated with thestresses created by the ferroelectric phase transition eg from cubic paraelectric phase to tetragonalparaelectric phase in PbTiO3 Both 180deg and 90deg domains minimize the energy associated with the

                                    depolarizing field but elastic energy is minimized only by the formation of 90deg domains Combinationof both effects leads to a complex domain structure in the material with both 90deg and 180deg domainwalls

                                    Now the question is Why is there a domain wall

                                    The driving force for the formation of domain walls is the minimization of the electrostatic energy ofthe depolarizing field (Ed) due to surface charges due to polarization and the elastic energy

                                    associated with the mechanical constraints arising due to ferroelectric-paraelectric phase transitionThis electrostatic energy associated with the depolarizing field can be minimized by

                                    splitting of the material into oppositely oriented domains or

                                    compensation of the electrical charge via electrical conduction through the crystal

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                                    Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                                    by transmission electron microscopy

                                    Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                    538 Analytical treatment of domain wall energy

                                    Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                                    (529)

                                    where Uc effect of applied field on the domain energy

                                    Up and Ux bulk electrical and elastic energies

                                    Ud depolarization energy and

                                    Uw domain energy

                                    Ud is the energy related to the internal field set up in the crystal by the polarization and not

                                    compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                                    (530)

                                    Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                                    is the polarization at the center of the domain

                                    Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                                    width (d) and crystal volume (V) and is given as

                                    (531)

                                    To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                                    in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                                    wrt domain wall thickness d ie dΔGdd = 0 resulting in

                                    (532)

                                    Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                    539 Ferroelectric Switching and Domains

                                    Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                                    At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                                    Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                                    If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                                    microCcm2and E is electric field across the sample in Vcm The process is something like this

                                    Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                                    Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                                    reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                                    polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                                    Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                                    of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                                    Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                                    Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                    5310 Measurement of Hysteresis Loop

                                    Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                                    The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                                    crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                                    This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                                    and coercive field Ec

                                    A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                                    Figure 5 15 Schematic representation of sawyer-tower circuit

                                    Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                    5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                                    Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                                    atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                                    Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                                    Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                                    a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                                    Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                                    becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                                    positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                                    The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                                    Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                    Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                    spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                    BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                    orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                    5312 Applications of Ferroelectrics

                                    In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                    Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                    (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                    Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                    where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                    53121 Nonvolatile Memories

                                    Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                    two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                    Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                    53122 Camera Flashes

                                    In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                    Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                    Module 5 Nonlinear Dielectrics

                                    Summary

                                    Summary

                                    In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                    can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                    and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                    binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                    One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                    5474 Actuators

                                    In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                    In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                    You can have it in two forms

                                    Direct Piezo Actuators with strokes lower than 100 microns or so and

                                    Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                    Some of the examples of applications are

                                    Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                    Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                    Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                    Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                    In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                    As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                    5475 Frequency Standards

                                    Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                    Quartz clocks

                                    Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                    Module 5 Nonlinear Dielectrics

                                    Summary

                                    Summary

                                    Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                    54 Piezoelectric Ceramics

                                    Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                    Pb(ZrTi)O3)

                                    An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                    For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                    541 Direct Piezoelectric Effect

                                    Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                    (533)

                                    where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                    542 Reverse or Converse Piezoelectric Effect

                                    The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                    (534)

                                    where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                    Figure 520 Direct and Converse PiezoelectricEffects

                                    The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                    543 Poling of Piezoelectric Materials

                                    As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                    The values of piezoelectric coefficient of some materials are given below

                                    Material Piezoelectric Constant d(pmV)

                                    Quartz 23

                                    Barium Titanate 100-149

                                    Lead Niobate 80-85

                                    Lead zirconate titanate 250-365

                                    So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                    Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                    field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                    Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                    544 Depolarization of Piezoelectrics

                                    Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                    polarization or rather result in alignment of dipoles gets lost

                                    Figure 522 Animation on depolarization offerroelectrics

                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                    545 Common PIezoelectric Materials

                                    5451 Barium Titanate (BaTiO3)

                                    This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                    used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                    Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                    1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                    must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                    5452 Pb(ZrTi)O3 or PZT

                                    PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                    The phase diagram of PZT is shown below

                                    Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                    The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                    lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                    few poling directions available making it a useful piezoelectric

                                    Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                    546 Measurement of Piezoelectric Properties

                                    Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                    In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                    Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                    The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                    (535)

                                    Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                    (536)

                                    Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                    One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                    547 Applications of Piezoelectric Ceramics

                                    Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                    5471 Power Generation

                                    Gas Lighter

                                    Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                    Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                    One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                    Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                    Power Transformer

                                    A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                    An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                    Figure 526 Schematic of a piezoelectrictransformer

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                                    Module 5 Special Dielectrics Piezoelectric Ceramics

                                    5472 Piezoelectric Sensors

                                    Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                    Other sensor applications are

                                    Detection and generation of sonar waves

                                    To detect detonation in automotive engine by sampling the vibrations of the engine block

                                    To detect the precise moment of fuel injection in an automotive engine

                                    Detection of acoustic emissions in acoustic emission testing

                                    Microbalances as very sensitive chemical and biological sensors

                                    Strain gauges

                                    Medical applications using ultrasound waves

                                    Kidney stone treatment

                                    In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                    Figure 527 Ultrasonic waves creation and

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                                    kidney stone treatment and ultrasound imagingof the fetus

                                    (Courtesy copy DoITPoMS University of Cambridge)

                                    5473 Ultrasound Imaging Using Transduction Effect

                                    Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                    55 Pyroelectric Ceramics

                                    Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                    Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                    Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                    551 Difference between Pyroelectric and Ferroelectric Material

                                    Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                    Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                    552 Theory of Piezoelectric Materials

                                    From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                    (537)

                                    Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                    Assuming electric field E as constant differentiating the above equation with temperature leads to

                                    (538)

                                    Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                    we write

                                    Δ OR

                                    Δ (539)

                                    Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                    Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                    (540)

                                    The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                    As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                    553 Measurement of Pyroelectric Coefficient

                                    One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                    (541)

                                    Where Ip is the pyrocurrent and is given as

                                    (542)

                                    where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                    respectively

                                    Figure 530 Circuit for measuring pyroelectriccoefficient

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                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                    554 Direct and Indirect Effect

                                    Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                    Since change in the polarization can also be expressed as depending

                                    upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                    Figure 531 Direct-Indirect effect animation

                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                    555 Common Pyroelectric Materials

                                    Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                    The most common materials are tabulated below

                                    Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                    LiTaO3 single crystal Hexagonal 665 -230

                                    075Pb(Mg13-Nb23)O3-025PbTiO3

                                    (PMN-PT) Ceramic

                                    Perovskite 150 -1300

                                    Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                    Triglycine sulphate

                                    (NH2CH2COOH)3H2SO4

                                    Sulphate 49 -280

                                    Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                    5551 Triglycine Sulphate (TGS)

                                    High pyroelectric coefficient

                                    Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                    Can be modified to withstand temperatures above Curie point without depoling

                                    Used in thermal imaging cameras

                                    5552 Polyvinylidene Fluoride (PVDF)

                                    Poor pyroelectric coefficient

                                    Readily available in large areas of thin film

                                    More stable to heat vacuum and moisture than TGS mechanically robust

                                    Low heat conductivity and low permittivity

                                    High loss tangent

                                    Commonly used for burglar alarms

                                    5553 Perovskite Ferroelectric Ceramics

                                    Generally robust and insensitive to moisture and vacuum

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                                    High pyroelectric coefficient and low loss

                                    Better operation near TC

                                    Strong dependence on composition

                                    As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                    RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                    556 Common Applications

                                    5561 Burglar Alarms

                                    Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                    Figure 532 Working of an IR intruder alarm

                                    (Courtesy copy DoITPoMS University ofCambridge)

                                    5562 Infrared or Thermal Imaging

                                    Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                    The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                    >

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                                    A typical photograph generated from IR imaging looks like this

                                    Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                    Here is a simple explanation of how IT imaging using pyroelectrics works

                                    A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                    This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                    Figure 534 Process of imagecreation

                                    5563 Pollutant Control

                                    The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                    Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                    Figure 535 Gas detection using a pyroelectricdetector

                                    (Courtesy copy DoITPoMS University of Cambridge)

                                    >

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                                    Module 5 Nonlinear Dielectrics

                                    Summary

                                    Summary

                                    Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                      Domains can also be seen by microscopy The following is an image of domains in BaTiO3 as seen

                                      by transmission electron microscopy

                                      Figure 5 12 Domains in BaTiO3 samples as seen by TEM(Courtesy DoITPoMS Micrograph Library University of Cambridge UK)

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                                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                      538 Analytical treatment of domain wall energy

                                      Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                                      (529)

                                      where Uc effect of applied field on the domain energy

                                      Up and Ux bulk electrical and elastic energies

                                      Ud depolarization energy and

                                      Uw domain energy

                                      Ud is the energy related to the internal field set up in the crystal by the polarization and not

                                      compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                                      (530)

                                      Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                                      is the polarization at the center of the domain

                                      Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                                      width (d) and crystal volume (V) and is given as

                                      (531)

                                      To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                                      in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                                      wrt domain wall thickness d ie dΔGdd = 0 resulting in

                                      (532)

                                      Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                      539 Ferroelectric Switching and Domains

                                      Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                                      At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                                      Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                                      If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                                      microCcm2and E is electric field across the sample in Vcm The process is something like this

                                      Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                                      Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                                      reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                                      polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                                      Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                                      of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                                      Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                                      Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                      5310 Measurement of Hysteresis Loop

                                      Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                                      The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                                      crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                                      This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                                      and coercive field Ec

                                      A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                                      Figure 5 15 Schematic representation of sawyer-tower circuit

                                      Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                      5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                                      Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                                      atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                                      Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                                      Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                                      a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                                      Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                                      becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                                      positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                                      The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                                      Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                      Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                      spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                      BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                      orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                      Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                      5312 Applications of Ferroelectrics

                                      In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                      Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                      (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                      Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                      where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                      53121 Nonvolatile Memories

                                      Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                      two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                      Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                      53122 Camera Flashes

                                      In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                      Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                      Module 5 Nonlinear Dielectrics

                                      Summary

                                      Summary

                                      In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                      can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                      and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                      binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                      One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                      5474 Actuators

                                      In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                      In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                      You can have it in two forms

                                      Direct Piezo Actuators with strokes lower than 100 microns or so and

                                      Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                      Some of the examples of applications are

                                      Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                      Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                      Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                      Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                      In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                      As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                      5475 Frequency Standards

                                      Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                      Quartz clocks

                                      Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                      Module 5 Nonlinear Dielectrics

                                      Summary

                                      Summary

                                      Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                      54 Piezoelectric Ceramics

                                      Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                      Pb(ZrTi)O3)

                                      An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                      For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                      541 Direct Piezoelectric Effect

                                      Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                      (533)

                                      where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                      542 Reverse or Converse Piezoelectric Effect

                                      The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                      (534)

                                      where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                      Figure 520 Direct and Converse PiezoelectricEffects

                                      The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                      543 Poling of Piezoelectric Materials

                                      As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                      The values of piezoelectric coefficient of some materials are given below

                                      Material Piezoelectric Constant d(pmV)

                                      Quartz 23

                                      Barium Titanate 100-149

                                      Lead Niobate 80-85

                                      Lead zirconate titanate 250-365

                                      So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                      Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                      field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                      Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                      544 Depolarization of Piezoelectrics

                                      Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                      polarization or rather result in alignment of dipoles gets lost

                                      Figure 522 Animation on depolarization offerroelectrics

                                      (Courtesy copy DoITPoMS University of Cambridge)

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                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                      545 Common PIezoelectric Materials

                                      5451 Barium Titanate (BaTiO3)

                                      This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                      used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                      Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                      1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                      must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                      5452 Pb(ZrTi)O3 or PZT

                                      PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                      The phase diagram of PZT is shown below

                                      Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                      The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                      lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                      few poling directions available making it a useful piezoelectric

                                      Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                      546 Measurement of Piezoelectric Properties

                                      Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                      In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                      Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                      The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                      (535)

                                      Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                      (536)

                                      Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                      One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                      547 Applications of Piezoelectric Ceramics

                                      Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                      5471 Power Generation

                                      Gas Lighter

                                      Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                      Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                      One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                      Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                      Power Transformer

                                      A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                      An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                      Figure 526 Schematic of a piezoelectrictransformer

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                                      Module 5 Special Dielectrics Piezoelectric Ceramics

                                      5472 Piezoelectric Sensors

                                      Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                      Other sensor applications are

                                      Detection and generation of sonar waves

                                      To detect detonation in automotive engine by sampling the vibrations of the engine block

                                      To detect the precise moment of fuel injection in an automotive engine

                                      Detection of acoustic emissions in acoustic emission testing

                                      Microbalances as very sensitive chemical and biological sensors

                                      Strain gauges

                                      Medical applications using ultrasound waves

                                      Kidney stone treatment

                                      In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                      Figure 527 Ultrasonic waves creation and

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                                      kidney stone treatment and ultrasound imagingof the fetus

                                      (Courtesy copy DoITPoMS University of Cambridge)

                                      5473 Ultrasound Imaging Using Transduction Effect

                                      Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                      55 Pyroelectric Ceramics

                                      Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                      Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                      Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                      551 Difference between Pyroelectric and Ferroelectric Material

                                      Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                      Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                      552 Theory of Piezoelectric Materials

                                      From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                      (537)

                                      Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                      Assuming electric field E as constant differentiating the above equation with temperature leads to

                                      (538)

                                      Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                      we write

                                      Δ OR

                                      Δ (539)

                                      Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                      Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                      (540)

                                      The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                      As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                      553 Measurement of Pyroelectric Coefficient

                                      One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                      (541)

                                      Where Ip is the pyrocurrent and is given as

                                      (542)

                                      where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                      respectively

                                      Figure 530 Circuit for measuring pyroelectriccoefficient

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                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                      554 Direct and Indirect Effect

                                      Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                      Since change in the polarization can also be expressed as depending

                                      upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                      Figure 531 Direct-Indirect effect animation

                                      (Courtesy copy DoITPoMS University of Cambridge)

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                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                      555 Common Pyroelectric Materials

                                      Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                      The most common materials are tabulated below

                                      Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                      LiTaO3 single crystal Hexagonal 665 -230

                                      075Pb(Mg13-Nb23)O3-025PbTiO3

                                      (PMN-PT) Ceramic

                                      Perovskite 150 -1300

                                      Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                      Triglycine sulphate

                                      (NH2CH2COOH)3H2SO4

                                      Sulphate 49 -280

                                      Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                      5551 Triglycine Sulphate (TGS)

                                      High pyroelectric coefficient

                                      Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                      Can be modified to withstand temperatures above Curie point without depoling

                                      Used in thermal imaging cameras

                                      5552 Polyvinylidene Fluoride (PVDF)

                                      Poor pyroelectric coefficient

                                      Readily available in large areas of thin film

                                      More stable to heat vacuum and moisture than TGS mechanically robust

                                      Low heat conductivity and low permittivity

                                      High loss tangent

                                      Commonly used for burglar alarms

                                      5553 Perovskite Ferroelectric Ceramics

                                      Generally robust and insensitive to moisture and vacuum

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                                      High pyroelectric coefficient and low loss

                                      Better operation near TC

                                      Strong dependence on composition

                                      As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                      RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                      556 Common Applications

                                      5561 Burglar Alarms

                                      Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                      Figure 532 Working of an IR intruder alarm

                                      (Courtesy copy DoITPoMS University ofCambridge)

                                      5562 Infrared or Thermal Imaging

                                      Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                      The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                      A typical photograph generated from IR imaging looks like this

                                      Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                      Here is a simple explanation of how IT imaging using pyroelectrics works

                                      A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                      This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                      Figure 534 Process of imagecreation

                                      5563 Pollutant Control

                                      The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                      Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                      Figure 535 Gas detection using a pyroelectricdetector

                                      (Courtesy copy DoITPoMS University of Cambridge)

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                                      Module 5 Nonlinear Dielectrics

                                      Summary

                                      Summary

                                      Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                        538 Analytical treatment of domain wall energy

                                        Ferroelectric domains form as a result of instabilities due to alignment of dipoles in a crystal Thefree energy change involved in the formation of a domain is given as

                                        (529)

                                        where Uc effect of applied field on the domain energy

                                        Up and Ux bulk electrical and elastic energies

                                        Ud depolarization energy and

                                        Uw domain energy

                                        Ud is the energy related to the internal field set up in the crystal by the polarization and not

                                        compensated The internal field opposes the applied field E and hence is called as depolarizingfieldThis is dependent on the domain size (d) and is expressed as

                                        (530)

                                        Here e is a constant determined by the dielectric constant of the material t is crystal thickness P0

                                        is the polarization at the center of the domain

                                        Uw is the domain energy and can be expressed in terms of surface energy of the wall (γ) domain

                                        width (d) and crystal volume (V) and is given as

                                        (531)

                                        To get a stable domain structure this ΔG has to be minimized In (529) Up and Ux are the same

                                        in each domain irrespective of domain thickness and so are independent of domain size and henceare treated as constant Therefore one only needs to consider Uw and Ud when ΔG is minimized

                                        wrt domain wall thickness d ie dΔGdd = 0 resulting in

                                        (532)

                                        Here one can see that domain size is dependent on surface energy crystal thickness andpolarization showing a competition between the surface energy of the wall and polarization(governing the depolarizing field) This shows that larger the surface energy is larger the domainsize is which makes sense because of large energy requirement the interface area needs to besmaller Secondly the larger the polarization is the larger the depolarizing field will be and largewould be the driving force for the domains to form and hence smaller domains will be preferred

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                                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                        539 Ferroelectric Switching and Domains

                                        Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                                        At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                                        Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                                        If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                                        microCcm2and E is electric field across the sample in Vcm The process is something like this

                                        Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                                        Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                                        reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                                        polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                                        Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                                        of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                                        Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                                        Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                        5310 Measurement of Hysteresis Loop

                                        Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                                        The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                                        crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                                        This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                                        and coercive field Ec

                                        A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                                        Figure 5 15 Schematic representation of sawyer-tower circuit

                                        Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                        5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                                        Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                                        atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                                        Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                                        Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                                        a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                                        Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                                        becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                                        positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                                        The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                                        Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                        Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                        spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                        BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                        orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                        Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                        5312 Applications of Ferroelectrics

                                        In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                        Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                        (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                        Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                        where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                        53121 Nonvolatile Memories

                                        Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                        two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                        Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                        53122 Camera Flashes

                                        In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                        Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                        Module 5 Nonlinear Dielectrics

                                        Summary

                                        Summary

                                        In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                        can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                        and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                        binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                        One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                        5474 Actuators

                                        In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                        In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                        You can have it in two forms

                                        Direct Piezo Actuators with strokes lower than 100 microns or so and

                                        Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                        Some of the examples of applications are

                                        Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                        Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                        Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                        Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                        In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                        As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                        5475 Frequency Standards

                                        Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                        Quartz clocks

                                        Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                        Module 5 Nonlinear Dielectrics

                                        Summary

                                        Summary

                                        Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                        54 Piezoelectric Ceramics

                                        Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                        Pb(ZrTi)O3)

                                        An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                        For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                        541 Direct Piezoelectric Effect

                                        Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                        (533)

                                        where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                        542 Reverse or Converse Piezoelectric Effect

                                        The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                        (534)

                                        where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                        Figure 520 Direct and Converse PiezoelectricEffects

                                        The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                        543 Poling of Piezoelectric Materials

                                        As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                        The values of piezoelectric coefficient of some materials are given below

                                        Material Piezoelectric Constant d(pmV)

                                        Quartz 23

                                        Barium Titanate 100-149

                                        Lead Niobate 80-85

                                        Lead zirconate titanate 250-365

                                        So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                        Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                        field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                        Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                        544 Depolarization of Piezoelectrics

                                        Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                        polarization or rather result in alignment of dipoles gets lost

                                        Figure 522 Animation on depolarization offerroelectrics

                                        (Courtesy copy DoITPoMS University of Cambridge)

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                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                        545 Common PIezoelectric Materials

                                        5451 Barium Titanate (BaTiO3)

                                        This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                        used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                        Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                        1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                        must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                        5452 Pb(ZrTi)O3 or PZT

                                        PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                        The phase diagram of PZT is shown below

                                        Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                        The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                        lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                        few poling directions available making it a useful piezoelectric

                                        Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                        546 Measurement of Piezoelectric Properties

                                        Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                        In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                        Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                        The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                        (535)

                                        Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                        (536)

                                        Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                        One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                        547 Applications of Piezoelectric Ceramics

                                        Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                        5471 Power Generation

                                        Gas Lighter

                                        Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                        Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                        One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                        Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                        Power Transformer

                                        A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                        An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                        Figure 526 Schematic of a piezoelectrictransformer

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                                        Module 5 Special Dielectrics Piezoelectric Ceramics

                                        5472 Piezoelectric Sensors

                                        Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                        Other sensor applications are

                                        Detection and generation of sonar waves

                                        To detect detonation in automotive engine by sampling the vibrations of the engine block

                                        To detect the precise moment of fuel injection in an automotive engine

                                        Detection of acoustic emissions in acoustic emission testing

                                        Microbalances as very sensitive chemical and biological sensors

                                        Strain gauges

                                        Medical applications using ultrasound waves

                                        Kidney stone treatment

                                        In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                        Figure 527 Ultrasonic waves creation and

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                                        kidney stone treatment and ultrasound imagingof the fetus

                                        (Courtesy copy DoITPoMS University of Cambridge)

                                        5473 Ultrasound Imaging Using Transduction Effect

                                        Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                        55 Pyroelectric Ceramics

                                        Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                        Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                        Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                        551 Difference between Pyroelectric and Ferroelectric Material

                                        Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                        Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                        552 Theory of Piezoelectric Materials

                                        From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                        (537)

                                        Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                        Assuming electric field E as constant differentiating the above equation with temperature leads to

                                        (538)

                                        Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                        we write

                                        Δ OR

                                        Δ (539)

                                        Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                        Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                        (540)

                                        The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                        As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                        553 Measurement of Pyroelectric Coefficient

                                        One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                        (541)

                                        Where Ip is the pyrocurrent and is given as

                                        (542)

                                        where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                        respectively

                                        Figure 530 Circuit for measuring pyroelectriccoefficient

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                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                        554 Direct and Indirect Effect

                                        Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                        Since change in the polarization can also be expressed as depending

                                        upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                        Figure 531 Direct-Indirect effect animation

                                        (Courtesy copy DoITPoMS University of Cambridge)

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                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                        555 Common Pyroelectric Materials

                                        Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                        The most common materials are tabulated below

                                        Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                        LiTaO3 single crystal Hexagonal 665 -230

                                        075Pb(Mg13-Nb23)O3-025PbTiO3

                                        (PMN-PT) Ceramic

                                        Perovskite 150 -1300

                                        Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                        Triglycine sulphate

                                        (NH2CH2COOH)3H2SO4

                                        Sulphate 49 -280

                                        Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                        5551 Triglycine Sulphate (TGS)

                                        High pyroelectric coefficient

                                        Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                        Can be modified to withstand temperatures above Curie point without depoling

                                        Used in thermal imaging cameras

                                        5552 Polyvinylidene Fluoride (PVDF)

                                        Poor pyroelectric coefficient

                                        Readily available in large areas of thin film

                                        More stable to heat vacuum and moisture than TGS mechanically robust

                                        Low heat conductivity and low permittivity

                                        High loss tangent

                                        Commonly used for burglar alarms

                                        5553 Perovskite Ferroelectric Ceramics

                                        Generally robust and insensitive to moisture and vacuum

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                                        High pyroelectric coefficient and low loss

                                        Better operation near TC

                                        Strong dependence on composition

                                        As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                        RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                        556 Common Applications

                                        5561 Burglar Alarms

                                        Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                        Figure 532 Working of an IR intruder alarm

                                        (Courtesy copy DoITPoMS University ofCambridge)

                                        5562 Infrared or Thermal Imaging

                                        Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                        The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                        A typical photograph generated from IR imaging looks like this

                                        Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                        Here is a simple explanation of how IT imaging using pyroelectrics works

                                        A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                        This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                        Figure 534 Process of imagecreation

                                        5563 Pollutant Control

                                        The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                        Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                        Figure 535 Gas detection using a pyroelectricdetector

                                        (Courtesy copy DoITPoMS University of Cambridge)

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                                        Module 5 Nonlinear Dielectrics

                                        Summary

                                        Summary

                                        Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                          539 Ferroelectric Switching and Domains

                                          Application of an electric field to a ferroelectric ceramic leads to the alignment of antiparallel or off-aligned dipoles to reorient themselves along the field

                                          At sufficiently large fields all the dipoles will be aligned along the field and the direction reverses byreversing the direction of the field This phenomenon of polarization reversal takes place by way ofnucleation and growth of favourably oriented domains into the unfavourably oriented domains andassociated domain wall motion

                                          Figure 5 13 Characteristic hysteresis loop of a ferroelectricmaterial

                                          If we assume that our hypothetical crystal has an equal number of positive and negative domains inthe virgin states then the net polarization of the crystal will be zero Now what happens when fieldE is applied The plot that we get is something like shown above where P is polarization in

                                          microCcm2and E is electric field across the sample in Vcm The process is something like this

                                          Initial polarization P increases linearly with the increasing electric field and the crystal behaves likea dielectric because the applied field is not large enough to switch any of the domains orientedopposite to its direction This linear region is shown as AB

                                          Further increase in the field strength forces nucleation and growth of favourably oriented domains atthe expense of oppositely oriented domains and polarization starts increasing rapidly (BC) until allthe domains are aligned in the direction of the electric field ie reach a single domain state(CD) when polarization saturates to a value called saturation polarization (PS) The domains

                                          reversal actually takes place by formation of new favourably oriented domains at the expense ofunfavourable domains Now when the field is decreased the polarization generally does not returnto zero but follows path DE and at zero field some of the domains still remain aligned in the positivedirection and the crystal exhibits a remanent polarization (PR) To bring the crystal back to zero

                                          polarization state a negative electric field is required (along the path EF) which is also called thecoercive field (EC)

                                          Further increase of electric field in the opposite direction will cause complete reversal of orientation

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                                          of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                                          Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                                          Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                          5310 Measurement of Hysteresis Loop

                                          Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                                          The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                                          crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                                          This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                                          and coercive field Ec

                                          A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                                          Figure 5 15 Schematic representation of sawyer-tower circuit

                                          Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                          5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                                          Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                                          atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                                          Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                                          Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                                          a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                                          Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                                          becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                                          positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                                          The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                                          Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                          Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                          spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                          BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                          orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                          Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                          5312 Applications of Ferroelectrics

                                          In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                          Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                          (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                          Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                          where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                          53121 Nonvolatile Memories

                                          Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                          two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                          Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                          53122 Camera Flashes

                                          In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                          Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                          Module 5 Nonlinear Dielectrics

                                          Summary

                                          Summary

                                          In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                          can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                          and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                          binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                          One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                          5474 Actuators

                                          In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                          In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                          You can have it in two forms

                                          Direct Piezo Actuators with strokes lower than 100 microns or so and

                                          Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                          Some of the examples of applications are

                                          Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                          Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                          Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                          Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                          In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                          As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                          5475 Frequency Standards

                                          Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                          Quartz clocks

                                          Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                          Module 5 Nonlinear Dielectrics

                                          Summary

                                          Summary

                                          Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                          54 Piezoelectric Ceramics

                                          Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                          Pb(ZrTi)O3)

                                          An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                          For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                          541 Direct Piezoelectric Effect

                                          Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                          (533)

                                          where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                          542 Reverse or Converse Piezoelectric Effect

                                          The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                          (534)

                                          where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                          Figure 520 Direct and Converse PiezoelectricEffects

                                          The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                          543 Poling of Piezoelectric Materials

                                          As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                          The values of piezoelectric coefficient of some materials are given below

                                          Material Piezoelectric Constant d(pmV)

                                          Quartz 23

                                          Barium Titanate 100-149

                                          Lead Niobate 80-85

                                          Lead zirconate titanate 250-365

                                          So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                          Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                          field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                          Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                          544 Depolarization of Piezoelectrics

                                          Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                          polarization or rather result in alignment of dipoles gets lost

                                          Figure 522 Animation on depolarization offerroelectrics

                                          (Courtesy copy DoITPoMS University of Cambridge)

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                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                          545 Common PIezoelectric Materials

                                          5451 Barium Titanate (BaTiO3)

                                          This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                          used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                          Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                          1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                          must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                          5452 Pb(ZrTi)O3 or PZT

                                          PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                          The phase diagram of PZT is shown below

                                          Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                          The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                          lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                          few poling directions available making it a useful piezoelectric

                                          Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                          546 Measurement of Piezoelectric Properties

                                          Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                          In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                          Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                          The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                          (535)

                                          Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                          (536)

                                          Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                          One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                          547 Applications of Piezoelectric Ceramics

                                          Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                          5471 Power Generation

                                          Gas Lighter

                                          Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                          Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                          One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                          Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                          Power Transformer

                                          A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                          An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                          Figure 526 Schematic of a piezoelectrictransformer

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                                          Module 5 Special Dielectrics Piezoelectric Ceramics

                                          5472 Piezoelectric Sensors

                                          Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                          Other sensor applications are

                                          Detection and generation of sonar waves

                                          To detect detonation in automotive engine by sampling the vibrations of the engine block

                                          To detect the precise moment of fuel injection in an automotive engine

                                          Detection of acoustic emissions in acoustic emission testing

                                          Microbalances as very sensitive chemical and biological sensors

                                          Strain gauges

                                          Medical applications using ultrasound waves

                                          Kidney stone treatment

                                          In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                          Figure 527 Ultrasonic waves creation and

                                          >

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                                          kidney stone treatment and ultrasound imagingof the fetus

                                          (Courtesy copy DoITPoMS University of Cambridge)

                                          5473 Ultrasound Imaging Using Transduction Effect

                                          Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                          55 Pyroelectric Ceramics

                                          Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                          Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                          Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                          551 Difference between Pyroelectric and Ferroelectric Material

                                          Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                          Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                          552 Theory of Piezoelectric Materials

                                          From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                          (537)

                                          Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                          Assuming electric field E as constant differentiating the above equation with temperature leads to

                                          (538)

                                          Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                          we write

                                          Δ OR

                                          Δ (539)

                                          Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                          Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                          (540)

                                          The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                          As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                          553 Measurement of Pyroelectric Coefficient

                                          One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                          (541)

                                          Where Ip is the pyrocurrent and is given as

                                          (542)

                                          where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                          respectively

                                          Figure 530 Circuit for measuring pyroelectriccoefficient

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                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                          554 Direct and Indirect Effect

                                          Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                          Since change in the polarization can also be expressed as depending

                                          upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                          Figure 531 Direct-Indirect effect animation

                                          (Courtesy copy DoITPoMS University of Cambridge)

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                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                          555 Common Pyroelectric Materials

                                          Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                          The most common materials are tabulated below

                                          Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                          LiTaO3 single crystal Hexagonal 665 -230

                                          075Pb(Mg13-Nb23)O3-025PbTiO3

                                          (PMN-PT) Ceramic

                                          Perovskite 150 -1300

                                          Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                          Triglycine sulphate

                                          (NH2CH2COOH)3H2SO4

                                          Sulphate 49 -280

                                          Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                          5551 Triglycine Sulphate (TGS)

                                          High pyroelectric coefficient

                                          Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                          Can be modified to withstand temperatures above Curie point without depoling

                                          Used in thermal imaging cameras

                                          5552 Polyvinylidene Fluoride (PVDF)

                                          Poor pyroelectric coefficient

                                          Readily available in large areas of thin film

                                          More stable to heat vacuum and moisture than TGS mechanically robust

                                          Low heat conductivity and low permittivity

                                          High loss tangent

                                          Commonly used for burglar alarms

                                          5553 Perovskite Ferroelectric Ceramics

                                          Generally robust and insensitive to moisture and vacuum

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                                          High pyroelectric coefficient and low loss

                                          Better operation near TC

                                          Strong dependence on composition

                                          As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                          RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                          556 Common Applications

                                          5561 Burglar Alarms

                                          Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                          Figure 532 Working of an IR intruder alarm

                                          (Courtesy copy DoITPoMS University ofCambridge)

                                          5562 Infrared or Thermal Imaging

                                          Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                          The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                          A typical photograph generated from IR imaging looks like this

                                          Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                          Here is a simple explanation of how IT imaging using pyroelectrics works

                                          A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                          This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                          Figure 534 Process of imagecreation

                                          5563 Pollutant Control

                                          The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                          Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                          Figure 535 Gas detection using a pyroelectricdetector

                                          (Courtesy copy DoITPoMS University of Cambridge)

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                                          Module 5 Nonlinear Dielectrics

                                          Summary

                                          Summary

                                          Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                            of all domains in the direction of field (path FG) and the loop can be completed by following thepath GHD This relation between P and E is called a ferroelectric hysteresis loop which is an importantcharacteristic of a ferroelectric crystal The principle feature of a ferroelectric crystal is not only thepresence of spontaneous polarization but also the fact that this polarization can be reversed byapplication of an electric field

                                            Domain switching in a previously polarized ferroelectric sample can also be viewed in the followinganimation

                                            Figure 5 14 Domain switching animation in a ferroelectricmaterial (Reproduced from DOITPOMS Library University ofCambridge UK)

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                                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                            5310 Measurement of Hysteresis Loop

                                            Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                                            The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                                            crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                                            This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                                            and coercive field Ec

                                            A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                                            Figure 5 15 Schematic representation of sawyer-tower circuit

                                            Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                            5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                                            Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                                            atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                                            Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                                            Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                                            a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                                            Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                                            becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                                            positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                                            The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                                            Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                            Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                            spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                            BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                            orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                            Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                            5312 Applications of Ferroelectrics

                                            In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                            Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                            (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                            Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                            where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                            53121 Nonvolatile Memories

                                            Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                            two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                            Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                            53122 Camera Flashes

                                            In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                            Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                            Module 5 Nonlinear Dielectrics

                                            Summary

                                            Summary

                                            In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                            can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                            and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                            binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                            One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                            5474 Actuators

                                            In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                            In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                            You can have it in two forms

                                            Direct Piezo Actuators with strokes lower than 100 microns or so and

                                            Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                            Some of the examples of applications are

                                            Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                            Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                            Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                            Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                            In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                            As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                            5475 Frequency Standards

                                            Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                            Quartz clocks

                                            Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                            Module 5 Nonlinear Dielectrics

                                            Summary

                                            Summary

                                            Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                            54 Piezoelectric Ceramics

                                            Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                            Pb(ZrTi)O3)

                                            An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                            For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                            541 Direct Piezoelectric Effect

                                            Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                            (533)

                                            where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                            542 Reverse or Converse Piezoelectric Effect

                                            The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                            (534)

                                            where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                            Figure 520 Direct and Converse PiezoelectricEffects

                                            The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                            543 Poling of Piezoelectric Materials

                                            As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                            The values of piezoelectric coefficient of some materials are given below

                                            Material Piezoelectric Constant d(pmV)

                                            Quartz 23

                                            Barium Titanate 100-149

                                            Lead Niobate 80-85

                                            Lead zirconate titanate 250-365

                                            So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                            Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                            field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                            Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                            544 Depolarization of Piezoelectrics

                                            Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                            polarization or rather result in alignment of dipoles gets lost

                                            Figure 522 Animation on depolarization offerroelectrics

                                            (Courtesy copy DoITPoMS University of Cambridge)

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                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                            545 Common PIezoelectric Materials

                                            5451 Barium Titanate (BaTiO3)

                                            This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                            used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                            Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                            1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                            must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                            5452 Pb(ZrTi)O3 or PZT

                                            PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                            The phase diagram of PZT is shown below

                                            Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                            The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                            lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                            few poling directions available making it a useful piezoelectric

                                            Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                            546 Measurement of Piezoelectric Properties

                                            Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                            In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                            Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                            The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                            (535)

                                            Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                            (536)

                                            Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                            One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                            547 Applications of Piezoelectric Ceramics

                                            Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                            5471 Power Generation

                                            Gas Lighter

                                            Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                            Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                            One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                            Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                            Power Transformer

                                            A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                            An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                            Figure 526 Schematic of a piezoelectrictransformer

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                                            Module 5 Special Dielectrics Piezoelectric Ceramics

                                            5472 Piezoelectric Sensors

                                            Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                            Other sensor applications are

                                            Detection and generation of sonar waves

                                            To detect detonation in automotive engine by sampling the vibrations of the engine block

                                            To detect the precise moment of fuel injection in an automotive engine

                                            Detection of acoustic emissions in acoustic emission testing

                                            Microbalances as very sensitive chemical and biological sensors

                                            Strain gauges

                                            Medical applications using ultrasound waves

                                            Kidney stone treatment

                                            In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                            Figure 527 Ultrasonic waves creation and

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                                            kidney stone treatment and ultrasound imagingof the fetus

                                            (Courtesy copy DoITPoMS University of Cambridge)

                                            5473 Ultrasound Imaging Using Transduction Effect

                                            Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                            55 Pyroelectric Ceramics

                                            Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                            Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                            Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                            551 Difference between Pyroelectric and Ferroelectric Material

                                            Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                            Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                            552 Theory of Piezoelectric Materials

                                            From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                            (537)

                                            Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                            Assuming electric field E as constant differentiating the above equation with temperature leads to

                                            (538)

                                            Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                            we write

                                            Δ OR

                                            Δ (539)

                                            Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                            Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                            (540)

                                            The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                            As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                            553 Measurement of Pyroelectric Coefficient

                                            One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                            (541)

                                            Where Ip is the pyrocurrent and is given as

                                            (542)

                                            where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                            respectively

                                            Figure 530 Circuit for measuring pyroelectriccoefficient

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                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                            554 Direct and Indirect Effect

                                            Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                            Since change in the polarization can also be expressed as depending

                                            upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                            Figure 531 Direct-Indirect effect animation

                                            (Courtesy copy DoITPoMS University of Cambridge)

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                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                            555 Common Pyroelectric Materials

                                            Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                            The most common materials are tabulated below

                                            Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                            LiTaO3 single crystal Hexagonal 665 -230

                                            075Pb(Mg13-Nb23)O3-025PbTiO3

                                            (PMN-PT) Ceramic

                                            Perovskite 150 -1300

                                            Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                            Triglycine sulphate

                                            (NH2CH2COOH)3H2SO4

                                            Sulphate 49 -280

                                            Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                            5551 Triglycine Sulphate (TGS)

                                            High pyroelectric coefficient

                                            Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                            Can be modified to withstand temperatures above Curie point without depoling

                                            Used in thermal imaging cameras

                                            5552 Polyvinylidene Fluoride (PVDF)

                                            Poor pyroelectric coefficient

                                            Readily available in large areas of thin film

                                            More stable to heat vacuum and moisture than TGS mechanically robust

                                            Low heat conductivity and low permittivity

                                            High loss tangent

                                            Commonly used for burglar alarms

                                            5553 Perovskite Ferroelectric Ceramics

                                            Generally robust and insensitive to moisture and vacuum

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                                            High pyroelectric coefficient and low loss

                                            Better operation near TC

                                            Strong dependence on composition

                                            As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                            RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                            556 Common Applications

                                            5561 Burglar Alarms

                                            Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                            Figure 532 Working of an IR intruder alarm

                                            (Courtesy copy DoITPoMS University ofCambridge)

                                            5562 Infrared or Thermal Imaging

                                            Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                            The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                            A typical photograph generated from IR imaging looks like this

                                            Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                            Here is a simple explanation of how IT imaging using pyroelectrics works

                                            A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                            This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                            Figure 534 Process of imagecreation

                                            5563 Pollutant Control

                                            The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                            Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                            Figure 535 Gas detection using a pyroelectricdetector

                                            (Courtesy copy DoITPoMS University of Cambridge)

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                                            Module 5 Nonlinear Dielectrics

                                            Summary

                                            Summary

                                            Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                              5310 Measurement of Hysteresis Loop

                                              Ferroelectric hysteresis loops can be experimentally measured using a Sawyer-Tower circuit using ahigh frequency ac field and are observed on the screen of an oscilloscope

                                              The circuit is schematically drawn below A linear capacitor C0 is connected in series with the

                                              crystal In this configuration the voltage across C0 is proportional to the polarization of the crystal

                                              This circuit not only measures the hysteresis loop it also quantifies the spontaneous polarization Ps

                                              and coercive field Ec

                                              A ferroelectric materials shows polarization of the order of 50-100 microCcm2

                                              Figure 5 15 Schematic representation of sawyer-tower circuit

                                              Nowadays one can get commercially available instruments such as Radiant Premier PrecisionStation from Radiant Technologies which can perform polarization measurements at varying field andfrequencies For device measurements one needs to establish top and bottom contacts to theferroelectric materials which is typically achieved using thin platinum electrodes in thin films andsilver paste in bulk ceramics

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                                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                              5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                                              Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                                              atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                                              Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                                              Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                                              a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                                              Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                                              becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                                              positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                                              The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                                              Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                              Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                              spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                              BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                              orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                              Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                              5312 Applications of Ferroelectrics

                                              In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                              Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                              (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                              Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                              where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                              53121 Nonvolatile Memories

                                              Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                              two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                              Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                              53122 Camera Flashes

                                              In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                              Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                              Module 5 Nonlinear Dielectrics

                                              Summary

                                              Summary

                                              In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                              can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                              and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                              binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                              One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                              5474 Actuators

                                              In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                              In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                              You can have it in two forms

                                              Direct Piezo Actuators with strokes lower than 100 microns or so and

                                              Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                              Some of the examples of applications are

                                              Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                              Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                              Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                              Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                              In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                              As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                              5475 Frequency Standards

                                              Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                              Quartz clocks

                                              Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                              Module 5 Nonlinear Dielectrics

                                              Summary

                                              Summary

                                              Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                              54 Piezoelectric Ceramics

                                              Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                              Pb(ZrTi)O3)

                                              An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                              For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                              541 Direct Piezoelectric Effect

                                              Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                              (533)

                                              where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                              542 Reverse or Converse Piezoelectric Effect

                                              The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                              (534)

                                              where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                              Figure 520 Direct and Converse PiezoelectricEffects

                                              The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                              543 Poling of Piezoelectric Materials

                                              As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                              The values of piezoelectric coefficient of some materials are given below

                                              Material Piezoelectric Constant d(pmV)

                                              Quartz 23

                                              Barium Titanate 100-149

                                              Lead Niobate 80-85

                                              Lead zirconate titanate 250-365

                                              So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                              Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                              field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                              Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                              544 Depolarization of Piezoelectrics

                                              Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                              polarization or rather result in alignment of dipoles gets lost

                                              Figure 522 Animation on depolarization offerroelectrics

                                              (Courtesy copy DoITPoMS University of Cambridge)

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                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                              545 Common PIezoelectric Materials

                                              5451 Barium Titanate (BaTiO3)

                                              This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                              used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                              Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                              1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                              must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                              5452 Pb(ZrTi)O3 or PZT

                                              PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                              The phase diagram of PZT is shown below

                                              Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                              The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                              lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                              few poling directions available making it a useful piezoelectric

                                              Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                              546 Measurement of Piezoelectric Properties

                                              Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                              In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                              Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                              The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                              (535)

                                              Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                              (536)

                                              Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                              One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                              547 Applications of Piezoelectric Ceramics

                                              Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                              5471 Power Generation

                                              Gas Lighter

                                              Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                              Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                              One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                              Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                              Power Transformer

                                              A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                              An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                              Figure 526 Schematic of a piezoelectrictransformer

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                                              Module 5 Special Dielectrics Piezoelectric Ceramics

                                              5472 Piezoelectric Sensors

                                              Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                              Other sensor applications are

                                              Detection and generation of sonar waves

                                              To detect detonation in automotive engine by sampling the vibrations of the engine block

                                              To detect the precise moment of fuel injection in an automotive engine

                                              Detection of acoustic emissions in acoustic emission testing

                                              Microbalances as very sensitive chemical and biological sensors

                                              Strain gauges

                                              Medical applications using ultrasound waves

                                              Kidney stone treatment

                                              In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                              Figure 527 Ultrasonic waves creation and

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                                              kidney stone treatment and ultrasound imagingof the fetus

                                              (Courtesy copy DoITPoMS University of Cambridge)

                                              5473 Ultrasound Imaging Using Transduction Effect

                                              Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                              55 Pyroelectric Ceramics

                                              Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                              Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                              Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                              551 Difference between Pyroelectric and Ferroelectric Material

                                              Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                              Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                              552 Theory of Piezoelectric Materials

                                              From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                              (537)

                                              Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                              Assuming electric field E as constant differentiating the above equation with temperature leads to

                                              (538)

                                              Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                              we write

                                              Δ OR

                                              Δ (539)

                                              Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                              Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                              (540)

                                              The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                              As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                              553 Measurement of Pyroelectric Coefficient

                                              One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                              (541)

                                              Where Ip is the pyrocurrent and is given as

                                              (542)

                                              where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                              respectively

                                              Figure 530 Circuit for measuring pyroelectriccoefficient

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                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                              554 Direct and Indirect Effect

                                              Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                              Since change in the polarization can also be expressed as depending

                                              upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                              Figure 531 Direct-Indirect effect animation

                                              (Courtesy copy DoITPoMS University of Cambridge)

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                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                              555 Common Pyroelectric Materials

                                              Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                              The most common materials are tabulated below

                                              Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                              LiTaO3 single crystal Hexagonal 665 -230

                                              075Pb(Mg13-Nb23)O3-025PbTiO3

                                              (PMN-PT) Ceramic

                                              Perovskite 150 -1300

                                              Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                              Triglycine sulphate

                                              (NH2CH2COOH)3H2SO4

                                              Sulphate 49 -280

                                              Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                              5551 Triglycine Sulphate (TGS)

                                              High pyroelectric coefficient

                                              Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                              Can be modified to withstand temperatures above Curie point without depoling

                                              Used in thermal imaging cameras

                                              5552 Polyvinylidene Fluoride (PVDF)

                                              Poor pyroelectric coefficient

                                              Readily available in large areas of thin film

                                              More stable to heat vacuum and moisture than TGS mechanically robust

                                              Low heat conductivity and low permittivity

                                              High loss tangent

                                              Commonly used for burglar alarms

                                              5553 Perovskite Ferroelectric Ceramics

                                              Generally robust and insensitive to moisture and vacuum

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                                              High pyroelectric coefficient and low loss

                                              Better operation near TC

                                              Strong dependence on composition

                                              As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                              RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                              556 Common Applications

                                              5561 Burglar Alarms

                                              Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                              Figure 532 Working of an IR intruder alarm

                                              (Courtesy copy DoITPoMS University ofCambridge)

                                              5562 Infrared or Thermal Imaging

                                              Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                              The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                              A typical photograph generated from IR imaging looks like this

                                              Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                              Here is a simple explanation of how IT imaging using pyroelectrics works

                                              A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                              This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                              Figure 534 Process of imagecreation

                                              5563 Pollutant Control

                                              The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                              Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                              Figure 535 Gas detection using a pyroelectricdetector

                                              (Courtesy copy DoITPoMS University of Cambridge)

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                                              Module 5 Nonlinear Dielectrics

                                              Summary

                                              Summary

                                              Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                                5311 Structural change and ferroelectricity in Barium Titanate (BaTiO3)

                                                Barium Titanate (BaTiO3) has a perovskite ABO3 type structure As shown below the central Ti

                                                atom is surrounded by six oxygen ions in a octahedral co-ordination determined by the radius ratio(See Module 1)

                                                Figure 5 16 Structure of Barium Titanate (ABa B Ti) For Cubic form a=b=c while fortetragonal a=bnec

                                                Above 120degC cubic form of (BaTiO3) has regular octahedrons of O2- ions around Ti4+ ion and has

                                                a center of symmetry As a result the six Ti-O dipole moments along plusmnx plusmny plusmnz cancel each otherand the material in such a state is called paraelectric

                                                Below 120degC BaTiO3 transforms to a noncentrosymmetric tetragonal phase with one of the axis

                                                becoming longer typically referred as z-axis or [001]-direction Unilateral displacement of the

                                                positively changed Ti4+ ions against surrounding O2- ions occurs to give rise to net permanent dipolemoment Coupling of such displacements and the associated dipole moment is a necessity forferroelectricity This transformation forces Ti ions go to lower energy off center positions giving riseto permanent dipoles (see the energy well diagram in section 536)

                                                The crystallographic dimension of the BaTiO3 lattice change with temperature as shown below

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                                                Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                                Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                                spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                                BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                                orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                                Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                                5312 Applications of Ferroelectrics

                                                In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                                Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                                (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                                Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                                where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                                53121 Nonvolatile Memories

                                                Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                                two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                                Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                                53122 Camera Flashes

                                                In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                                Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                                Module 5 Nonlinear Dielectrics

                                                Summary

                                                Summary

                                                In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                                can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                                and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                                binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                                One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                5474 Actuators

                                                In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                                In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                                You can have it in two forms

                                                Direct Piezo Actuators with strokes lower than 100 microns or so and

                                                Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                                Some of the examples of applications are

                                                Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                                Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                                Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                                Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                                In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                                As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                5475 Frequency Standards

                                                Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                                Quartz clocks

                                                Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                                Module 5 Nonlinear Dielectrics

                                                Summary

                                                Summary

                                                Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                54 Piezoelectric Ceramics

                                                Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                                Pb(ZrTi)O3)

                                                An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                                For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                541 Direct Piezoelectric Effect

                                                Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                (533)

                                                where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                542 Reverse or Converse Piezoelectric Effect

                                                The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                (534)

                                                where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                Figure 520 Direct and Converse PiezoelectricEffects

                                                The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                543 Poling of Piezoelectric Materials

                                                As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                The values of piezoelectric coefficient of some materials are given below

                                                Material Piezoelectric Constant d(pmV)

                                                Quartz 23

                                                Barium Titanate 100-149

                                                Lead Niobate 80-85

                                                Lead zirconate titanate 250-365

                                                So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                544 Depolarization of Piezoelectrics

                                                Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                polarization or rather result in alignment of dipoles gets lost

                                                Figure 522 Animation on depolarization offerroelectrics

                                                (Courtesy copy DoITPoMS University of Cambridge)

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                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                545 Common PIezoelectric Materials

                                                5451 Barium Titanate (BaTiO3)

                                                This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                5452 Pb(ZrTi)O3 or PZT

                                                PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                The phase diagram of PZT is shown below

                                                Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                few poling directions available making it a useful piezoelectric

                                                Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                546 Measurement of Piezoelectric Properties

                                                Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                (535)

                                                Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                (536)

                                                Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                547 Applications of Piezoelectric Ceramics

                                                Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                5471 Power Generation

                                                Gas Lighter

                                                Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                Power Transformer

                                                A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                Figure 526 Schematic of a piezoelectrictransformer

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                                                Module 5 Special Dielectrics Piezoelectric Ceramics

                                                5472 Piezoelectric Sensors

                                                Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                Other sensor applications are

                                                Detection and generation of sonar waves

                                                To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                To detect the precise moment of fuel injection in an automotive engine

                                                Detection of acoustic emissions in acoustic emission testing

                                                Microbalances as very sensitive chemical and biological sensors

                                                Strain gauges

                                                Medical applications using ultrasound waves

                                                Kidney stone treatment

                                                In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                Figure 527 Ultrasonic waves creation and

                                                >

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                                                kidney stone treatment and ultrasound imagingof the fetus

                                                (Courtesy copy DoITPoMS University of Cambridge)

                                                5473 Ultrasound Imaging Using Transduction Effect

                                                Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                55 Pyroelectric Ceramics

                                                Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                551 Difference between Pyroelectric and Ferroelectric Material

                                                Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                552 Theory of Piezoelectric Materials

                                                From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                (537)

                                                Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                (538)

                                                Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                we write

                                                Δ OR

                                                Δ (539)

                                                Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                (540)

                                                The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                553 Measurement of Pyroelectric Coefficient

                                                One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                (541)

                                                Where Ip is the pyrocurrent and is given as

                                                (542)

                                                where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                respectively

                                                Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                554 Direct and Indirect Effect

                                                Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                Since change in the polarization can also be expressed as depending

                                                upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                Figure 531 Direct-Indirect effect animation

                                                (Courtesy copy DoITPoMS University of Cambridge)

                                                >

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                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                555 Common Pyroelectric Materials

                                                Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                The most common materials are tabulated below

                                                Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                LiTaO3 single crystal Hexagonal 665 -230

                                                075Pb(Mg13-Nb23)O3-025PbTiO3

                                                (PMN-PT) Ceramic

                                                Perovskite 150 -1300

                                                Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                Triglycine sulphate

                                                (NH2CH2COOH)3H2SO4

                                                Sulphate 49 -280

                                                Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                5551 Triglycine Sulphate (TGS)

                                                High pyroelectric coefficient

                                                Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                Can be modified to withstand temperatures above Curie point without depoling

                                                Used in thermal imaging cameras

                                                5552 Polyvinylidene Fluoride (PVDF)

                                                Poor pyroelectric coefficient

                                                Readily available in large areas of thin film

                                                More stable to heat vacuum and moisture than TGS mechanically robust

                                                Low heat conductivity and low permittivity

                                                High loss tangent

                                                Commonly used for burglar alarms

                                                5553 Perovskite Ferroelectric Ceramics

                                                Generally robust and insensitive to moisture and vacuum

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                                                High pyroelectric coefficient and low loss

                                                Better operation near TC

                                                Strong dependence on composition

                                                As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                556 Common Applications

                                                5561 Burglar Alarms

                                                Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                Figure 532 Working of an IR intruder alarm

                                                (Courtesy copy DoITPoMS University ofCambridge)

                                                5562 Infrared or Thermal Imaging

                                                Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                >

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                                                A typical photograph generated from IR imaging looks like this

                                                Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                Here is a simple explanation of how IT imaging using pyroelectrics works

                                                A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                Figure 534 Process of imagecreation

                                                5563 Pollutant Control

                                                The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                Figure 535 Gas detection using a pyroelectricdetector

                                                (Courtesy copy DoITPoMS University of Cambridge)

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                                                Module 5 Nonlinear Dielectrics

                                                Summary

                                                Summary

                                                Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                  Figure 5 17 Distortion in BaTiO3 upon cooling from cubicphase

                                                  Because the distorted octahedra are coupled together in ferroelectric form there is a very large

                                                  spontaneous polarization ~25 microCcm2 giving rise to a large dielectric constant ~160 and largetemperature dependence of dielectric constant

                                                  BaTiO3 shows two more structural transitions when cooled further below 120degC It transforms to

                                                  orthorhombic structure at ~5degC and then again to a rhombohedral structure at ~ -90degC and as resultof change in the symmetry the polarization vector also changes from [001] for tetragonal to [110] inorthorhombic and [111] in rhombohedral structure

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                                                  Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                                  5312 Applications of Ferroelectrics

                                                  In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                                  Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                                  (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                                  Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                                  where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                                  53121 Nonvolatile Memories

                                                  Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                                  two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                                  Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                                  53122 Camera Flashes

                                                  In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                                  Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                                  Module 5 Nonlinear Dielectrics

                                                  Summary

                                                  Summary

                                                  In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                                  can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                                  and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                                  binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                                  One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                  5474 Actuators

                                                  In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                                  In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                                  You can have it in two forms

                                                  Direct Piezo Actuators with strokes lower than 100 microns or so and

                                                  Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                                  Some of the examples of applications are

                                                  Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                                  Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                                  Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                                  Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                                  In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                                  As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                  5475 Frequency Standards

                                                  Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                                  Quartz clocks

                                                  Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                                  Module 5 Nonlinear Dielectrics

                                                  Summary

                                                  Summary

                                                  Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                  54 Piezoelectric Ceramics

                                                  Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                                  Pb(ZrTi)O3)

                                                  An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                                  For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                  541 Direct Piezoelectric Effect

                                                  Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                  (533)

                                                  where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                  542 Reverse or Converse Piezoelectric Effect

                                                  The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                  (534)

                                                  where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                  Figure 520 Direct and Converse PiezoelectricEffects

                                                  The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                  543 Poling of Piezoelectric Materials

                                                  As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                  The values of piezoelectric coefficient of some materials are given below

                                                  Material Piezoelectric Constant d(pmV)

                                                  Quartz 23

                                                  Barium Titanate 100-149

                                                  Lead Niobate 80-85

                                                  Lead zirconate titanate 250-365

                                                  So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                  Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                  field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                  Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                  544 Depolarization of Piezoelectrics

                                                  Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                  polarization or rather result in alignment of dipoles gets lost

                                                  Figure 522 Animation on depolarization offerroelectrics

                                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                  545 Common PIezoelectric Materials

                                                  5451 Barium Titanate (BaTiO3)

                                                  This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                  used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                  Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                  1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                  must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                  5452 Pb(ZrTi)O3 or PZT

                                                  PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                  The phase diagram of PZT is shown below

                                                  Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                  The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                  lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                  few poling directions available making it a useful piezoelectric

                                                  Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                  546 Measurement of Piezoelectric Properties

                                                  Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                  In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                  Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                  The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                  (535)

                                                  Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                  (536)

                                                  Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                  One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                  547 Applications of Piezoelectric Ceramics

                                                  Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                  5471 Power Generation

                                                  Gas Lighter

                                                  Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                  Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                  One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                  Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                  Power Transformer

                                                  A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                  An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                  Figure 526 Schematic of a piezoelectrictransformer

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                                                  Module 5 Special Dielectrics Piezoelectric Ceramics

                                                  5472 Piezoelectric Sensors

                                                  Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                  Other sensor applications are

                                                  Detection and generation of sonar waves

                                                  To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                  To detect the precise moment of fuel injection in an automotive engine

                                                  Detection of acoustic emissions in acoustic emission testing

                                                  Microbalances as very sensitive chemical and biological sensors

                                                  Strain gauges

                                                  Medical applications using ultrasound waves

                                                  Kidney stone treatment

                                                  In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                  Figure 527 Ultrasonic waves creation and

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                                                  kidney stone treatment and ultrasound imagingof the fetus

                                                  (Courtesy copy DoITPoMS University of Cambridge)

                                                  5473 Ultrasound Imaging Using Transduction Effect

                                                  Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                  55 Pyroelectric Ceramics

                                                  Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                  Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                  Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                  551 Difference between Pyroelectric and Ferroelectric Material

                                                  Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                  Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                  552 Theory of Piezoelectric Materials

                                                  From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                  (537)

                                                  Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                  Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                  (538)

                                                  Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                  we write

                                                  Δ OR

                                                  Δ (539)

                                                  Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                  Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                  (540)

                                                  The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                  As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                  553 Measurement of Pyroelectric Coefficient

                                                  One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                  (541)

                                                  Where Ip is the pyrocurrent and is given as

                                                  (542)

                                                  where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                  respectively

                                                  Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                  554 Direct and Indirect Effect

                                                  Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                  Since change in the polarization can also be expressed as depending

                                                  upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                  Figure 531 Direct-Indirect effect animation

                                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                  555 Common Pyroelectric Materials

                                                  Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                  The most common materials are tabulated below

                                                  Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                  LiTaO3 single crystal Hexagonal 665 -230

                                                  075Pb(Mg13-Nb23)O3-025PbTiO3

                                                  (PMN-PT) Ceramic

                                                  Perovskite 150 -1300

                                                  Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                  Triglycine sulphate

                                                  (NH2CH2COOH)3H2SO4

                                                  Sulphate 49 -280

                                                  Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                  5551 Triglycine Sulphate (TGS)

                                                  High pyroelectric coefficient

                                                  Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                  Can be modified to withstand temperatures above Curie point without depoling

                                                  Used in thermal imaging cameras

                                                  5552 Polyvinylidene Fluoride (PVDF)

                                                  Poor pyroelectric coefficient

                                                  Readily available in large areas of thin film

                                                  More stable to heat vacuum and moisture than TGS mechanically robust

                                                  Low heat conductivity and low permittivity

                                                  High loss tangent

                                                  Commonly used for burglar alarms

                                                  5553 Perovskite Ferroelectric Ceramics

                                                  Generally robust and insensitive to moisture and vacuum

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                                                  High pyroelectric coefficient and low loss

                                                  Better operation near TC

                                                  Strong dependence on composition

                                                  As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                  RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                  556 Common Applications

                                                  5561 Burglar Alarms

                                                  Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                  Figure 532 Working of an IR intruder alarm

                                                  (Courtesy copy DoITPoMS University ofCambridge)

                                                  5562 Infrared or Thermal Imaging

                                                  Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                  The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                  A typical photograph generated from IR imaging looks like this

                                                  Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                  Here is a simple explanation of how IT imaging using pyroelectrics works

                                                  A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                  This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                  Figure 534 Process of imagecreation

                                                  5563 Pollutant Control

                                                  The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                  Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                  Figure 535 Gas detection using a pyroelectricdetector

                                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                                  Module 5 Nonlinear Dielectrics

                                                  Summary

                                                  Summary

                                                  Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                    Module 5 Nonlinear Dielectrics Ferroelectric Ceramics

                                                    5312 Applications of Ferroelectrics

                                                    In addition to BaTiO3 extensively studied ferroelectric materials have been PbTiO3 Pb(ZrTi)O3

                                                    Bi4Ti3 O12 and SrBi2Ta2O9 While the first two show large polarization and a reasonably high Tc

                                                    (above 400degC) the latter two do not contain lead and have higher Curie transition temperatures

                                                    Although many applications of ferroelectrics are for their piezoelectric properties (see section 54)ferroelectrics can be used for applications like non-volatile data storage below their Tc Above Tc

                                                    where their dielectric constant increases linearly with temperature they can be used for cameraflashes

                                                    53121 Nonvolatile Memories

                                                    Since ferroelectric materials show a hysteresis loop and remnant polarization plusmnPR at zero field these

                                                    two polarization states can be used as lsquo0rsquo and lsquo1rsquo states of binary data storage in memory devicesThe advantages are that data will be stored when power is lost during operation leading to non-volatile data storage Other advantages are that ferroelectric switching is a very fast phenomenonand hence memories can operate very fast Many of these materials tend to be radiation resistantand hence can be used in space applications

                                                    Figure 5 18 Ferroelectric memory states of +PR and ndashPR ie1 and 0

                                                    53122 Camera Flashes

                                                    In this application the battery charges the ferroelectric capacitor first Then once fully charged theferroelectric is connected to the bulb and causes it to flash

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                                                    Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                                    Module 5 Nonlinear Dielectrics

                                                    Summary

                                                    Summary

                                                    In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                                    can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                                    and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                                    binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                                    One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                    5474 Actuators

                                                    In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                                    In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                                    You can have it in two forms

                                                    Direct Piezo Actuators with strokes lower than 100 microns or so and

                                                    Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                                    Some of the examples of applications are

                                                    Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                                    Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                                    Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                                    Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                                    In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                                    As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                    5475 Frequency Standards

                                                    Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                                    Quartz clocks

                                                    Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                                    Module 5 Nonlinear Dielectrics

                                                    Summary

                                                    Summary

                                                    Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                    54 Piezoelectric Ceramics

                                                    Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                                    Pb(ZrTi)O3)

                                                    An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                                    For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                    541 Direct Piezoelectric Effect

                                                    Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                    (533)

                                                    where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                    542 Reverse or Converse Piezoelectric Effect

                                                    The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                    (534)

                                                    where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                    Figure 520 Direct and Converse PiezoelectricEffects

                                                    The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                    543 Poling of Piezoelectric Materials

                                                    As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                    The values of piezoelectric coefficient of some materials are given below

                                                    Material Piezoelectric Constant d(pmV)

                                                    Quartz 23

                                                    Barium Titanate 100-149

                                                    Lead Niobate 80-85

                                                    Lead zirconate titanate 250-365

                                                    So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                    Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                    field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                    Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                    544 Depolarization of Piezoelectrics

                                                    Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                    polarization or rather result in alignment of dipoles gets lost

                                                    Figure 522 Animation on depolarization offerroelectrics

                                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                    545 Common PIezoelectric Materials

                                                    5451 Barium Titanate (BaTiO3)

                                                    This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                    used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                    Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                    1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                    must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                    5452 Pb(ZrTi)O3 or PZT

                                                    PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                    The phase diagram of PZT is shown below

                                                    Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                    The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                    lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                    few poling directions available making it a useful piezoelectric

                                                    Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                    546 Measurement of Piezoelectric Properties

                                                    Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                    In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                    Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                    The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                    (535)

                                                    Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                    (536)

                                                    Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                    One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                    547 Applications of Piezoelectric Ceramics

                                                    Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                    5471 Power Generation

                                                    Gas Lighter

                                                    Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                    Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                    One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                    Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                    Power Transformer

                                                    A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                    An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                    Figure 526 Schematic of a piezoelectrictransformer

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                                                    Module 5 Special Dielectrics Piezoelectric Ceramics

                                                    5472 Piezoelectric Sensors

                                                    Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                    Other sensor applications are

                                                    Detection and generation of sonar waves

                                                    To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                    To detect the precise moment of fuel injection in an automotive engine

                                                    Detection of acoustic emissions in acoustic emission testing

                                                    Microbalances as very sensitive chemical and biological sensors

                                                    Strain gauges

                                                    Medical applications using ultrasound waves

                                                    Kidney stone treatment

                                                    In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                    Figure 527 Ultrasonic waves creation and

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                                                    kidney stone treatment and ultrasound imagingof the fetus

                                                    (Courtesy copy DoITPoMS University of Cambridge)

                                                    5473 Ultrasound Imaging Using Transduction Effect

                                                    Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                    55 Pyroelectric Ceramics

                                                    Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                    Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                    Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                    551 Difference between Pyroelectric and Ferroelectric Material

                                                    Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                    Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                    552 Theory of Piezoelectric Materials

                                                    From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                    (537)

                                                    Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                    Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                    (538)

                                                    Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                    we write

                                                    Δ OR

                                                    Δ (539)

                                                    Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                    Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                    (540)

                                                    The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                    As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                    553 Measurement of Pyroelectric Coefficient

                                                    One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                    (541)

                                                    Where Ip is the pyrocurrent and is given as

                                                    (542)

                                                    where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                    respectively

                                                    Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                    554 Direct and Indirect Effect

                                                    Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                    Since change in the polarization can also be expressed as depending

                                                    upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                    Figure 531 Direct-Indirect effect animation

                                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                    555 Common Pyroelectric Materials

                                                    Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                    The most common materials are tabulated below

                                                    Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                    LiTaO3 single crystal Hexagonal 665 -230

                                                    075Pb(Mg13-Nb23)O3-025PbTiO3

                                                    (PMN-PT) Ceramic

                                                    Perovskite 150 -1300

                                                    Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                    Triglycine sulphate

                                                    (NH2CH2COOH)3H2SO4

                                                    Sulphate 49 -280

                                                    Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                    5551 Triglycine Sulphate (TGS)

                                                    High pyroelectric coefficient

                                                    Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                    Can be modified to withstand temperatures above Curie point without depoling

                                                    Used in thermal imaging cameras

                                                    5552 Polyvinylidene Fluoride (PVDF)

                                                    Poor pyroelectric coefficient

                                                    Readily available in large areas of thin film

                                                    More stable to heat vacuum and moisture than TGS mechanically robust

                                                    Low heat conductivity and low permittivity

                                                    High loss tangent

                                                    Commonly used for burglar alarms

                                                    5553 Perovskite Ferroelectric Ceramics

                                                    Generally robust and insensitive to moisture and vacuum

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                                                    High pyroelectric coefficient and low loss

                                                    Better operation near TC

                                                    Strong dependence on composition

                                                    As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                    RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                    556 Common Applications

                                                    5561 Burglar Alarms

                                                    Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                    Figure 532 Working of an IR intruder alarm

                                                    (Courtesy copy DoITPoMS University ofCambridge)

                                                    5562 Infrared or Thermal Imaging

                                                    Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                    The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                    A typical photograph generated from IR imaging looks like this

                                                    Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                    Here is a simple explanation of how IT imaging using pyroelectrics works

                                                    A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                    This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                    Figure 534 Process of imagecreation

                                                    5563 Pollutant Control

                                                    The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                    Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                    Figure 535 Gas detection using a pyroelectricdetector

                                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                                    Module 5 Nonlinear Dielectrics

                                                    Summary

                                                    Summary

                                                    Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                      Figure 5 19 Animation of a camera flash using aferroelectric (Reproduced from DOITPOMSLibrary University of Cambridge UK)

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                                                      Module 5 Nonlinear Dielectrics

                                                      Summary

                                                      Summary

                                                      In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                                      can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                                      and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                                      binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                                      One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                      5474 Actuators

                                                      In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                                      In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                                      You can have it in two forms

                                                      Direct Piezo Actuators with strokes lower than 100 microns or so and

                                                      Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                                      Some of the examples of applications are

                                                      Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                                      Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                                      Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                                      Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                                      In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                                      As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                      5475 Frequency Standards

                                                      Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                                      Quartz clocks

                                                      Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                                      Module 5 Nonlinear Dielectrics

                                                      Summary

                                                      Summary

                                                      Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                      54 Piezoelectric Ceramics

                                                      Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                                      Pb(ZrTi)O3)

                                                      An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                                      For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                      541 Direct Piezoelectric Effect

                                                      Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                      (533)

                                                      where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                      542 Reverse or Converse Piezoelectric Effect

                                                      The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                      (534)

                                                      where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                      Figure 520 Direct and Converse PiezoelectricEffects

                                                      The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                      543 Poling of Piezoelectric Materials

                                                      As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                      The values of piezoelectric coefficient of some materials are given below

                                                      Material Piezoelectric Constant d(pmV)

                                                      Quartz 23

                                                      Barium Titanate 100-149

                                                      Lead Niobate 80-85

                                                      Lead zirconate titanate 250-365

                                                      So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                      Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                      field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                      Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                      544 Depolarization of Piezoelectrics

                                                      Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                      polarization or rather result in alignment of dipoles gets lost

                                                      Figure 522 Animation on depolarization offerroelectrics

                                                      (Courtesy copy DoITPoMS University of Cambridge)

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                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                      545 Common PIezoelectric Materials

                                                      5451 Barium Titanate (BaTiO3)

                                                      This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                      used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                      Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                      1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                      must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                      5452 Pb(ZrTi)O3 or PZT

                                                      PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                      The phase diagram of PZT is shown below

                                                      Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                      The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                      lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                      few poling directions available making it a useful piezoelectric

                                                      Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                      546 Measurement of Piezoelectric Properties

                                                      Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                      In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                      Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                      The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                      (535)

                                                      Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                      (536)

                                                      Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                      One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                      547 Applications of Piezoelectric Ceramics

                                                      Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                      5471 Power Generation

                                                      Gas Lighter

                                                      Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                      Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                      One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                      Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                      Power Transformer

                                                      A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                      An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                      Figure 526 Schematic of a piezoelectrictransformer

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                                                      Module 5 Special Dielectrics Piezoelectric Ceramics

                                                      5472 Piezoelectric Sensors

                                                      Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                      Other sensor applications are

                                                      Detection and generation of sonar waves

                                                      To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                      To detect the precise moment of fuel injection in an automotive engine

                                                      Detection of acoustic emissions in acoustic emission testing

                                                      Microbalances as very sensitive chemical and biological sensors

                                                      Strain gauges

                                                      Medical applications using ultrasound waves

                                                      Kidney stone treatment

                                                      In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                      Figure 527 Ultrasonic waves creation and

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                                                      kidney stone treatment and ultrasound imagingof the fetus

                                                      (Courtesy copy DoITPoMS University of Cambridge)

                                                      5473 Ultrasound Imaging Using Transduction Effect

                                                      Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                      55 Pyroelectric Ceramics

                                                      Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                      Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                      Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                      551 Difference between Pyroelectric and Ferroelectric Material

                                                      Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                      Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                      552 Theory of Piezoelectric Materials

                                                      From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                      (537)

                                                      Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                      Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                      (538)

                                                      Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                      we write

                                                      Δ OR

                                                      Δ (539)

                                                      Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                      Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                      (540)

                                                      The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                      As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                      553 Measurement of Pyroelectric Coefficient

                                                      One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                      (541)

                                                      Where Ip is the pyrocurrent and is given as

                                                      (542)

                                                      where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                      respectively

                                                      Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                      554 Direct and Indirect Effect

                                                      Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                      Since change in the polarization can also be expressed as depending

                                                      upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                      Figure 531 Direct-Indirect effect animation

                                                      (Courtesy copy DoITPoMS University of Cambridge)

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                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                      555 Common Pyroelectric Materials

                                                      Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                      The most common materials are tabulated below

                                                      Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                      LiTaO3 single crystal Hexagonal 665 -230

                                                      075Pb(Mg13-Nb23)O3-025PbTiO3

                                                      (PMN-PT) Ceramic

                                                      Perovskite 150 -1300

                                                      Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                      Triglycine sulphate

                                                      (NH2CH2COOH)3H2SO4

                                                      Sulphate 49 -280

                                                      Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                      5551 Triglycine Sulphate (TGS)

                                                      High pyroelectric coefficient

                                                      Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                      Can be modified to withstand temperatures above Curie point without depoling

                                                      Used in thermal imaging cameras

                                                      5552 Polyvinylidene Fluoride (PVDF)

                                                      Poor pyroelectric coefficient

                                                      Readily available in large areas of thin film

                                                      More stable to heat vacuum and moisture than TGS mechanically robust

                                                      Low heat conductivity and low permittivity

                                                      High loss tangent

                                                      Commonly used for burglar alarms

                                                      5553 Perovskite Ferroelectric Ceramics

                                                      Generally robust and insensitive to moisture and vacuum

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                                                      High pyroelectric coefficient and low loss

                                                      Better operation near TC

                                                      Strong dependence on composition

                                                      As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                      RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                      556 Common Applications

                                                      5561 Burglar Alarms

                                                      Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                      Figure 532 Working of an IR intruder alarm

                                                      (Courtesy copy DoITPoMS University ofCambridge)

                                                      5562 Infrared or Thermal Imaging

                                                      Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                      The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                      A typical photograph generated from IR imaging looks like this

                                                      Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                      Here is a simple explanation of how IT imaging using pyroelectrics works

                                                      A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                      This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                      Figure 534 Process of imagecreation

                                                      5563 Pollutant Control

                                                      The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                      Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                      Figure 535 Gas detection using a pyroelectricdetector

                                                      (Courtesy copy DoITPoMS University of Cambridge)

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                                                      Module 5 Nonlinear Dielectrics

                                                      Summary

                                                      Summary

                                                      Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                        Module 5 Nonlinear Dielectrics

                                                        Summary

                                                        Summary

                                                        In this section we discussed ferroelectric materials which are characterized by Noncentrosymmetricstructure materials exhibiting a polar axis whose direction can be reversed by changing the directionof applied field These materials also follow a Curie-Weiss behavior ie a transition from ferroelectricto paraelectric phase upon heating across a Curie temperature Tc The nature of phase transition

                                                        can be first or second order depending upon the type of material which is reflected in the waypolarization changes as a function of temperature Ferroelectric materials when switched underalternating fields show a typical hysteresis like behavior showing two stable polarization states +PR

                                                        and ndashPR which are useful for memory application where these can be used as stated lsquo0rsquo and lsquo1rsquo for

                                                        binary data storage The reversal of polarization takes place by domain reversal which is aphenomenon happening by nucleation and growth of new domains Typical examples of commonlyused ferroelectric materials are perovskite structured compounds eg PbTiO3 BaTiO3 Pb(ZrTi)O3

                                                        One of the most touted applications of ferroelectric materials is in nonvolatile ferroelectric memoriesbesides other applications such as flash bulbs and sensors and actuators

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                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                        5474 Actuators

                                                        In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                                        In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                                        You can have it in two forms

                                                        Direct Piezo Actuators with strokes lower than 100 microns or so and

                                                        Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                                        Some of the examples of applications are

                                                        Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                                        Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                                        Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                                        Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                                        In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                                        As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                        5475 Frequency Standards

                                                        Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                                        Quartz clocks

                                                        Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                                        Module 5 Nonlinear Dielectrics

                                                        Summary

                                                        Summary

                                                        Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                        54 Piezoelectric Ceramics

                                                        Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                                        Pb(ZrTi)O3)

                                                        An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                                        For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                        541 Direct Piezoelectric Effect

                                                        Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                        (533)

                                                        where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                        542 Reverse or Converse Piezoelectric Effect

                                                        The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                        (534)

                                                        where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                        Figure 520 Direct and Converse PiezoelectricEffects

                                                        The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                        543 Poling of Piezoelectric Materials

                                                        As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                        The values of piezoelectric coefficient of some materials are given below

                                                        Material Piezoelectric Constant d(pmV)

                                                        Quartz 23

                                                        Barium Titanate 100-149

                                                        Lead Niobate 80-85

                                                        Lead zirconate titanate 250-365

                                                        So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                        Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                        field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                        Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                        544 Depolarization of Piezoelectrics

                                                        Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                        polarization or rather result in alignment of dipoles gets lost

                                                        Figure 522 Animation on depolarization offerroelectrics

                                                        (Courtesy copy DoITPoMS University of Cambridge)

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                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                        545 Common PIezoelectric Materials

                                                        5451 Barium Titanate (BaTiO3)

                                                        This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                        used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                        Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                        1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                        must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                        5452 Pb(ZrTi)O3 or PZT

                                                        PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                        The phase diagram of PZT is shown below

                                                        Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                        The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                        lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                        few poling directions available making it a useful piezoelectric

                                                        Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                        546 Measurement of Piezoelectric Properties

                                                        Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                        In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                        Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                        The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                        (535)

                                                        Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                        (536)

                                                        Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                        One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                        547 Applications of Piezoelectric Ceramics

                                                        Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                        5471 Power Generation

                                                        Gas Lighter

                                                        Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                        Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                        One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                        Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                        Power Transformer

                                                        A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                        An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                        Figure 526 Schematic of a piezoelectrictransformer

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                                                        Module 5 Special Dielectrics Piezoelectric Ceramics

                                                        5472 Piezoelectric Sensors

                                                        Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                        Other sensor applications are

                                                        Detection and generation of sonar waves

                                                        To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                        To detect the precise moment of fuel injection in an automotive engine

                                                        Detection of acoustic emissions in acoustic emission testing

                                                        Microbalances as very sensitive chemical and biological sensors

                                                        Strain gauges

                                                        Medical applications using ultrasound waves

                                                        Kidney stone treatment

                                                        In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                        Figure 527 Ultrasonic waves creation and

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                                                        kidney stone treatment and ultrasound imagingof the fetus

                                                        (Courtesy copy DoITPoMS University of Cambridge)

                                                        5473 Ultrasound Imaging Using Transduction Effect

                                                        Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                        55 Pyroelectric Ceramics

                                                        Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                        Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                        Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                        551 Difference between Pyroelectric and Ferroelectric Material

                                                        Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                        Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                        552 Theory of Piezoelectric Materials

                                                        From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                        (537)

                                                        Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                        Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                        (538)

                                                        Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                        we write

                                                        Δ OR

                                                        Δ (539)

                                                        Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                        Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                        (540)

                                                        The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                        As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                        553 Measurement of Pyroelectric Coefficient

                                                        One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                        (541)

                                                        Where Ip is the pyrocurrent and is given as

                                                        (542)

                                                        where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                        respectively

                                                        Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                        554 Direct and Indirect Effect

                                                        Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                        Since change in the polarization can also be expressed as depending

                                                        upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                        Figure 531 Direct-Indirect effect animation

                                                        (Courtesy copy DoITPoMS University of Cambridge)

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                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                        555 Common Pyroelectric Materials

                                                        Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                        The most common materials are tabulated below

                                                        Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                        LiTaO3 single crystal Hexagonal 665 -230

                                                        075Pb(Mg13-Nb23)O3-025PbTiO3

                                                        (PMN-PT) Ceramic

                                                        Perovskite 150 -1300

                                                        Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                        Triglycine sulphate

                                                        (NH2CH2COOH)3H2SO4

                                                        Sulphate 49 -280

                                                        Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                        5551 Triglycine Sulphate (TGS)

                                                        High pyroelectric coefficient

                                                        Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                        Can be modified to withstand temperatures above Curie point without depoling

                                                        Used in thermal imaging cameras

                                                        5552 Polyvinylidene Fluoride (PVDF)

                                                        Poor pyroelectric coefficient

                                                        Readily available in large areas of thin film

                                                        More stable to heat vacuum and moisture than TGS mechanically robust

                                                        Low heat conductivity and low permittivity

                                                        High loss tangent

                                                        Commonly used for burglar alarms

                                                        5553 Perovskite Ferroelectric Ceramics

                                                        Generally robust and insensitive to moisture and vacuum

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                                                        High pyroelectric coefficient and low loss

                                                        Better operation near TC

                                                        Strong dependence on composition

                                                        As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                        RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                        556 Common Applications

                                                        5561 Burglar Alarms

                                                        Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                        Figure 532 Working of an IR intruder alarm

                                                        (Courtesy copy DoITPoMS University ofCambridge)

                                                        5562 Infrared or Thermal Imaging

                                                        Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                        The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                        A typical photograph generated from IR imaging looks like this

                                                        Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                        Here is a simple explanation of how IT imaging using pyroelectrics works

                                                        A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                        This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                        Figure 534 Process of imagecreation

                                                        5563 Pollutant Control

                                                        The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                        Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                        Figure 535 Gas detection using a pyroelectricdetector

                                                        (Courtesy copy DoITPoMS University of Cambridge)

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                                                        Module 5 Nonlinear Dielectrics

                                                        Summary

                                                        Summary

                                                        Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                          5474 Actuators

                                                          In the precision engineering applications precise linear or rotational movements are required forachieving technological perfection In piezoelectrics application of high electric fields (without usingoscillations) correspond to only tiny changes in the crystal dimension and these changes can be veryprecise achieving better than a micrometer precision This ability makes these materials useful asprecise actuators for achieving very precise motions

                                                          In these applications typically multilayer ceramics consisting of layers thinner than 100 microns areused One can achieve very high field in the multilayered materials using voltages lower than 150-200 V not very high voltages

                                                          You can have it in two forms

                                                          Direct Piezo Actuators with strokes lower than 100 microns or so and

                                                          Amplified Piezoelectric Actuators which can yield millimeter long strokes

                                                          Some of the examples of applications are

                                                          Piezoelectric motors consisting of piezoelectric elements which apply a directional force to anaxle causing it to rotate As the distances travelled are extremely small it is a very high-precision replacement for the conventional stepper motor

                                                          Scanning force microscopes use inverse piezoelectric effect to keep the sensing needle closeto the probe

                                                          Laser mirror alignment in the laser electronics helping maintain accurate optical conditionsinside the laser cavity to optimize the beam output

                                                          Loudspeakers Voltage is converted to mechanical movement of a piezoelectric polymer film

                                                          In inkjet printers where piezoelectrics are used to control ink flow from the print head to thepaper

                                                          As fuel injectors in diesel engines in place of commonly used solenoid valve devices

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                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                          5475 Frequency Standards

                                                          Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                                          Quartz clocks

                                                          Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                                          Module 5 Nonlinear Dielectrics

                                                          Summary

                                                          Summary

                                                          Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                          54 Piezoelectric Ceramics

                                                          Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                                          Pb(ZrTi)O3)

                                                          An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                                          For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                          541 Direct Piezoelectric Effect

                                                          Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                          (533)

                                                          where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                          542 Reverse or Converse Piezoelectric Effect

                                                          The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                          (534)

                                                          where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                          Figure 520 Direct and Converse PiezoelectricEffects

                                                          The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                          543 Poling of Piezoelectric Materials

                                                          As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                          The values of piezoelectric coefficient of some materials are given below

                                                          Material Piezoelectric Constant d(pmV)

                                                          Quartz 23

                                                          Barium Titanate 100-149

                                                          Lead Niobate 80-85

                                                          Lead zirconate titanate 250-365

                                                          So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                          Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                          field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                          Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                          544 Depolarization of Piezoelectrics

                                                          Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                          polarization or rather result in alignment of dipoles gets lost

                                                          Figure 522 Animation on depolarization offerroelectrics

                                                          (Courtesy copy DoITPoMS University of Cambridge)

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                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                          545 Common PIezoelectric Materials

                                                          5451 Barium Titanate (BaTiO3)

                                                          This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                          used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                          Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                          1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                          must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                          5452 Pb(ZrTi)O3 or PZT

                                                          PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                          The phase diagram of PZT is shown below

                                                          Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                          The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                          lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                          few poling directions available making it a useful piezoelectric

                                                          Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                          546 Measurement of Piezoelectric Properties

                                                          Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                          In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                          Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                          The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                          (535)

                                                          Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                          (536)

                                                          Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                          One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                          547 Applications of Piezoelectric Ceramics

                                                          Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                          5471 Power Generation

                                                          Gas Lighter

                                                          Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                          Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                          One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                          Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                          Power Transformer

                                                          A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                          An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                          Figure 526 Schematic of a piezoelectrictransformer

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                                                          Module 5 Special Dielectrics Piezoelectric Ceramics

                                                          5472 Piezoelectric Sensors

                                                          Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                          Other sensor applications are

                                                          Detection and generation of sonar waves

                                                          To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                          To detect the precise moment of fuel injection in an automotive engine

                                                          Detection of acoustic emissions in acoustic emission testing

                                                          Microbalances as very sensitive chemical and biological sensors

                                                          Strain gauges

                                                          Medical applications using ultrasound waves

                                                          Kidney stone treatment

                                                          In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                          Figure 527 Ultrasonic waves creation and

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                                                          kidney stone treatment and ultrasound imagingof the fetus

                                                          (Courtesy copy DoITPoMS University of Cambridge)

                                                          5473 Ultrasound Imaging Using Transduction Effect

                                                          Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                          55 Pyroelectric Ceramics

                                                          Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                          Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                          Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                          551 Difference between Pyroelectric and Ferroelectric Material

                                                          Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                          Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                          552 Theory of Piezoelectric Materials

                                                          From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                          (537)

                                                          Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                          Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                          (538)

                                                          Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                          we write

                                                          Δ OR

                                                          Δ (539)

                                                          Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                          Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                          (540)

                                                          The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                          As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                          553 Measurement of Pyroelectric Coefficient

                                                          One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                          (541)

                                                          Where Ip is the pyrocurrent and is given as

                                                          (542)

                                                          where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                          respectively

                                                          Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                          554 Direct and Indirect Effect

                                                          Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                          Since change in the polarization can also be expressed as depending

                                                          upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                          Figure 531 Direct-Indirect effect animation

                                                          (Courtesy copy DoITPoMS University of Cambridge)

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                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                          555 Common Pyroelectric Materials

                                                          Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                          The most common materials are tabulated below

                                                          Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                          LiTaO3 single crystal Hexagonal 665 -230

                                                          075Pb(Mg13-Nb23)O3-025PbTiO3

                                                          (PMN-PT) Ceramic

                                                          Perovskite 150 -1300

                                                          Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                          Triglycine sulphate

                                                          (NH2CH2COOH)3H2SO4

                                                          Sulphate 49 -280

                                                          Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                          5551 Triglycine Sulphate (TGS)

                                                          High pyroelectric coefficient

                                                          Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                          Can be modified to withstand temperatures above Curie point without depoling

                                                          Used in thermal imaging cameras

                                                          5552 Polyvinylidene Fluoride (PVDF)

                                                          Poor pyroelectric coefficient

                                                          Readily available in large areas of thin film

                                                          More stable to heat vacuum and moisture than TGS mechanically robust

                                                          Low heat conductivity and low permittivity

                                                          High loss tangent

                                                          Commonly used for burglar alarms

                                                          5553 Perovskite Ferroelectric Ceramics

                                                          Generally robust and insensitive to moisture and vacuum

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                                                          High pyroelectric coefficient and low loss

                                                          Better operation near TC

                                                          Strong dependence on composition

                                                          As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                          RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                          556 Common Applications

                                                          5561 Burglar Alarms

                                                          Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                          Figure 532 Working of an IR intruder alarm

                                                          (Courtesy copy DoITPoMS University ofCambridge)

                                                          5562 Infrared or Thermal Imaging

                                                          Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                          The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                          A typical photograph generated from IR imaging looks like this

                                                          Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                          Here is a simple explanation of how IT imaging using pyroelectrics works

                                                          A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                          This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                          Figure 534 Process of imagecreation

                                                          5563 Pollutant Control

                                                          The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                          Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                          Figure 535 Gas detection using a pyroelectricdetector

                                                          (Courtesy copy DoITPoMS University of Cambridge)

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                                                          Module 5 Nonlinear Dielectrics

                                                          Summary

                                                          Summary

                                                          Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                            5475 Frequency Standards

                                                            Here quartz is most commonly used material as its piezoelectric properties are useful as standard offrequency

                                                            Quartz clocks

                                                            Watches use a quartz tuning fork which uses a combination of both direct and conversepiezoelectricity to give rise to a regularly timed series of electrical pulses that is used to mark time The quartz crystal has a very accurately defined natural frequency of vibration at which it prefers tooscillate and this is used to stabilize the frequency of a periodic voltage applied to the crystalThe same principle is critical in all radio transmitters and receivers and in computers where itcreates a clock pulse Both of these usually use a frequency multiplier to reach the megahertz andgigahertz ranges

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                                                            Module 5 Nonlinear Dielectrics

                                                            Summary

                                                            Summary

                                                            Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                            54 Piezoelectric Ceramics

                                                            Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                                            Pb(ZrTi)O3)

                                                            An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                                            For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                            541 Direct Piezoelectric Effect

                                                            Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                            (533)

                                                            where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                            542 Reverse or Converse Piezoelectric Effect

                                                            The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                            (534)

                                                            where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                            Figure 520 Direct and Converse PiezoelectricEffects

                                                            The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                            543 Poling of Piezoelectric Materials

                                                            As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                            The values of piezoelectric coefficient of some materials are given below

                                                            Material Piezoelectric Constant d(pmV)

                                                            Quartz 23

                                                            Barium Titanate 100-149

                                                            Lead Niobate 80-85

                                                            Lead zirconate titanate 250-365

                                                            So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                            Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                            field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                            Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                            544 Depolarization of Piezoelectrics

                                                            Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                            polarization or rather result in alignment of dipoles gets lost

                                                            Figure 522 Animation on depolarization offerroelectrics

                                                            (Courtesy copy DoITPoMS University of Cambridge)

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                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                            545 Common PIezoelectric Materials

                                                            5451 Barium Titanate (BaTiO3)

                                                            This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                            used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                            Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                            1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                            must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                            5452 Pb(ZrTi)O3 or PZT

                                                            PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                            The phase diagram of PZT is shown below

                                                            Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                            The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                            lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                            few poling directions available making it a useful piezoelectric

                                                            Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                            546 Measurement of Piezoelectric Properties

                                                            Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                            In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                            Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                            The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                            (535)

                                                            Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                            (536)

                                                            Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                            One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                            547 Applications of Piezoelectric Ceramics

                                                            Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                            5471 Power Generation

                                                            Gas Lighter

                                                            Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                            Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                            One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                            Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                            Power Transformer

                                                            A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                            An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                            Figure 526 Schematic of a piezoelectrictransformer

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                                                            Module 5 Special Dielectrics Piezoelectric Ceramics

                                                            5472 Piezoelectric Sensors

                                                            Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                            Other sensor applications are

                                                            Detection and generation of sonar waves

                                                            To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                            To detect the precise moment of fuel injection in an automotive engine

                                                            Detection of acoustic emissions in acoustic emission testing

                                                            Microbalances as very sensitive chemical and biological sensors

                                                            Strain gauges

                                                            Medical applications using ultrasound waves

                                                            Kidney stone treatment

                                                            In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                            Figure 527 Ultrasonic waves creation and

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                                                            kidney stone treatment and ultrasound imagingof the fetus

                                                            (Courtesy copy DoITPoMS University of Cambridge)

                                                            5473 Ultrasound Imaging Using Transduction Effect

                                                            Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                            55 Pyroelectric Ceramics

                                                            Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                            Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                            Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                            551 Difference between Pyroelectric and Ferroelectric Material

                                                            Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                            Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                            552 Theory of Piezoelectric Materials

                                                            From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                            (537)

                                                            Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                            Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                            (538)

                                                            Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                            we write

                                                            Δ OR

                                                            Δ (539)

                                                            Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                            Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                            (540)

                                                            The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                            As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                            553 Measurement of Pyroelectric Coefficient

                                                            One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                            (541)

                                                            Where Ip is the pyrocurrent and is given as

                                                            (542)

                                                            where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                            respectively

                                                            Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                            554 Direct and Indirect Effect

                                                            Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                            Since change in the polarization can also be expressed as depending

                                                            upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                            Figure 531 Direct-Indirect effect animation

                                                            (Courtesy copy DoITPoMS University of Cambridge)

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                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                            555 Common Pyroelectric Materials

                                                            Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                            The most common materials are tabulated below

                                                            Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                            LiTaO3 single crystal Hexagonal 665 -230

                                                            075Pb(Mg13-Nb23)O3-025PbTiO3

                                                            (PMN-PT) Ceramic

                                                            Perovskite 150 -1300

                                                            Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                            Triglycine sulphate

                                                            (NH2CH2COOH)3H2SO4

                                                            Sulphate 49 -280

                                                            Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                            5551 Triglycine Sulphate (TGS)

                                                            High pyroelectric coefficient

                                                            Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                            Can be modified to withstand temperatures above Curie point without depoling

                                                            Used in thermal imaging cameras

                                                            5552 Polyvinylidene Fluoride (PVDF)

                                                            Poor pyroelectric coefficient

                                                            Readily available in large areas of thin film

                                                            More stable to heat vacuum and moisture than TGS mechanically robust

                                                            Low heat conductivity and low permittivity

                                                            High loss tangent

                                                            Commonly used for burglar alarms

                                                            5553 Perovskite Ferroelectric Ceramics

                                                            Generally robust and insensitive to moisture and vacuum

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                                                            High pyroelectric coefficient and low loss

                                                            Better operation near TC

                                                            Strong dependence on composition

                                                            As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                            RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                            556 Common Applications

                                                            5561 Burglar Alarms

                                                            Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                            Figure 532 Working of an IR intruder alarm

                                                            (Courtesy copy DoITPoMS University ofCambridge)

                                                            5562 Infrared or Thermal Imaging

                                                            Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                            The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                            A typical photograph generated from IR imaging looks like this

                                                            Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                            Here is a simple explanation of how IT imaging using pyroelectrics works

                                                            A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                            This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                            Figure 534 Process of imagecreation

                                                            5563 Pollutant Control

                                                            The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                            Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                            Figure 535 Gas detection using a pyroelectricdetector

                                                            (Courtesy copy DoITPoMS University of Cambridge)

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                                                            Module 5 Nonlinear Dielectrics

                                                            Summary

                                                            Summary

                                                            Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                              Module 5 Nonlinear Dielectrics

                                                              Summary

                                                              Summary

                                                              Piezoelectric materials are noncentrosymmetric materials which show coupling of mechanical andelectrical properties The characteristics of these materials in giving rise to a potential when strainedor a strain induced displacement when subjected to a varying electric potential gives rise to a varietyof useful applications such as sensors actuators transducers etc Interestingly many ferroelectricshave also found useful applications in such applications mainly because of their superiorpiezoelectric properties

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                                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                              54 Piezoelectric Ceramics

                                                              Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                                              Pb(ZrTi)O3)

                                                              An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                                              For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                              541 Direct Piezoelectric Effect

                                                              Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                              (533)

                                                              where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                              542 Reverse or Converse Piezoelectric Effect

                                                              The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                              (534)

                                                              where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                              Figure 520 Direct and Converse PiezoelectricEffects

                                                              The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                              543 Poling of Piezoelectric Materials

                                                              As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                              The values of piezoelectric coefficient of some materials are given below

                                                              Material Piezoelectric Constant d(pmV)

                                                              Quartz 23

                                                              Barium Titanate 100-149

                                                              Lead Niobate 80-85

                                                              Lead zirconate titanate 250-365

                                                              So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                              Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                              field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                              Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                              544 Depolarization of Piezoelectrics

                                                              Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                              polarization or rather result in alignment of dipoles gets lost

                                                              Figure 522 Animation on depolarization offerroelectrics

                                                              (Courtesy copy DoITPoMS University of Cambridge)

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                                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                              545 Common PIezoelectric Materials

                                                              5451 Barium Titanate (BaTiO3)

                                                              This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                              used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                              Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                              1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                              must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                              5452 Pb(ZrTi)O3 or PZT

                                                              PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                              The phase diagram of PZT is shown below

                                                              Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                              The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                              lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                              few poling directions available making it a useful piezoelectric

                                                              Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                              546 Measurement of Piezoelectric Properties

                                                              Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                              In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                              Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                              The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                              (535)

                                                              Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                              (536)

                                                              Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                              One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                              547 Applications of Piezoelectric Ceramics

                                                              Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                              5471 Power Generation

                                                              Gas Lighter

                                                              Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                              Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                              One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                              Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                              Power Transformer

                                                              A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                              An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                              Figure 526 Schematic of a piezoelectrictransformer

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                                                              Module 5 Special Dielectrics Piezoelectric Ceramics

                                                              5472 Piezoelectric Sensors

                                                              Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                              Other sensor applications are

                                                              Detection and generation of sonar waves

                                                              To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                              To detect the precise moment of fuel injection in an automotive engine

                                                              Detection of acoustic emissions in acoustic emission testing

                                                              Microbalances as very sensitive chemical and biological sensors

                                                              Strain gauges

                                                              Medical applications using ultrasound waves

                                                              Kidney stone treatment

                                                              In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                              Figure 527 Ultrasonic waves creation and

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                                                              kidney stone treatment and ultrasound imagingof the fetus

                                                              (Courtesy copy DoITPoMS University of Cambridge)

                                                              5473 Ultrasound Imaging Using Transduction Effect

                                                              Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                              55 Pyroelectric Ceramics

                                                              Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                              Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                              Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                              551 Difference between Pyroelectric and Ferroelectric Material

                                                              Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                              Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                              552 Theory of Piezoelectric Materials

                                                              From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                              (537)

                                                              Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                              Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                              (538)

                                                              Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                              we write

                                                              Δ OR

                                                              Δ (539)

                                                              Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                              Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                              (540)

                                                              The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                              As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                              553 Measurement of Pyroelectric Coefficient

                                                              One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                              (541)

                                                              Where Ip is the pyrocurrent and is given as

                                                              (542)

                                                              where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                              respectively

                                                              Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                              554 Direct and Indirect Effect

                                                              Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                              Since change in the polarization can also be expressed as depending

                                                              upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                              Figure 531 Direct-Indirect effect animation

                                                              (Courtesy copy DoITPoMS University of Cambridge)

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                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                              555 Common Pyroelectric Materials

                                                              Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                              The most common materials are tabulated below

                                                              Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                              LiTaO3 single crystal Hexagonal 665 -230

                                                              075Pb(Mg13-Nb23)O3-025PbTiO3

                                                              (PMN-PT) Ceramic

                                                              Perovskite 150 -1300

                                                              Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                              Triglycine sulphate

                                                              (NH2CH2COOH)3H2SO4

                                                              Sulphate 49 -280

                                                              Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                              5551 Triglycine Sulphate (TGS)

                                                              High pyroelectric coefficient

                                                              Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                              Can be modified to withstand temperatures above Curie point without depoling

                                                              Used in thermal imaging cameras

                                                              5552 Polyvinylidene Fluoride (PVDF)

                                                              Poor pyroelectric coefficient

                                                              Readily available in large areas of thin film

                                                              More stable to heat vacuum and moisture than TGS mechanically robust

                                                              Low heat conductivity and low permittivity

                                                              High loss tangent

                                                              Commonly used for burglar alarms

                                                              5553 Perovskite Ferroelectric Ceramics

                                                              Generally robust and insensitive to moisture and vacuum

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                                                              High pyroelectric coefficient and low loss

                                                              Better operation near TC

                                                              Strong dependence on composition

                                                              As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                              RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                              556 Common Applications

                                                              5561 Burglar Alarms

                                                              Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                              Figure 532 Working of an IR intruder alarm

                                                              (Courtesy copy DoITPoMS University ofCambridge)

                                                              5562 Infrared or Thermal Imaging

                                                              Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                              The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                              A typical photograph generated from IR imaging looks like this

                                                              Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                              Here is a simple explanation of how IT imaging using pyroelectrics works

                                                              A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                              This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                              Figure 534 Process of imagecreation

                                                              5563 Pollutant Control

                                                              The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                              Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                              Figure 535 Gas detection using a pyroelectricdetector

                                                              (Courtesy copy DoITPoMS University of Cambridge)

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                                                              Module 5 Nonlinear Dielectrics

                                                              Summary

                                                              Summary

                                                              Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                54 Piezoelectric Ceramics

                                                                Piezoelectric effect was discovered by Jacques and Pierre Curie in 1888 Direct piezoelectric effectis the ability of some materials to create an electric potential in response to applied mechanicalstress The applied stress changes the polarization density within the materials volume leading tothe observed potential As a requirement only materials with non-centrosymmetric crystal structurecan exhibit piezoelectric effect Some of the commonly usedknown piezoelectric materials arequartz (SiO2) zinc oxide (ZnO) polyvinylidenefluoride (PVDF) and lead zirconate titanate (PZT or

                                                                Pb(ZrTi)O3)

                                                                An oscillating applied stress on a piezoelectric material can give rise to the field which can beapplied to an electrical load such as a bulb Another example can be charging of your mobile or anyother device in your backpack while you walk You could not achieve the same while standing

                                                                For a detailed discussion on the piezoelectric properties materials and applications readers canrefer to the bibliography provided in the beginning of the module

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                                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                541 Direct Piezoelectric Effect

                                                                Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                                (533)

                                                                where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                                542 Reverse or Converse Piezoelectric Effect

                                                                The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                                (534)

                                                                where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                                Figure 520 Direct and Converse PiezoelectricEffects

                                                                The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                543 Poling of Piezoelectric Materials

                                                                As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                                The values of piezoelectric coefficient of some materials are given below

                                                                Material Piezoelectric Constant d(pmV)

                                                                Quartz 23

                                                                Barium Titanate 100-149

                                                                Lead Niobate 80-85

                                                                Lead zirconate titanate 250-365

                                                                So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                                Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                                field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                                Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                544 Depolarization of Piezoelectrics

                                                                Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                                polarization or rather result in alignment of dipoles gets lost

                                                                Figure 522 Animation on depolarization offerroelectrics

                                                                (Courtesy copy DoITPoMS University of Cambridge)

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                                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                545 Common PIezoelectric Materials

                                                                5451 Barium Titanate (BaTiO3)

                                                                This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                                used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                                Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                                1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                                must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                                5452 Pb(ZrTi)O3 or PZT

                                                                PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                                The phase diagram of PZT is shown below

                                                                Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                                The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                                lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                                few poling directions available making it a useful piezoelectric

                                                                Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                546 Measurement of Piezoelectric Properties

                                                                Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                                In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                                Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                                The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                                (535)

                                                                Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                                (536)

                                                                Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                                One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                547 Applications of Piezoelectric Ceramics

                                                                Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                5471 Power Generation

                                                                Gas Lighter

                                                                Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                Power Transformer

                                                                A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                Figure 526 Schematic of a piezoelectrictransformer

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                                                                Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                5472 Piezoelectric Sensors

                                                                Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                Other sensor applications are

                                                                Detection and generation of sonar waves

                                                                To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                To detect the precise moment of fuel injection in an automotive engine

                                                                Detection of acoustic emissions in acoustic emission testing

                                                                Microbalances as very sensitive chemical and biological sensors

                                                                Strain gauges

                                                                Medical applications using ultrasound waves

                                                                Kidney stone treatment

                                                                In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                Figure 527 Ultrasonic waves creation and

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                                                                kidney stone treatment and ultrasound imagingof the fetus

                                                                (Courtesy copy DoITPoMS University of Cambridge)

                                                                5473 Ultrasound Imaging Using Transduction Effect

                                                                Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                55 Pyroelectric Ceramics

                                                                Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                551 Difference between Pyroelectric and Ferroelectric Material

                                                                Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                552 Theory of Piezoelectric Materials

                                                                From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                (537)

                                                                Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                (538)

                                                                Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                we write

                                                                Δ OR

                                                                Δ (539)

                                                                Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                (540)

                                                                The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                553 Measurement of Pyroelectric Coefficient

                                                                One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                (541)

                                                                Where Ip is the pyrocurrent and is given as

                                                                (542)

                                                                where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                respectively

                                                                Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                554 Direct and Indirect Effect

                                                                Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                Since change in the polarization can also be expressed as depending

                                                                upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                Figure 531 Direct-Indirect effect animation

                                                                (Courtesy copy DoITPoMS University of Cambridge)

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                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                555 Common Pyroelectric Materials

                                                                Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                The most common materials are tabulated below

                                                                Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                LiTaO3 single crystal Hexagonal 665 -230

                                                                075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                (PMN-PT) Ceramic

                                                                Perovskite 150 -1300

                                                                Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                Triglycine sulphate

                                                                (NH2CH2COOH)3H2SO4

                                                                Sulphate 49 -280

                                                                Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                5551 Triglycine Sulphate (TGS)

                                                                High pyroelectric coefficient

                                                                Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                Can be modified to withstand temperatures above Curie point without depoling

                                                                Used in thermal imaging cameras

                                                                5552 Polyvinylidene Fluoride (PVDF)

                                                                Poor pyroelectric coefficient

                                                                Readily available in large areas of thin film

                                                                More stable to heat vacuum and moisture than TGS mechanically robust

                                                                Low heat conductivity and low permittivity

                                                                High loss tangent

                                                                Commonly used for burglar alarms

                                                                5553 Perovskite Ferroelectric Ceramics

                                                                Generally robust and insensitive to moisture and vacuum

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                                                                High pyroelectric coefficient and low loss

                                                                Better operation near TC

                                                                Strong dependence on composition

                                                                As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                556 Common Applications

                                                                5561 Burglar Alarms

                                                                Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                Figure 532 Working of an IR intruder alarm

                                                                (Courtesy copy DoITPoMS University ofCambridge)

                                                                5562 Infrared or Thermal Imaging

                                                                Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                A typical photograph generated from IR imaging looks like this

                                                                Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                Figure 534 Process of imagecreation

                                                                5563 Pollutant Control

                                                                The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                Figure 535 Gas detection using a pyroelectricdetector

                                                                (Courtesy copy DoITPoMS University of Cambridge)

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                                                                Module 5 Nonlinear Dielectrics

                                                                Summary

                                                                Summary

                                                                Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                  541 Direct Piezoelectric Effect

                                                                  Direct effect occurs when an applied stress to a material gives rise to a change in the polarizationdensity which in turn can be detected as electric field or potential across the sample Here thepolarization is directly proportional to the stress applied as described by the equation

                                                                  (533)

                                                                  where P is polarization s is applied stress and d is piezoelectric coefficient (actually a third ranktensor)

                                                                  542 Reverse or Converse Piezoelectric Effect

                                                                  The reverse is true is when an electric field is applied to the material and as a result a strain isinduced expressed as

                                                                  (534)

                                                                  where e is the strain induced d is the piezoelectric coefficient and E is the applied electric field

                                                                  Figure 520 Direct and Converse PiezoelectricEffects

                                                                  The direct piezoelectric effect is used as the basis for force pressure vibration and accelerationsensors while converse effect is used as a basis for actuator and displacement devices

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                                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                  543 Poling of Piezoelectric Materials

                                                                  As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                                  The values of piezoelectric coefficient of some materials are given below

                                                                  Material Piezoelectric Constant d(pmV)

                                                                  Quartz 23

                                                                  Barium Titanate 100-149

                                                                  Lead Niobate 80-85

                                                                  Lead zirconate titanate 250-365

                                                                  So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                                  Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                                  field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                                  Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                  544 Depolarization of Piezoelectrics

                                                                  Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                                  polarization or rather result in alignment of dipoles gets lost

                                                                  Figure 522 Animation on depolarization offerroelectrics

                                                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                  545 Common PIezoelectric Materials

                                                                  5451 Barium Titanate (BaTiO3)

                                                                  This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                                  used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                                  Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                                  1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                                  must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                                  5452 Pb(ZrTi)O3 or PZT

                                                                  PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                                  The phase diagram of PZT is shown below

                                                                  Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                                  The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                                  lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                                  few poling directions available making it a useful piezoelectric

                                                                  Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                  546 Measurement of Piezoelectric Properties

                                                                  Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                                  In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                                  Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                                  The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                                  (535)

                                                                  Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                                  (536)

                                                                  Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                                  One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                  547 Applications of Piezoelectric Ceramics

                                                                  Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                  5471 Power Generation

                                                                  Gas Lighter

                                                                  Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                  Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                  One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                  Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                  Power Transformer

                                                                  A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                  An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                  Figure 526 Schematic of a piezoelectrictransformer

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                                                                  Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                  5472 Piezoelectric Sensors

                                                                  Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                  Other sensor applications are

                                                                  Detection and generation of sonar waves

                                                                  To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                  To detect the precise moment of fuel injection in an automotive engine

                                                                  Detection of acoustic emissions in acoustic emission testing

                                                                  Microbalances as very sensitive chemical and biological sensors

                                                                  Strain gauges

                                                                  Medical applications using ultrasound waves

                                                                  Kidney stone treatment

                                                                  In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                  Figure 527 Ultrasonic waves creation and

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                                                                  kidney stone treatment and ultrasound imagingof the fetus

                                                                  (Courtesy copy DoITPoMS University of Cambridge)

                                                                  5473 Ultrasound Imaging Using Transduction Effect

                                                                  Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                  55 Pyroelectric Ceramics

                                                                  Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                  Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                  Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                  551 Difference between Pyroelectric and Ferroelectric Material

                                                                  Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                  Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                  552 Theory of Piezoelectric Materials

                                                                  From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                  (537)

                                                                  Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                  Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                  (538)

                                                                  Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                  we write

                                                                  Δ OR

                                                                  Δ (539)

                                                                  Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                  Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                  (540)

                                                                  The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                  As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                  553 Measurement of Pyroelectric Coefficient

                                                                  One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                  (541)

                                                                  Where Ip is the pyrocurrent and is given as

                                                                  (542)

                                                                  where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                  respectively

                                                                  Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                  554 Direct and Indirect Effect

                                                                  Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                  Since change in the polarization can also be expressed as depending

                                                                  upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                  Figure 531 Direct-Indirect effect animation

                                                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                  555 Common Pyroelectric Materials

                                                                  Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                  The most common materials are tabulated below

                                                                  Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                  LiTaO3 single crystal Hexagonal 665 -230

                                                                  075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                  (PMN-PT) Ceramic

                                                                  Perovskite 150 -1300

                                                                  Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                  Triglycine sulphate

                                                                  (NH2CH2COOH)3H2SO4

                                                                  Sulphate 49 -280

                                                                  Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                  5551 Triglycine Sulphate (TGS)

                                                                  High pyroelectric coefficient

                                                                  Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                  Can be modified to withstand temperatures above Curie point without depoling

                                                                  Used in thermal imaging cameras

                                                                  5552 Polyvinylidene Fluoride (PVDF)

                                                                  Poor pyroelectric coefficient

                                                                  Readily available in large areas of thin film

                                                                  More stable to heat vacuum and moisture than TGS mechanically robust

                                                                  Low heat conductivity and low permittivity

                                                                  High loss tangent

                                                                  Commonly used for burglar alarms

                                                                  5553 Perovskite Ferroelectric Ceramics

                                                                  Generally robust and insensitive to moisture and vacuum

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                                                                  High pyroelectric coefficient and low loss

                                                                  Better operation near TC

                                                                  Strong dependence on composition

                                                                  As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                  RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                  556 Common Applications

                                                                  5561 Burglar Alarms

                                                                  Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                  Figure 532 Working of an IR intruder alarm

                                                                  (Courtesy copy DoITPoMS University ofCambridge)

                                                                  5562 Infrared or Thermal Imaging

                                                                  Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                  The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                  A typical photograph generated from IR imaging looks like this

                                                                  Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                  Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                  A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                  This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                  Figure 534 Process of imagecreation

                                                                  5563 Pollutant Control

                                                                  The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                  Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                  Figure 535 Gas detection using a pyroelectricdetector

                                                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                                                  Module 5 Nonlinear Dielectrics

                                                                  Summary

                                                                  Summary

                                                                  Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                    543 Poling of Piezoelectric Materials

                                                                    As obvious from the previous sections (51 and 52) there are some piezoelectrics such as quartzwhich are not spontaneously polarized but get polarized upon application of stress while ferroelectricwhich are anyway piezoelectric in nature are spontaneously polarized and show a change ofpolarization upon application of stress

                                                                    The values of piezoelectric coefficient of some materials are given below

                                                                    Material Piezoelectric Constant d(pmV)

                                                                    Quartz 23

                                                                    Barium Titanate 100-149

                                                                    Lead Niobate 80-85

                                                                    Lead zirconate titanate 250-365

                                                                    So you can observe from this table that the level of strain generated is not so massive but is stillimportant because of preciseness and reversibility of the effect

                                                                    Most ferroelectrics have to be poled to be useful as a piezoelectric In the unpoled virgin state of thematerial the ferroelectric domains of single polarization direction are randomly distributed across thematerial and in such a situation the net polarization would be zero Application of stress to such amaterial would not achieve any change in the net polarization thus making it useless as apiezoelectric Poling ie application of a large electric field near Tc (just below Tc) orients the domains along the

                                                                    field and when the field is removed the domain structure does not get back to the original conditiongiving rise to a net polarization along a certain direction Now when stress is applied to such acrystal a noticeable change in the polarization can be observed

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                                                                    Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                    544 Depolarization of Piezoelectrics

                                                                    Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                                    polarization or rather result in alignment of dipoles gets lost

                                                                    Figure 522 Animation on depolarization offerroelectrics

                                                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                    545 Common PIezoelectric Materials

                                                                    5451 Barium Titanate (BaTiO3)

                                                                    This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                                    used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                                    Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                                    1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                                    must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                                    5452 Pb(ZrTi)O3 or PZT

                                                                    PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                                    The phase diagram of PZT is shown below

                                                                    Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                                    The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                                    lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                                    few poling directions available making it a useful piezoelectric

                                                                    Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                    546 Measurement of Piezoelectric Properties

                                                                    Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                                    In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                                    Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                                    The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                                    (535)

                                                                    Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                                    (536)

                                                                    Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                                    One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                                    Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                    547 Applications of Piezoelectric Ceramics

                                                                    Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                    5471 Power Generation

                                                                    Gas Lighter

                                                                    Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                    Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                    One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                    Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                    Power Transformer

                                                                    A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                    An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                    Figure 526 Schematic of a piezoelectrictransformer

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                                                                    Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                    5472 Piezoelectric Sensors

                                                                    Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                    Other sensor applications are

                                                                    Detection and generation of sonar waves

                                                                    To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                    To detect the precise moment of fuel injection in an automotive engine

                                                                    Detection of acoustic emissions in acoustic emission testing

                                                                    Microbalances as very sensitive chemical and biological sensors

                                                                    Strain gauges

                                                                    Medical applications using ultrasound waves

                                                                    Kidney stone treatment

                                                                    In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                    Figure 527 Ultrasonic waves creation and

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                                                                    kidney stone treatment and ultrasound imagingof the fetus

                                                                    (Courtesy copy DoITPoMS University of Cambridge)

                                                                    5473 Ultrasound Imaging Using Transduction Effect

                                                                    Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                    55 Pyroelectric Ceramics

                                                                    Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                    Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                    Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                    551 Difference between Pyroelectric and Ferroelectric Material

                                                                    Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                    Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                    552 Theory of Piezoelectric Materials

                                                                    From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                    (537)

                                                                    Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                    Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                    (538)

                                                                    Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                    we write

                                                                    Δ OR

                                                                    Δ (539)

                                                                    Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                    Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                    (540)

                                                                    The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                    As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                    553 Measurement of Pyroelectric Coefficient

                                                                    One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                    (541)

                                                                    Where Ip is the pyrocurrent and is given as

                                                                    (542)

                                                                    where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                    respectively

                                                                    Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                    554 Direct and Indirect Effect

                                                                    Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                    Since change in the polarization can also be expressed as depending

                                                                    upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                    Figure 531 Direct-Indirect effect animation

                                                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                    555 Common Pyroelectric Materials

                                                                    Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                    The most common materials are tabulated below

                                                                    Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                    LiTaO3 single crystal Hexagonal 665 -230

                                                                    075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                    (PMN-PT) Ceramic

                                                                    Perovskite 150 -1300

                                                                    Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                    Triglycine sulphate

                                                                    (NH2CH2COOH)3H2SO4

                                                                    Sulphate 49 -280

                                                                    Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                    5551 Triglycine Sulphate (TGS)

                                                                    High pyroelectric coefficient

                                                                    Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                    Can be modified to withstand temperatures above Curie point without depoling

                                                                    Used in thermal imaging cameras

                                                                    5552 Polyvinylidene Fluoride (PVDF)

                                                                    Poor pyroelectric coefficient

                                                                    Readily available in large areas of thin film

                                                                    More stable to heat vacuum and moisture than TGS mechanically robust

                                                                    Low heat conductivity and low permittivity

                                                                    High loss tangent

                                                                    Commonly used for burglar alarms

                                                                    5553 Perovskite Ferroelectric Ceramics

                                                                    Generally robust and insensitive to moisture and vacuum

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                                                                    High pyroelectric coefficient and low loss

                                                                    Better operation near TC

                                                                    Strong dependence on composition

                                                                    As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                    RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                    556 Common Applications

                                                                    5561 Burglar Alarms

                                                                    Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                    Figure 532 Working of an IR intruder alarm

                                                                    (Courtesy copy DoITPoMS University ofCambridge)

                                                                    5562 Infrared or Thermal Imaging

                                                                    Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                    The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                    A typical photograph generated from IR imaging looks like this

                                                                    Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                    Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                    A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                    This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                    Figure 534 Process of imagecreation

                                                                    5563 Pollutant Control

                                                                    The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                    Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                    Figure 535 Gas detection using a pyroelectricdetector

                                                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                                                    Module 5 Nonlinear Dielectrics

                                                                    Summary

                                                                    Summary

                                                                    Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                      Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

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                                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                      544 Depolarization of Piezoelectrics

                                                                      Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                                      polarization or rather result in alignment of dipoles gets lost

                                                                      Figure 522 Animation on depolarization offerroelectrics

                                                                      (Courtesy copy DoITPoMS University of Cambridge)

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                                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                      545 Common PIezoelectric Materials

                                                                      5451 Barium Titanate (BaTiO3)

                                                                      This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                                      used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                                      Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                                      1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                                      must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                                      5452 Pb(ZrTi)O3 or PZT

                                                                      PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                                      The phase diagram of PZT is shown below

                                                                      Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                                      The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                                      lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                                      few poling directions available making it a useful piezoelectric

                                                                      Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                      546 Measurement of Piezoelectric Properties

                                                                      Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                                      In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                                      Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                                      The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                                      (535)

                                                                      Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                                      (536)

                                                                      Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                                      One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                                      Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                      547 Applications of Piezoelectric Ceramics

                                                                      Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                      5471 Power Generation

                                                                      Gas Lighter

                                                                      Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                      Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                      One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                      Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                      Power Transformer

                                                                      A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                      An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                      Figure 526 Schematic of a piezoelectrictransformer

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                                                                      Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                      5472 Piezoelectric Sensors

                                                                      Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                      Other sensor applications are

                                                                      Detection and generation of sonar waves

                                                                      To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                      To detect the precise moment of fuel injection in an automotive engine

                                                                      Detection of acoustic emissions in acoustic emission testing

                                                                      Microbalances as very sensitive chemical and biological sensors

                                                                      Strain gauges

                                                                      Medical applications using ultrasound waves

                                                                      Kidney stone treatment

                                                                      In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                      Figure 527 Ultrasonic waves creation and

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                                                                      kidney stone treatment and ultrasound imagingof the fetus

                                                                      (Courtesy copy DoITPoMS University of Cambridge)

                                                                      5473 Ultrasound Imaging Using Transduction Effect

                                                                      Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                      55 Pyroelectric Ceramics

                                                                      Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                      Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                      Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                      551 Difference between Pyroelectric and Ferroelectric Material

                                                                      Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                      Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                      552 Theory of Piezoelectric Materials

                                                                      From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                      (537)

                                                                      Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                      Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                      (538)

                                                                      Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                      we write

                                                                      Δ OR

                                                                      Δ (539)

                                                                      Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                      Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                      (540)

                                                                      The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                      As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                      553 Measurement of Pyroelectric Coefficient

                                                                      One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                      (541)

                                                                      Where Ip is the pyrocurrent and is given as

                                                                      (542)

                                                                      where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                      respectively

                                                                      Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                      554 Direct and Indirect Effect

                                                                      Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                      Since change in the polarization can also be expressed as depending

                                                                      upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                      Figure 531 Direct-Indirect effect animation

                                                                      (Courtesy copy DoITPoMS University of Cambridge)

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                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                      555 Common Pyroelectric Materials

                                                                      Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                      The most common materials are tabulated below

                                                                      Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                      LiTaO3 single crystal Hexagonal 665 -230

                                                                      075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                      (PMN-PT) Ceramic

                                                                      Perovskite 150 -1300

                                                                      Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                      Triglycine sulphate

                                                                      (NH2CH2COOH)3H2SO4

                                                                      Sulphate 49 -280

                                                                      Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                      5551 Triglycine Sulphate (TGS)

                                                                      High pyroelectric coefficient

                                                                      Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                      Can be modified to withstand temperatures above Curie point without depoling

                                                                      Used in thermal imaging cameras

                                                                      5552 Polyvinylidene Fluoride (PVDF)

                                                                      Poor pyroelectric coefficient

                                                                      Readily available in large areas of thin film

                                                                      More stable to heat vacuum and moisture than TGS mechanically robust

                                                                      Low heat conductivity and low permittivity

                                                                      High loss tangent

                                                                      Commonly used for burglar alarms

                                                                      5553 Perovskite Ferroelectric Ceramics

                                                                      Generally robust and insensitive to moisture and vacuum

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                                                                      High pyroelectric coefficient and low loss

                                                                      Better operation near TC

                                                                      Strong dependence on composition

                                                                      As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                      RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                      556 Common Applications

                                                                      5561 Burglar Alarms

                                                                      Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                      Figure 532 Working of an IR intruder alarm

                                                                      (Courtesy copy DoITPoMS University ofCambridge)

                                                                      5562 Infrared or Thermal Imaging

                                                                      Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                      The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                      A typical photograph generated from IR imaging looks like this

                                                                      Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                      Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                      A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                      This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                      Figure 534 Process of imagecreation

                                                                      5563 Pollutant Control

                                                                      The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                      Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                      Figure 535 Gas detection using a pyroelectricdetector

                                                                      (Courtesy copy DoITPoMS University of Cambridge)

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                                                                      Module 5 Nonlinear Dielectrics

                                                                      Summary

                                                                      Summary

                                                                      Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                        544 Depolarization of Piezoelectrics

                                                                        Just like a ferroelectric material can be poled opposing polarity high electric field or thermal cyclingclose to Tc or the application of large mechanical stresses can lead to the disappearance of

                                                                        polarization or rather result in alignment of dipoles gets lost

                                                                        Figure 522 Animation on depolarization offerroelectrics

                                                                        (Courtesy copy DoITPoMS University of Cambridge)

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                                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                        545 Common PIezoelectric Materials

                                                                        5451 Barium Titanate (BaTiO3)

                                                                        This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                                        used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                                        Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                                        1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                                        must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                                        5452 Pb(ZrTi)O3 or PZT

                                                                        PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                                        The phase diagram of PZT is shown below

                                                                        Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                                        The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                                        lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                                        few poling directions available making it a useful piezoelectric

                                                                        Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                        546 Measurement of Piezoelectric Properties

                                                                        Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                                        In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                                        Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                                        The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                                        (535)

                                                                        Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                                        (536)

                                                                        Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                                        One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                                        Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                        547 Applications of Piezoelectric Ceramics

                                                                        Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                        5471 Power Generation

                                                                        Gas Lighter

                                                                        Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                        Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                        One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                        Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                        Power Transformer

                                                                        A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                        An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                        Figure 526 Schematic of a piezoelectrictransformer

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                                                                        Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                        5472 Piezoelectric Sensors

                                                                        Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                        Other sensor applications are

                                                                        Detection and generation of sonar waves

                                                                        To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                        To detect the precise moment of fuel injection in an automotive engine

                                                                        Detection of acoustic emissions in acoustic emission testing

                                                                        Microbalances as very sensitive chemical and biological sensors

                                                                        Strain gauges

                                                                        Medical applications using ultrasound waves

                                                                        Kidney stone treatment

                                                                        In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                        Figure 527 Ultrasonic waves creation and

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                                                                        kidney stone treatment and ultrasound imagingof the fetus

                                                                        (Courtesy copy DoITPoMS University of Cambridge)

                                                                        5473 Ultrasound Imaging Using Transduction Effect

                                                                        Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                        55 Pyroelectric Ceramics

                                                                        Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                        Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                        Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                        551 Difference between Pyroelectric and Ferroelectric Material

                                                                        Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                        Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                        552 Theory of Piezoelectric Materials

                                                                        From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                        (537)

                                                                        Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                        Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                        (538)

                                                                        Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                        we write

                                                                        Δ OR

                                                                        Δ (539)

                                                                        Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                        Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                        (540)

                                                                        The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                        As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                        553 Measurement of Pyroelectric Coefficient

                                                                        One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                        (541)

                                                                        Where Ip is the pyrocurrent and is given as

                                                                        (542)

                                                                        where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                        respectively

                                                                        Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                        554 Direct and Indirect Effect

                                                                        Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                        Since change in the polarization can also be expressed as depending

                                                                        upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                        Figure 531 Direct-Indirect effect animation

                                                                        (Courtesy copy DoITPoMS University of Cambridge)

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                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                        555 Common Pyroelectric Materials

                                                                        Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                        The most common materials are tabulated below

                                                                        Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                        LiTaO3 single crystal Hexagonal 665 -230

                                                                        075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                        (PMN-PT) Ceramic

                                                                        Perovskite 150 -1300

                                                                        Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                        Triglycine sulphate

                                                                        (NH2CH2COOH)3H2SO4

                                                                        Sulphate 49 -280

                                                                        Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                        5551 Triglycine Sulphate (TGS)

                                                                        High pyroelectric coefficient

                                                                        Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                        Can be modified to withstand temperatures above Curie point without depoling

                                                                        Used in thermal imaging cameras

                                                                        5552 Polyvinylidene Fluoride (PVDF)

                                                                        Poor pyroelectric coefficient

                                                                        Readily available in large areas of thin film

                                                                        More stable to heat vacuum and moisture than TGS mechanically robust

                                                                        Low heat conductivity and low permittivity

                                                                        High loss tangent

                                                                        Commonly used for burglar alarms

                                                                        5553 Perovskite Ferroelectric Ceramics

                                                                        Generally robust and insensitive to moisture and vacuum

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                                                                        High pyroelectric coefficient and low loss

                                                                        Better operation near TC

                                                                        Strong dependence on composition

                                                                        As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                        RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                        556 Common Applications

                                                                        5561 Burglar Alarms

                                                                        Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                        Figure 532 Working of an IR intruder alarm

                                                                        (Courtesy copy DoITPoMS University ofCambridge)

                                                                        5562 Infrared or Thermal Imaging

                                                                        Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                        The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                        A typical photograph generated from IR imaging looks like this

                                                                        Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                        Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                        A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                        This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                        Figure 534 Process of imagecreation

                                                                        5563 Pollutant Control

                                                                        The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                        Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                        Figure 535 Gas detection using a pyroelectricdetector

                                                                        (Courtesy copy DoITPoMS University of Cambridge)

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                                                                        Module 5 Nonlinear Dielectrics

                                                                        Summary

                                                                        Summary

                                                                        Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                          545 Common PIezoelectric Materials

                                                                          5451 Barium Titanate (BaTiO3)

                                                                          This was the first piezoelectric material which was developed commercially for application in thegeneration and detection of acoustic and ultrasonic energy We discussed its structure and transitionsin the previous section (5311) The transition temperature can be modified by chemicalsubstitutionsBa substitution by Pb and Ca lowers the Tc of tetragonal to orthorhombic transition This has been

                                                                          used to control the piezoelectric properties around 0degC and is important for underwater detectionand echo sounding

                                                                          Ti substitution by Zr or Sn increases the transition temperature for both the tetragonalndashorthorhomicand orthorhomicndashrhombohedral transitions and enhances piezoelectric properties Ti substitution by

                                                                          1-2 at Co3+ leads to much reduced losses as high fields useful in ultrasonic applications Care

                                                                          must be taken during processing to avoid reduction of Co3+ to Co2+ which occurs very easily

                                                                          5452 Pb(ZrTi)O3 or PZT

                                                                          PZT is one of the most used piezoelectric in a variety of applications due to its excellent propertiesand high enough transition temperatures It has a perovskite structure with B sites randomlyoccupied by either of isovalent Ti and Zr ions

                                                                          The phase diagram of PZT is shown below

                                                                          Figure 523 Phase diagram of PZT (Courtesy copy DoITPoMSUniversity of Cambridge UK)

                                                                          The typically used composition is about ZrTi5050 which gives excellent properties The reason forthis is that this is closed to morphotropic phase boundary and here rhombohedral and tetragonalstructures co-exist As we know that PS vector is along [001]-direction in tetragonal phase and

                                                                          lt111gt- direction in rhombohedral phase it permit material to be poled easily as there are quite a

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                                                                          few poling directions available making it a useful piezoelectric

                                                                          Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                          546 Measurement of Piezoelectric Properties

                                                                          Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                                          In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                                          Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                                          The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                                          (535)

                                                                          Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                                          (536)

                                                                          Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                                          One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                                          Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                          547 Applications of Piezoelectric Ceramics

                                                                          Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                          5471 Power Generation

                                                                          Gas Lighter

                                                                          Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                          Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                          One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                          Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                          Power Transformer

                                                                          A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                          An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                          Figure 526 Schematic of a piezoelectrictransformer

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                                                                          Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                          5472 Piezoelectric Sensors

                                                                          Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                          Other sensor applications are

                                                                          Detection and generation of sonar waves

                                                                          To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                          To detect the precise moment of fuel injection in an automotive engine

                                                                          Detection of acoustic emissions in acoustic emission testing

                                                                          Microbalances as very sensitive chemical and biological sensors

                                                                          Strain gauges

                                                                          Medical applications using ultrasound waves

                                                                          Kidney stone treatment

                                                                          In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                          Figure 527 Ultrasonic waves creation and

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                                                                          kidney stone treatment and ultrasound imagingof the fetus

                                                                          (Courtesy copy DoITPoMS University of Cambridge)

                                                                          5473 Ultrasound Imaging Using Transduction Effect

                                                                          Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                          55 Pyroelectric Ceramics

                                                                          Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                          Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                          Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                          551 Difference between Pyroelectric and Ferroelectric Material

                                                                          Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                          Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                          552 Theory of Piezoelectric Materials

                                                                          From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                          (537)

                                                                          Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                          Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                          (538)

                                                                          Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                          we write

                                                                          Δ OR

                                                                          Δ (539)

                                                                          Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                          Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                          (540)

                                                                          The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                          As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                          553 Measurement of Pyroelectric Coefficient

                                                                          One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                          (541)

                                                                          Where Ip is the pyrocurrent and is given as

                                                                          (542)

                                                                          where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                          respectively

                                                                          Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                          554 Direct and Indirect Effect

                                                                          Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                          Since change in the polarization can also be expressed as depending

                                                                          upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                          Figure 531 Direct-Indirect effect animation

                                                                          (Courtesy copy DoITPoMS University of Cambridge)

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                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                          555 Common Pyroelectric Materials

                                                                          Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                          The most common materials are tabulated below

                                                                          Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                          LiTaO3 single crystal Hexagonal 665 -230

                                                                          075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                          (PMN-PT) Ceramic

                                                                          Perovskite 150 -1300

                                                                          Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                          Triglycine sulphate

                                                                          (NH2CH2COOH)3H2SO4

                                                                          Sulphate 49 -280

                                                                          Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                          5551 Triglycine Sulphate (TGS)

                                                                          High pyroelectric coefficient

                                                                          Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                          Can be modified to withstand temperatures above Curie point without depoling

                                                                          Used in thermal imaging cameras

                                                                          5552 Polyvinylidene Fluoride (PVDF)

                                                                          Poor pyroelectric coefficient

                                                                          Readily available in large areas of thin film

                                                                          More stable to heat vacuum and moisture than TGS mechanically robust

                                                                          Low heat conductivity and low permittivity

                                                                          High loss tangent

                                                                          Commonly used for burglar alarms

                                                                          5553 Perovskite Ferroelectric Ceramics

                                                                          Generally robust and insensitive to moisture and vacuum

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                                                                          High pyroelectric coefficient and low loss

                                                                          Better operation near TC

                                                                          Strong dependence on composition

                                                                          As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                          RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                          556 Common Applications

                                                                          5561 Burglar Alarms

                                                                          Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                          Figure 532 Working of an IR intruder alarm

                                                                          (Courtesy copy DoITPoMS University ofCambridge)

                                                                          5562 Infrared or Thermal Imaging

                                                                          Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                          The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                          A typical photograph generated from IR imaging looks like this

                                                                          Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                          Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                          A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                          This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                          Figure 534 Process of imagecreation

                                                                          5563 Pollutant Control

                                                                          The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                          Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                          Figure 535 Gas detection using a pyroelectricdetector

                                                                          (Courtesy copy DoITPoMS University of Cambridge)

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                                                                          Module 5 Nonlinear Dielectrics

                                                                          Summary

                                                                          Summary

                                                                          Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                            few poling directions available making it a useful piezoelectric

                                                                            Donor doping in PZT such as La3+ on Pb site reduces the concentration of oxygen vacancies Thisin turn reduces the concentration of defect pairs which otherwise impede the domain wall motionThis leads to noticeable increases in the permittivity dielectric losses elastic compliance andcoupling coefficients and reduction in the coercivity

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                                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                            546 Measurement of Piezoelectric Properties

                                                                            Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                                            In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                                            Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                                            The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                                            (535)

                                                                            Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                                            (536)

                                                                            Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                                            One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                                            Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                            547 Applications of Piezoelectric Ceramics

                                                                            Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                            5471 Power Generation

                                                                            Gas Lighter

                                                                            Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                            Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                            One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                            Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                            Power Transformer

                                                                            A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                            An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                            Figure 526 Schematic of a piezoelectrictransformer

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                                                                            Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                            5472 Piezoelectric Sensors

                                                                            Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                            Other sensor applications are

                                                                            Detection and generation of sonar waves

                                                                            To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                            To detect the precise moment of fuel injection in an automotive engine

                                                                            Detection of acoustic emissions in acoustic emission testing

                                                                            Microbalances as very sensitive chemical and biological sensors

                                                                            Strain gauges

                                                                            Medical applications using ultrasound waves

                                                                            Kidney stone treatment

                                                                            In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                            Figure 527 Ultrasonic waves creation and

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                                                                            kidney stone treatment and ultrasound imagingof the fetus

                                                                            (Courtesy copy DoITPoMS University of Cambridge)

                                                                            5473 Ultrasound Imaging Using Transduction Effect

                                                                            Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                            55 Pyroelectric Ceramics

                                                                            Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                            Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                            Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                            551 Difference between Pyroelectric and Ferroelectric Material

                                                                            Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                            Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                            552 Theory of Piezoelectric Materials

                                                                            From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                            (537)

                                                                            Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                            Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                            (538)

                                                                            Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                            we write

                                                                            Δ OR

                                                                            Δ (539)

                                                                            Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                            Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                            (540)

                                                                            The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                            As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                            553 Measurement of Pyroelectric Coefficient

                                                                            One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                            (541)

                                                                            Where Ip is the pyrocurrent and is given as

                                                                            (542)

                                                                            where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                            respectively

                                                                            Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                            554 Direct and Indirect Effect

                                                                            Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                            Since change in the polarization can also be expressed as depending

                                                                            upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                            Figure 531 Direct-Indirect effect animation

                                                                            (Courtesy copy DoITPoMS University of Cambridge)

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                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                            555 Common Pyroelectric Materials

                                                                            Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                            The most common materials are tabulated below

                                                                            Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                            LiTaO3 single crystal Hexagonal 665 -230

                                                                            075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                            (PMN-PT) Ceramic

                                                                            Perovskite 150 -1300

                                                                            Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                            Triglycine sulphate

                                                                            (NH2CH2COOH)3H2SO4

                                                                            Sulphate 49 -280

                                                                            Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                            5551 Triglycine Sulphate (TGS)

                                                                            High pyroelectric coefficient

                                                                            Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                            Can be modified to withstand temperatures above Curie point without depoling

                                                                            Used in thermal imaging cameras

                                                                            5552 Polyvinylidene Fluoride (PVDF)

                                                                            Poor pyroelectric coefficient

                                                                            Readily available in large areas of thin film

                                                                            More stable to heat vacuum and moisture than TGS mechanically robust

                                                                            Low heat conductivity and low permittivity

                                                                            High loss tangent

                                                                            Commonly used for burglar alarms

                                                                            5553 Perovskite Ferroelectric Ceramics

                                                                            Generally robust and insensitive to moisture and vacuum

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                                                                            High pyroelectric coefficient and low loss

                                                                            Better operation near TC

                                                                            Strong dependence on composition

                                                                            As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                            RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                            556 Common Applications

                                                                            5561 Burglar Alarms

                                                                            Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                            Figure 532 Working of an IR intruder alarm

                                                                            (Courtesy copy DoITPoMS University ofCambridge)

                                                                            5562 Infrared or Thermal Imaging

                                                                            Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                            The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                            A typical photograph generated from IR imaging looks like this

                                                                            Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                            Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                            A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                            This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                            Figure 534 Process of imagecreation

                                                                            5563 Pollutant Control

                                                                            The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                            Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                            Figure 535 Gas detection using a pyroelectricdetector

                                                                            (Courtesy copy DoITPoMS University of Cambridge)

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                                                                            Module 5 Nonlinear Dielectrics

                                                                            Summary

                                                                            Summary

                                                                            Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                              546 Measurement of Piezoelectric Properties

                                                                              Piezoelectric measurements are usually made to measure the displacement of the material when anelectric field is applied These techniques are resonance or subresonance techniques

                                                                              In the resonance methods one conducts the measurement of the characteristic frequencies of thematerials upon the application of alternating electric field and is widely used for bulk samples To afirst approximation the electromechanical response of a piezoelectric material close to thecharacteristics frequency can represented by the electrical equivalent circuit as shown in the figure524 Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch anddiameter ~frac14 inch along its length

                                                                              Figure 524 Schematic representation of (a) equivalentelectrical circuit of a piezoelectric sample close to itscharacteristic frequency (b) Plot of electrical reactance of thesample a function of frequency

                                                                              The coupling coefficient k33 is expressed in terms of series and parallel resonance frequencies (fsand fp respectively) as

                                                                              (535)

                                                                              Using this relation along with elastic compliance and low frequency dielectric constant thepiezoelectric coefficient d33 can be calculated by using the following relation

                                                                              (536)

                                                                              Measurements are limited to the specific frequencies determined by the fundamental vibration modesof the sample In the case of piezoelectric thin films the thickness resonance occurs in the GHzrange in which the measurements involve considerable difficulties In such cases the resonance inthe substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thinfilm The disadvantage of this method is that measurements are limited by the number ofcharacteristics frequencies determined by the electromechanical response of a material

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                                                                              One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                                              Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                              547 Applications of Piezoelectric Ceramics

                                                                              Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                              5471 Power Generation

                                                                              Gas Lighter

                                                                              Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                              Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                              One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                              Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                              Power Transformer

                                                                              A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                              An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                              Figure 526 Schematic of a piezoelectrictransformer

                                                                              >

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                                                                              Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                              5472 Piezoelectric Sensors

                                                                              Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                              Other sensor applications are

                                                                              Detection and generation of sonar waves

                                                                              To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                              To detect the precise moment of fuel injection in an automotive engine

                                                                              Detection of acoustic emissions in acoustic emission testing

                                                                              Microbalances as very sensitive chemical and biological sensors

                                                                              Strain gauges

                                                                              Medical applications using ultrasound waves

                                                                              Kidney stone treatment

                                                                              In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                              Figure 527 Ultrasonic waves creation and

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                                                                              kidney stone treatment and ultrasound imagingof the fetus

                                                                              (Courtesy copy DoITPoMS University of Cambridge)

                                                                              5473 Ultrasound Imaging Using Transduction Effect

                                                                              Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                              55 Pyroelectric Ceramics

                                                                              Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                              Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                              Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                              551 Difference between Pyroelectric and Ferroelectric Material

                                                                              Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                              Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                              552 Theory of Piezoelectric Materials

                                                                              From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                              (537)

                                                                              Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                              Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                              (538)

                                                                              Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                              we write

                                                                              Δ OR

                                                                              Δ (539)

                                                                              Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                              Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                              (540)

                                                                              The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                              As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                              553 Measurement of Pyroelectric Coefficient

                                                                              One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                              (541)

                                                                              Where Ip is the pyrocurrent and is given as

                                                                              (542)

                                                                              where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                              respectively

                                                                              Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                              554 Direct and Indirect Effect

                                                                              Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                              Since change in the polarization can also be expressed as depending

                                                                              upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                              Figure 531 Direct-Indirect effect animation

                                                                              (Courtesy copy DoITPoMS University of Cambridge)

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                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                              555 Common Pyroelectric Materials

                                                                              Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                              The most common materials are tabulated below

                                                                              Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                              LiTaO3 single crystal Hexagonal 665 -230

                                                                              075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                              (PMN-PT) Ceramic

                                                                              Perovskite 150 -1300

                                                                              Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                              Triglycine sulphate

                                                                              (NH2CH2COOH)3H2SO4

                                                                              Sulphate 49 -280

                                                                              Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                              5551 Triglycine Sulphate (TGS)

                                                                              High pyroelectric coefficient

                                                                              Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                              Can be modified to withstand temperatures above Curie point without depoling

                                                                              Used in thermal imaging cameras

                                                                              5552 Polyvinylidene Fluoride (PVDF)

                                                                              Poor pyroelectric coefficient

                                                                              Readily available in large areas of thin film

                                                                              More stable to heat vacuum and moisture than TGS mechanically robust

                                                                              Low heat conductivity and low permittivity

                                                                              High loss tangent

                                                                              Commonly used for burglar alarms

                                                                              5553 Perovskite Ferroelectric Ceramics

                                                                              Generally robust and insensitive to moisture and vacuum

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                                                                              High pyroelectric coefficient and low loss

                                                                              Better operation near TC

                                                                              Strong dependence on composition

                                                                              As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                              RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                              556 Common Applications

                                                                              5561 Burglar Alarms

                                                                              Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                              Figure 532 Working of an IR intruder alarm

                                                                              (Courtesy copy DoITPoMS University ofCambridge)

                                                                              5562 Infrared or Thermal Imaging

                                                                              Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                              The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                              A typical photograph generated from IR imaging looks like this

                                                                              Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                              Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                              A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                              This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                              Figure 534 Process of imagecreation

                                                                              5563 Pollutant Control

                                                                              The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                              Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                              Figure 535 Gas detection using a pyroelectricdetector

                                                                              (Courtesy copy DoITPoMS University of Cambridge)

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                                                                              Module 5 Nonlinear Dielectrics

                                                                              Summary

                                                                              Summary

                                                                              Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                One can use subresonance techniques for the measurement of piezoelectric properties at thefrequencies which are much below the characteristics fundamental resonance frequencies Thisincludes measurement of direct effect ie charge developed on a piezoelectric material underapplication of an external mechanical stress and measurement of converse effect ie measurementof electric field induced displacements Although displacements can be rather small to measureaccurately technological advances have allowed accurate measurements using techniques like straingauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic forcemicroscopes Appropriate electrical circuits needs to drawn and modeled to clearly elucidate thematerial properties

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                                                                                Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                                547 Applications of Piezoelectric Ceramics

                                                                                Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                                5471 Power Generation

                                                                                Gas Lighter

                                                                                Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                                Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                                One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                                Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                                Power Transformer

                                                                                A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                                An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                                Figure 526 Schematic of a piezoelectrictransformer

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                                                                                Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                                5472 Piezoelectric Sensors

                                                                                Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                                Other sensor applications are

                                                                                Detection and generation of sonar waves

                                                                                To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                                To detect the precise moment of fuel injection in an automotive engine

                                                                                Detection of acoustic emissions in acoustic emission testing

                                                                                Microbalances as very sensitive chemical and biological sensors

                                                                                Strain gauges

                                                                                Medical applications using ultrasound waves

                                                                                Kidney stone treatment

                                                                                In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                                Figure 527 Ultrasonic waves creation and

                                                                                >

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                                                                                kidney stone treatment and ultrasound imagingof the fetus

                                                                                (Courtesy copy DoITPoMS University of Cambridge)

                                                                                5473 Ultrasound Imaging Using Transduction Effect

                                                                                Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                55 Pyroelectric Ceramics

                                                                                Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                                Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                                Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                551 Difference between Pyroelectric and Ferroelectric Material

                                                                                Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                                Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                552 Theory of Piezoelectric Materials

                                                                                From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                                (537)

                                                                                Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                                Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                                (538)

                                                                                Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                                we write

                                                                                Δ OR

                                                                                Δ (539)

                                                                                Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                                Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                                (540)

                                                                                The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                                As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                553 Measurement of Pyroelectric Coefficient

                                                                                One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                                (541)

                                                                                Where Ip is the pyrocurrent and is given as

                                                                                (542)

                                                                                where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                                respectively

                                                                                Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                554 Direct and Indirect Effect

                                                                                Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                Since change in the polarization can also be expressed as depending

                                                                                upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                Figure 531 Direct-Indirect effect animation

                                                                                (Courtesy copy DoITPoMS University of Cambridge)

                                                                                >

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                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                555 Common Pyroelectric Materials

                                                                                Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                The most common materials are tabulated below

                                                                                Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                LiTaO3 single crystal Hexagonal 665 -230

                                                                                075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                (PMN-PT) Ceramic

                                                                                Perovskite 150 -1300

                                                                                Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                Triglycine sulphate

                                                                                (NH2CH2COOH)3H2SO4

                                                                                Sulphate 49 -280

                                                                                Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                5551 Triglycine Sulphate (TGS)

                                                                                High pyroelectric coefficient

                                                                                Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                Can be modified to withstand temperatures above Curie point without depoling

                                                                                Used in thermal imaging cameras

                                                                                5552 Polyvinylidene Fluoride (PVDF)

                                                                                Poor pyroelectric coefficient

                                                                                Readily available in large areas of thin film

                                                                                More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                Low heat conductivity and low permittivity

                                                                                High loss tangent

                                                                                Commonly used for burglar alarms

                                                                                5553 Perovskite Ferroelectric Ceramics

                                                                                Generally robust and insensitive to moisture and vacuum

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                                                                                High pyroelectric coefficient and low loss

                                                                                Better operation near TC

                                                                                Strong dependence on composition

                                                                                As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                556 Common Applications

                                                                                5561 Burglar Alarms

                                                                                Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                Figure 532 Working of an IR intruder alarm

                                                                                (Courtesy copy DoITPoMS University ofCambridge)

                                                                                5562 Infrared or Thermal Imaging

                                                                                Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                                A typical photograph generated from IR imaging looks like this

                                                                                Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                Figure 534 Process of imagecreation

                                                                                5563 Pollutant Control

                                                                                The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                                Figure 535 Gas detection using a pyroelectricdetector

                                                                                (Courtesy copy DoITPoMS University of Cambridge)

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                                                                                Module 5 Nonlinear Dielectrics

                                                                                Summary

                                                                                Summary

                                                                                Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                  Module 5 Nonlinear Dielectrics Piezoelectric Ceramics

                                                                                  547 Applications of Piezoelectric Ceramics

                                                                                  Piezoelectric ceramics are used in a variety of applications utilizing either direct or conversepiezoelectric effect The following are some applications of the piezoelectric ceramics

                                                                                  5471 Power Generation

                                                                                  Gas Lighter

                                                                                  Piezoelectric material can ignite the gases by generating a spark via an electric current Thisrequires two piezoelectrics with opposite polarization states which are brought close to each other sothose polarization vectors are in the opposite directions ie faces containing similar charges aretogether The piezoelectric are placed in a circuit with a spark gap

                                                                                  Now application of a mechanical stress or force will induce change in the polarization The forcebrings together these two pieces which then gives rise to creation of charges The charges flow fromthe end faces and the middle (pressed) faces through the circuit giving rise to a spark in the sparkgap which can be used to ignite a gas

                                                                                  One must apply the force quickly otherwise the voltage generated disappears because the chargesleaks away through the piezoceramic across its surfaces and via the apparatus

                                                                                  Figure 525 Schematic of operation of a gas lighter made usingpiezoelectric material (you can also refer to the animation made byDOITPOMS University of Cambridge UK)

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                                                                                  Power Transformer

                                                                                  A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                                  An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                                  Figure 526 Schematic of a piezoelectrictransformer

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                                                                                  Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                                  5472 Piezoelectric Sensors

                                                                                  Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                                  Other sensor applications are

                                                                                  Detection and generation of sonar waves

                                                                                  To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                                  To detect the precise moment of fuel injection in an automotive engine

                                                                                  Detection of acoustic emissions in acoustic emission testing

                                                                                  Microbalances as very sensitive chemical and biological sensors

                                                                                  Strain gauges

                                                                                  Medical applications using ultrasound waves

                                                                                  Kidney stone treatment

                                                                                  In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                                  Figure 527 Ultrasonic waves creation and

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                                                                                  kidney stone treatment and ultrasound imagingof the fetus

                                                                                  (Courtesy copy DoITPoMS University of Cambridge)

                                                                                  5473 Ultrasound Imaging Using Transduction Effect

                                                                                  Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                  55 Pyroelectric Ceramics

                                                                                  Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                                  Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                                  Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                  551 Difference between Pyroelectric and Ferroelectric Material

                                                                                  Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                                  Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                  552 Theory of Piezoelectric Materials

                                                                                  From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                                  (537)

                                                                                  Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                                  Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                                  (538)

                                                                                  Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                                  we write

                                                                                  Δ OR

                                                                                  Δ (539)

                                                                                  Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                                  Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                                  (540)

                                                                                  The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                                  As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                  553 Measurement of Pyroelectric Coefficient

                                                                                  One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                                  (541)

                                                                                  Where Ip is the pyrocurrent and is given as

                                                                                  (542)

                                                                                  where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                                  respectively

                                                                                  Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                  554 Direct and Indirect Effect

                                                                                  Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                  Since change in the polarization can also be expressed as depending

                                                                                  upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                  Figure 531 Direct-Indirect effect animation

                                                                                  (Courtesy copy DoITPoMS University of Cambridge)

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                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                  555 Common Pyroelectric Materials

                                                                                  Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                  The most common materials are tabulated below

                                                                                  Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                  LiTaO3 single crystal Hexagonal 665 -230

                                                                                  075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                  (PMN-PT) Ceramic

                                                                                  Perovskite 150 -1300

                                                                                  Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                  Triglycine sulphate

                                                                                  (NH2CH2COOH)3H2SO4

                                                                                  Sulphate 49 -280

                                                                                  Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                  5551 Triglycine Sulphate (TGS)

                                                                                  High pyroelectric coefficient

                                                                                  Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                  Can be modified to withstand temperatures above Curie point without depoling

                                                                                  Used in thermal imaging cameras

                                                                                  5552 Polyvinylidene Fluoride (PVDF)

                                                                                  Poor pyroelectric coefficient

                                                                                  Readily available in large areas of thin film

                                                                                  More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                  Low heat conductivity and low permittivity

                                                                                  High loss tangent

                                                                                  Commonly used for burglar alarms

                                                                                  5553 Perovskite Ferroelectric Ceramics

                                                                                  Generally robust and insensitive to moisture and vacuum

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                                                                                  High pyroelectric coefficient and low loss

                                                                                  Better operation near TC

                                                                                  Strong dependence on composition

                                                                                  As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                  RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                  556 Common Applications

                                                                                  5561 Burglar Alarms

                                                                                  Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                  Figure 532 Working of an IR intruder alarm

                                                                                  (Courtesy copy DoITPoMS University ofCambridge)

                                                                                  5562 Infrared or Thermal Imaging

                                                                                  Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                  The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                  >

                                                                                  Objectives_template

                                                                                  fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                  A typical photograph generated from IR imaging looks like this

                                                                                  Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                  Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                  A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                  This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                  Figure 534 Process of imagecreation

                                                                                  5563 Pollutant Control

                                                                                  The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                  Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                                  Figure 535 Gas detection using a pyroelectricdetector

                                                                                  (Courtesy copy DoITPoMS University of Cambridge)

                                                                                  >

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                                                                                  Module 5 Nonlinear Dielectrics

                                                                                  Summary

                                                                                  Summary

                                                                                  Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                    Power Transformer

                                                                                    A piezoelectric transformer works like an AC voltage multiplier While conventional transformersutilize magnetic coupling between input and output the piezoelectric transformer exploits theacoustic coupling utilizing inverse piezoelectric effect Piezo transformers can be quite compact highvoltage sources

                                                                                    An input smaller voltage across the thickness of a piezoceramic creates an alternating stress in thebar by the inverse piezoelectric effect This causes the bar to vibrate with vibration frequency chosento be the resonant frequency of the block typically in the 100 kHz to 1 MHz range This generates ahigher output voltage in the other section of the bar by the direct piezoelectric effect One canachieve the step-up ratios of more than 10001 using this technique

                                                                                    Figure 526 Schematic of a piezoelectrictransformer

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                                                                                    Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                                    5472 Piezoelectric Sensors

                                                                                    Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                                    Other sensor applications are

                                                                                    Detection and generation of sonar waves

                                                                                    To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                                    To detect the precise moment of fuel injection in an automotive engine

                                                                                    Detection of acoustic emissions in acoustic emission testing

                                                                                    Microbalances as very sensitive chemical and biological sensors

                                                                                    Strain gauges

                                                                                    Medical applications using ultrasound waves

                                                                                    Kidney stone treatment

                                                                                    In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                                    Figure 527 Ultrasonic waves creation and

                                                                                    >

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                                                                                    kidney stone treatment and ultrasound imagingof the fetus

                                                                                    (Courtesy copy DoITPoMS University of Cambridge)

                                                                                    5473 Ultrasound Imaging Using Transduction Effect

                                                                                    Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                    55 Pyroelectric Ceramics

                                                                                    Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                                    Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                                    Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                    551 Difference between Pyroelectric and Ferroelectric Material

                                                                                    Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                                    Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                    552 Theory of Piezoelectric Materials

                                                                                    From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                                    (537)

                                                                                    Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                                    Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                                    (538)

                                                                                    Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                                    we write

                                                                                    Δ OR

                                                                                    Δ (539)

                                                                                    Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                                    Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                                    (540)

                                                                                    The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                                    As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                    553 Measurement of Pyroelectric Coefficient

                                                                                    One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                                    (541)

                                                                                    Where Ip is the pyrocurrent and is given as

                                                                                    (542)

                                                                                    where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                                    respectively

                                                                                    Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                    554 Direct and Indirect Effect

                                                                                    Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                    Since change in the polarization can also be expressed as depending

                                                                                    upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                    Figure 531 Direct-Indirect effect animation

                                                                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                    555 Common Pyroelectric Materials

                                                                                    Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                    The most common materials are tabulated below

                                                                                    Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                    LiTaO3 single crystal Hexagonal 665 -230

                                                                                    075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                    (PMN-PT) Ceramic

                                                                                    Perovskite 150 -1300

                                                                                    Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                    Triglycine sulphate

                                                                                    (NH2CH2COOH)3H2SO4

                                                                                    Sulphate 49 -280

                                                                                    Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                    5551 Triglycine Sulphate (TGS)

                                                                                    High pyroelectric coefficient

                                                                                    Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                    Can be modified to withstand temperatures above Curie point without depoling

                                                                                    Used in thermal imaging cameras

                                                                                    5552 Polyvinylidene Fluoride (PVDF)

                                                                                    Poor pyroelectric coefficient

                                                                                    Readily available in large areas of thin film

                                                                                    More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                    Low heat conductivity and low permittivity

                                                                                    High loss tangent

                                                                                    Commonly used for burglar alarms

                                                                                    5553 Perovskite Ferroelectric Ceramics

                                                                                    Generally robust and insensitive to moisture and vacuum

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                                                                                    High pyroelectric coefficient and low loss

                                                                                    Better operation near TC

                                                                                    Strong dependence on composition

                                                                                    As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                    RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                    556 Common Applications

                                                                                    5561 Burglar Alarms

                                                                                    Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                    Figure 532 Working of an IR intruder alarm

                                                                                    (Courtesy copy DoITPoMS University ofCambridge)

                                                                                    5562 Infrared or Thermal Imaging

                                                                                    Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                    The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

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                                                                                    A typical photograph generated from IR imaging looks like this

                                                                                    Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                    Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                    A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                    This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                    Figure 534 Process of imagecreation

                                                                                    5563 Pollutant Control

                                                                                    The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                    Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                                    Figure 535 Gas detection using a pyroelectricdetector

                                                                                    (Courtesy copy DoITPoMS University of Cambridge)

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                                                                                    Module 5 Nonlinear Dielectrics

                                                                                    Summary

                                                                                    Summary

                                                                                    Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                      Module 5 Special Dielectrics Piezoelectric Ceramics

                                                                                      5472 Piezoelectric Sensors

                                                                                      Here typically pressure or force is used to create an electrical signal out of a piezoelectric materialFor instance in a microphone sound waves can deform the piezoelectric element by bending it andthus giving a changing voltage Similar principle can also be used for pickup guitars andmicrophones

                                                                                      Other sensor applications are

                                                                                      Detection and generation of sonar waves

                                                                                      To detect detonation in automotive engine by sampling the vibrations of the engine block

                                                                                      To detect the precise moment of fuel injection in an automotive engine

                                                                                      Detection of acoustic emissions in acoustic emission testing

                                                                                      Microbalances as very sensitive chemical and biological sensors

                                                                                      Strain gauges

                                                                                      Medical applications using ultrasound waves

                                                                                      Kidney stone treatment

                                                                                      In this application electricity of high frequency is applied to the sample which gives rise to a changein the shape of the material The shape change leads to emission of waves of frequencies in theultrasound range These powerful ultrasound waves can be used to shatter pieces of materialsinside the body such as kidney stone which can then pass out through the urine

                                                                                      Figure 527 Ultrasonic waves creation and

                                                                                      >

                                                                                      Objectives_template

                                                                                      fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_9htm[5252012 125802 PM]

                                                                                      kidney stone treatment and ultrasound imagingof the fetus

                                                                                      (Courtesy copy DoITPoMS University of Cambridge)

                                                                                      5473 Ultrasound Imaging Using Transduction Effect

                                                                                      Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

                                                                                      Objectives_template

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                                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                      55 Pyroelectric Ceramics

                                                                                      Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                                      Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                                      Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                      551 Difference between Pyroelectric and Ferroelectric Material

                                                                                      Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                                      Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                      552 Theory of Piezoelectric Materials

                                                                                      From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                                      (537)

                                                                                      Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                                      Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                                      (538)

                                                                                      Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                                      we write

                                                                                      Δ OR

                                                                                      Δ (539)

                                                                                      Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                                      Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                                      (540)

                                                                                      The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                                      As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                      553 Measurement of Pyroelectric Coefficient

                                                                                      One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                                      (541)

                                                                                      Where Ip is the pyrocurrent and is given as

                                                                                      (542)

                                                                                      where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                                      respectively

                                                                                      Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                      554 Direct and Indirect Effect

                                                                                      Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                      Since change in the polarization can also be expressed as depending

                                                                                      upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                      Figure 531 Direct-Indirect effect animation

                                                                                      (Courtesy copy DoITPoMS University of Cambridge)

                                                                                      >

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                                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                      555 Common Pyroelectric Materials

                                                                                      Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                      The most common materials are tabulated below

                                                                                      Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                      LiTaO3 single crystal Hexagonal 665 -230

                                                                                      075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                      (PMN-PT) Ceramic

                                                                                      Perovskite 150 -1300

                                                                                      Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                      Triglycine sulphate

                                                                                      (NH2CH2COOH)3H2SO4

                                                                                      Sulphate 49 -280

                                                                                      Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                      5551 Triglycine Sulphate (TGS)

                                                                                      High pyroelectric coefficient

                                                                                      Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                      Can be modified to withstand temperatures above Curie point without depoling

                                                                                      Used in thermal imaging cameras

                                                                                      5552 Polyvinylidene Fluoride (PVDF)

                                                                                      Poor pyroelectric coefficient

                                                                                      Readily available in large areas of thin film

                                                                                      More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                      Low heat conductivity and low permittivity

                                                                                      High loss tangent

                                                                                      Commonly used for burglar alarms

                                                                                      5553 Perovskite Ferroelectric Ceramics

                                                                                      Generally robust and insensitive to moisture and vacuum

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                                                                                      High pyroelectric coefficient and low loss

                                                                                      Better operation near TC

                                                                                      Strong dependence on composition

                                                                                      As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                      RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                      556 Common Applications

                                                                                      5561 Burglar Alarms

                                                                                      Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                      Figure 532 Working of an IR intruder alarm

                                                                                      (Courtesy copy DoITPoMS University ofCambridge)

                                                                                      5562 Infrared or Thermal Imaging

                                                                                      Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                      The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                      >

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                                                                                      A typical photograph generated from IR imaging looks like this

                                                                                      Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                      Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                      A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                      This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                      Figure 534 Process of imagecreation

                                                                                      5563 Pollutant Control

                                                                                      The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                      Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                                      Figure 535 Gas detection using a pyroelectricdetector

                                                                                      (Courtesy copy DoITPoMS University of Cambridge)

                                                                                      >

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                                                                                      Module 5 Nonlinear Dielectrics

                                                                                      Summary

                                                                                      Summary

                                                                                      Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                        kidney stone treatment and ultrasound imagingof the fetus

                                                                                        (Courtesy copy DoITPoMS University of Cambridge)

                                                                                        5473 Ultrasound Imaging Using Transduction Effect

                                                                                        Another application is its use in the ultrasound imaging of the fetus where piezoelectric acts as atransducer utilizing both direct and inverse effects Since a high frequency field application to apiezoelectric can lead to emission of ultrasonic waves by direct effect these waves when they meetthe tissues in the body some of these waves get reflected The reflected waves come back topiezoelectric exploit the inverse effect which leads to creation of charges from the piezoelectric whichcan then be modeled to generate an image of the fetus

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                                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                        55 Pyroelectric Ceramics

                                                                                        Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                                        Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                                        Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                        551 Difference between Pyroelectric and Ferroelectric Material

                                                                                        Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                                        Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                        552 Theory of Piezoelectric Materials

                                                                                        From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                                        (537)

                                                                                        Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                                        Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                                        (538)

                                                                                        Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                                        we write

                                                                                        Δ OR

                                                                                        Δ (539)

                                                                                        Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                                        Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                                        (540)

                                                                                        The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                                        As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

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                                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                        553 Measurement of Pyroelectric Coefficient

                                                                                        One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                                        (541)

                                                                                        Where Ip is the pyrocurrent and is given as

                                                                                        (542)

                                                                                        where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                                        respectively

                                                                                        Figure 530 Circuit for measuring pyroelectriccoefficient

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                                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                        554 Direct and Indirect Effect

                                                                                        Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                        Since change in the polarization can also be expressed as depending

                                                                                        upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                        Figure 531 Direct-Indirect effect animation

                                                                                        (Courtesy copy DoITPoMS University of Cambridge)

                                                                                        >

                                                                                        Objectives_template

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                                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                        555 Common Pyroelectric Materials

                                                                                        Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                        The most common materials are tabulated below

                                                                                        Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                        LiTaO3 single crystal Hexagonal 665 -230

                                                                                        075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                        (PMN-PT) Ceramic

                                                                                        Perovskite 150 -1300

                                                                                        Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                        Triglycine sulphate

                                                                                        (NH2CH2COOH)3H2SO4

                                                                                        Sulphate 49 -280

                                                                                        Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                        5551 Triglycine Sulphate (TGS)

                                                                                        High pyroelectric coefficient

                                                                                        Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                        Can be modified to withstand temperatures above Curie point without depoling

                                                                                        Used in thermal imaging cameras

                                                                                        5552 Polyvinylidene Fluoride (PVDF)

                                                                                        Poor pyroelectric coefficient

                                                                                        Readily available in large areas of thin film

                                                                                        More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                        Low heat conductivity and low permittivity

                                                                                        High loss tangent

                                                                                        Commonly used for burglar alarms

                                                                                        5553 Perovskite Ferroelectric Ceramics

                                                                                        Generally robust and insensitive to moisture and vacuum

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                                                                                        High pyroelectric coefficient and low loss

                                                                                        Better operation near TC

                                                                                        Strong dependence on composition

                                                                                        As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                        RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

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                                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                        556 Common Applications

                                                                                        5561 Burglar Alarms

                                                                                        Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                        Figure 532 Working of an IR intruder alarm

                                                                                        (Courtesy copy DoITPoMS University ofCambridge)

                                                                                        5562 Infrared or Thermal Imaging

                                                                                        Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                        The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                        >

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                                                                                        A typical photograph generated from IR imaging looks like this

                                                                                        Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                        Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                        A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                        This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                        Figure 534 Process of imagecreation

                                                                                        5563 Pollutant Control

                                                                                        The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                        Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

                                                                                        Objectives_template

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                                                                                        Figure 535 Gas detection using a pyroelectricdetector

                                                                                        (Courtesy copy DoITPoMS University of Cambridge)

                                                                                        >

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                                                                                        Module 5 Nonlinear Dielectrics

                                                                                        Summary

                                                                                        Summary

                                                                                        Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                          55 Pyroelectric Ceramics

                                                                                          Pyroelectric materials possess a spontaneous polarization along a unique crystallographic directionwhich may or may not be reversible by changing the polarity of the applied field If the latter is truethen a pyroelectric material is also ferroelectric If it is ferroelectric material too then the materialcan either be in a single crystalline state or in a poled state

                                                                                          Pyroelectricity in itself is the ability of materials to generate a voltage when they are heated orcooled It is temperature dependence of the spontaneous polarization in polar materials due tominute changes in the atomic positions as a result of change in the temperature If the temperatureis constant then voltage gradually disappears due to leakage of charges through the material or airor the apparatus Change in the polarization on a sample surface can be measured as an inducedcurrent

                                                                                          Pyroelectricity was first observed by the Greek philosopher Theophrastus in 314 BC who found thatTourmaline attracted small pieces of straw and ash when it was heated The first scientificdescription of this phenomenon was described by Louis Lemery in 1717 In 1747 Linnaeus firstrelated the phenomenon to electricity although this was not proven until Franz Ulrich TheodorAepinus did so in 1756

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                                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                          551 Difference between Pyroelectric and Ferroelectric Material

                                                                                          Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                                          Figure 529 Difference between a ferroelectric and pyroelectricmaterial

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                                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                          552 Theory of Piezoelectric Materials

                                                                                          From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                                          (537)

                                                                                          Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                                          Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                                          (538)

                                                                                          Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                                          we write

                                                                                          Δ OR

                                                                                          Δ (539)

                                                                                          Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                                          Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                                          (540)

                                                                                          The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                                          As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

                                                                                          Objectives_template

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                                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                          553 Measurement of Pyroelectric Coefficient

                                                                                          One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                                          (541)

                                                                                          Where Ip is the pyrocurrent and is given as

                                                                                          (542)

                                                                                          where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                                          respectively

                                                                                          Figure 530 Circuit for measuring pyroelectriccoefficient

                                                                                          Objectives_template

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                                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                          554 Direct and Indirect Effect

                                                                                          Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                          Since change in the polarization can also be expressed as depending

                                                                                          upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                          Figure 531 Direct-Indirect effect animation

                                                                                          (Courtesy copy DoITPoMS University of Cambridge)

                                                                                          >

                                                                                          Objectives_template

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                                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                          555 Common Pyroelectric Materials

                                                                                          Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                          The most common materials are tabulated below

                                                                                          Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                          LiTaO3 single crystal Hexagonal 665 -230

                                                                                          075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                          (PMN-PT) Ceramic

                                                                                          Perovskite 150 -1300

                                                                                          Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                          Triglycine sulphate

                                                                                          (NH2CH2COOH)3H2SO4

                                                                                          Sulphate 49 -280

                                                                                          Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                          5551 Triglycine Sulphate (TGS)

                                                                                          High pyroelectric coefficient

                                                                                          Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                          Can be modified to withstand temperatures above Curie point without depoling

                                                                                          Used in thermal imaging cameras

                                                                                          5552 Polyvinylidene Fluoride (PVDF)

                                                                                          Poor pyroelectric coefficient

                                                                                          Readily available in large areas of thin film

                                                                                          More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                          Low heat conductivity and low permittivity

                                                                                          High loss tangent

                                                                                          Commonly used for burglar alarms

                                                                                          5553 Perovskite Ferroelectric Ceramics

                                                                                          Generally robust and insensitive to moisture and vacuum

                                                                                          Objectives_template

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                                                                                          High pyroelectric coefficient and low loss

                                                                                          Better operation near TC

                                                                                          Strong dependence on composition

                                                                                          As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                          RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

                                                                                          Objectives_template

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                                                                                          Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                          556 Common Applications

                                                                                          5561 Burglar Alarms

                                                                                          Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                          Figure 532 Working of an IR intruder alarm

                                                                                          (Courtesy copy DoITPoMS University ofCambridge)

                                                                                          5562 Infrared or Thermal Imaging

                                                                                          Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                          The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                          >

                                                                                          Objectives_template

                                                                                          fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                          A typical photograph generated from IR imaging looks like this

                                                                                          Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                          Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                          A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                          This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                          Figure 534 Process of imagecreation

                                                                                          5563 Pollutant Control

                                                                                          The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                          Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

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                                                                                          Figure 535 Gas detection using a pyroelectricdetector

                                                                                          (Courtesy copy DoITPoMS University of Cambridge)

                                                                                          >

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                                                                                          Module 5 Nonlinear Dielectrics

                                                                                          Summary

                                                                                          Summary

                                                                                          Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_3htm[5252012 125803 PM]

                                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                            551 Difference between Pyroelectric and Ferroelectric Material

                                                                                            Although both ferroelectric and pyroelectric materials must be non-centrosymmetric and polar theessential difference between them lies when an electric field is applied While a change intemperature below Curie temperature leads to the creation of dipole along the polar axis by slightmovement of atoms from their neutral positions (A) a reverse electric field can reverse the directionof polarization in a ferroelectric but not in a pyroelectric material (B) However when the material isheated above Curie temperature the atoms come back to their equilibrium positions (C)

                                                                                            Figure 529 Difference between a ferroelectric and pyroelectricmaterial

                                                                                            Objectives_template

                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_4htm[5252012 125803 PM]

                                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                            552 Theory of Piezoelectric Materials

                                                                                            From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                                            (537)

                                                                                            Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                                            Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                                            (538)

                                                                                            Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                                            we write

                                                                                            Δ OR

                                                                                            Δ (539)

                                                                                            Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                                            Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                                            (540)

                                                                                            The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                                            As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

                                                                                            Objectives_template

                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_5htm[5252012 125803 PM]

                                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                            553 Measurement of Pyroelectric Coefficient

                                                                                            One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                                            (541)

                                                                                            Where Ip is the pyrocurrent and is given as

                                                                                            (542)

                                                                                            where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                                            respectively

                                                                                            Figure 530 Circuit for measuring pyroelectriccoefficient

                                                                                            Objectives_template

                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_6htm[5252012 125803 PM]

                                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                            554 Direct and Indirect Effect

                                                                                            Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                            Since change in the polarization can also be expressed as depending

                                                                                            upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                            Figure 531 Direct-Indirect effect animation

                                                                                            (Courtesy copy DoITPoMS University of Cambridge)

                                                                                            >

                                                                                            Objectives_template

                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                            555 Common Pyroelectric Materials

                                                                                            Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                            The most common materials are tabulated below

                                                                                            Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                            LiTaO3 single crystal Hexagonal 665 -230

                                                                                            075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                            (PMN-PT) Ceramic

                                                                                            Perovskite 150 -1300

                                                                                            Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                            Triglycine sulphate

                                                                                            (NH2CH2COOH)3H2SO4

                                                                                            Sulphate 49 -280

                                                                                            Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                            5551 Triglycine Sulphate (TGS)

                                                                                            High pyroelectric coefficient

                                                                                            Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                            Can be modified to withstand temperatures above Curie point without depoling

                                                                                            Used in thermal imaging cameras

                                                                                            5552 Polyvinylidene Fluoride (PVDF)

                                                                                            Poor pyroelectric coefficient

                                                                                            Readily available in large areas of thin film

                                                                                            More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                            Low heat conductivity and low permittivity

                                                                                            High loss tangent

                                                                                            Commonly used for burglar alarms

                                                                                            5553 Perovskite Ferroelectric Ceramics

                                                                                            Generally robust and insensitive to moisture and vacuum

                                                                                            Objectives_template

                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                            High pyroelectric coefficient and low loss

                                                                                            Better operation near TC

                                                                                            Strong dependence on composition

                                                                                            As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                            RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

                                                                                            Objectives_template

                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                            Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                            556 Common Applications

                                                                                            5561 Burglar Alarms

                                                                                            Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                            Figure 532 Working of an IR intruder alarm

                                                                                            (Courtesy copy DoITPoMS University ofCambridge)

                                                                                            5562 Infrared or Thermal Imaging

                                                                                            Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                            The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                            >

                                                                                            Objectives_template

                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                            A typical photograph generated from IR imaging looks like this

                                                                                            Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                            Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                            A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                            This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                            Figure 534 Process of imagecreation

                                                                                            5563 Pollutant Control

                                                                                            The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                            Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

                                                                                            Objectives_template

                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                            Figure 535 Gas detection using a pyroelectricdetector

                                                                                            (Courtesy copy DoITPoMS University of Cambridge)

                                                                                            >

                                                                                            Objectives_template

                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                            Module 5 Nonlinear Dielectrics

                                                                                            Summary

                                                                                            Summary

                                                                                            Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                              552 Theory of Piezoelectric Materials

                                                                                              From the fundamentals discussed in Module 4 we can write that when an electric field E is appliedto a material the total dielectric displacement ie charge per unit area of the plates on both side ofpyroelectric material ie D can be expressed as

                                                                                              (537)

                                                                                              Here e is permittivity of the pyroelectric material and Ps is the spontaneous polarization

                                                                                              Assuming electric field E as constant differentiating the above equation with temperature leads to

                                                                                              (538)

                                                                                              Now defining generalized pyroelectric coefficient Δpg as change in polarization with temperature

                                                                                              we write

                                                                                              Δ OR

                                                                                              Δ (539)

                                                                                              Here p is defined as true pyroelectric coefficient The last term in the above equation is thetemperature dependence of the permittivity of the material which we can measure

                                                                                              Since polarization is a vector the pyroelectric coefficient is also a vector and has three componentsas defined by

                                                                                              (540)

                                                                                              The above equation neglects the change in dielectric constant with temperature and is valid onlywhen such assumption is true However in practice the electrodes collecting the charges arenormal to the polar axis and we treat these quantities as scalars The coefficient is usually negativebecause polarization decreases with temperature

                                                                                              As you have seen in previous sections the behavior of polarization with temperature is dependenton the nature of transition naturally the pyroelectric coefficients are much larger in magnitude forsecond order transition than for first order transition and hence are more useful

                                                                                              Objectives_template

                                                                                              fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_5htm[5252012 125803 PM]

                                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                              553 Measurement of Pyroelectric Coefficient

                                                                                              One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                                              (541)

                                                                                              Where Ip is the pyrocurrent and is given as

                                                                                              (542)

                                                                                              where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                                              respectively

                                                                                              Figure 530 Circuit for measuring pyroelectriccoefficient

                                                                                              Objectives_template

                                                                                              fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_6htm[5252012 125803 PM]

                                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                              554 Direct and Indirect Effect

                                                                                              Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                              Since change in the polarization can also be expressed as depending

                                                                                              upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                              Figure 531 Direct-Indirect effect animation

                                                                                              (Courtesy copy DoITPoMS University of Cambridge)

                                                                                              >

                                                                                              Objectives_template

                                                                                              fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                              555 Common Pyroelectric Materials

                                                                                              Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                              The most common materials are tabulated below

                                                                                              Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                              LiTaO3 single crystal Hexagonal 665 -230

                                                                                              075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                              (PMN-PT) Ceramic

                                                                                              Perovskite 150 -1300

                                                                                              Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                              Triglycine sulphate

                                                                                              (NH2CH2COOH)3H2SO4

                                                                                              Sulphate 49 -280

                                                                                              Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                              5551 Triglycine Sulphate (TGS)

                                                                                              High pyroelectric coefficient

                                                                                              Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                              Can be modified to withstand temperatures above Curie point without depoling

                                                                                              Used in thermal imaging cameras

                                                                                              5552 Polyvinylidene Fluoride (PVDF)

                                                                                              Poor pyroelectric coefficient

                                                                                              Readily available in large areas of thin film

                                                                                              More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                              Low heat conductivity and low permittivity

                                                                                              High loss tangent

                                                                                              Commonly used for burglar alarms

                                                                                              5553 Perovskite Ferroelectric Ceramics

                                                                                              Generally robust and insensitive to moisture and vacuum

                                                                                              Objectives_template

                                                                                              fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                              High pyroelectric coefficient and low loss

                                                                                              Better operation near TC

                                                                                              Strong dependence on composition

                                                                                              As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                              RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

                                                                                              Objectives_template

                                                                                              fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                              Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                              556 Common Applications

                                                                                              5561 Burglar Alarms

                                                                                              Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                              Figure 532 Working of an IR intruder alarm

                                                                                              (Courtesy copy DoITPoMS University ofCambridge)

                                                                                              5562 Infrared or Thermal Imaging

                                                                                              Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                              The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                              >

                                                                                              Objectives_template

                                                                                              fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                              A typical photograph generated from IR imaging looks like this

                                                                                              Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                              Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                              A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                              This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                              Figure 534 Process of imagecreation

                                                                                              5563 Pollutant Control

                                                                                              The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                              Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

                                                                                              Objectives_template

                                                                                              fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                              Figure 535 Gas detection using a pyroelectricdetector

                                                                                              (Courtesy copy DoITPoMS University of Cambridge)

                                                                                              >

                                                                                              Objectives_template

                                                                                              fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                              Module 5 Nonlinear Dielectrics

                                                                                              Summary

                                                                                              Summary

                                                                                              Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                                fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_5htm[5252012 125803 PM]

                                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                553 Measurement of Pyroelectric Coefficient

                                                                                                One of the direct methods of measurement of pyroelectric measurement is shown below The circuitconnecting a pyroelectric material (held inside an oven) with an amplifier and then measuring thepyro-current The pyroelectric coefficient is given as

                                                                                                (541)

                                                                                                Where Ip is the pyrocurrent and is given as

                                                                                                (542)

                                                                                                where Rs and Ra are the leakage resistance of the sample and input resistance of the amplifier

                                                                                                respectively

                                                                                                Figure 530 Circuit for measuring pyroelectriccoefficient

                                                                                                Objectives_template

                                                                                                fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_6htm[5252012 125803 PM]

                                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                554 Direct and Indirect Effect

                                                                                                Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                                Since change in the polarization can also be expressed as depending

                                                                                                upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                                Figure 531 Direct-Indirect effect animation

                                                                                                (Courtesy copy DoITPoMS University of Cambridge)

                                                                                                >

                                                                                                Objectives_template

                                                                                                fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                555 Common Pyroelectric Materials

                                                                                                Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                                The most common materials are tabulated below

                                                                                                Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                                LiTaO3 single crystal Hexagonal 665 -230

                                                                                                075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                                (PMN-PT) Ceramic

                                                                                                Perovskite 150 -1300

                                                                                                Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                                Triglycine sulphate

                                                                                                (NH2CH2COOH)3H2SO4

                                                                                                Sulphate 49 -280

                                                                                                Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                                5551 Triglycine Sulphate (TGS)

                                                                                                High pyroelectric coefficient

                                                                                                Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                                Can be modified to withstand temperatures above Curie point without depoling

                                                                                                Used in thermal imaging cameras

                                                                                                5552 Polyvinylidene Fluoride (PVDF)

                                                                                                Poor pyroelectric coefficient

                                                                                                Readily available in large areas of thin film

                                                                                                More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                                Low heat conductivity and low permittivity

                                                                                                High loss tangent

                                                                                                Commonly used for burglar alarms

                                                                                                5553 Perovskite Ferroelectric Ceramics

                                                                                                Generally robust and insensitive to moisture and vacuum

                                                                                                Objectives_template

                                                                                                fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                                High pyroelectric coefficient and low loss

                                                                                                Better operation near TC

                                                                                                Strong dependence on composition

                                                                                                As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                                RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

                                                                                                Objectives_template

                                                                                                fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                556 Common Applications

                                                                                                5561 Burglar Alarms

                                                                                                Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                                Figure 532 Working of an IR intruder alarm

                                                                                                (Courtesy copy DoITPoMS University ofCambridge)

                                                                                                5562 Infrared or Thermal Imaging

                                                                                                Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                                The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                                >

                                                                                                Objectives_template

                                                                                                fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                A typical photograph generated from IR imaging looks like this

                                                                                                Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                                Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                                A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                                This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                                Figure 534 Process of imagecreation

                                                                                                5563 Pollutant Control

                                                                                                The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                                Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

                                                                                                Objectives_template

                                                                                                fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                Figure 535 Gas detection using a pyroelectricdetector

                                                                                                (Courtesy copy DoITPoMS University of Cambridge)

                                                                                                >

                                                                                                Objectives_template

                                                                                                fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                                Module 5 Nonlinear Dielectrics

                                                                                                Summary

                                                                                                Summary

                                                                                                Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                                  fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_6htm[5252012 125803 PM]

                                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                  554 Direct and Indirect Effect

                                                                                                  Since all pyroelectric materials are naturally piezoelectric in nature the thermalexpansioncontraction of the material while heating or cooling induces thermal stresses in thematerial which in turn induce their own polarization and hence changing the overall polarization

                                                                                                  Since change in the polarization can also be expressed as depending

                                                                                                  upon the sign of each of these term the polarization will either decrease or increase with increasingtemperature

                                                                                                  Figure 531 Direct-Indirect effect animation

                                                                                                  (Courtesy copy DoITPoMS University of Cambridge)

                                                                                                  >

                                                                                                  Objectives_template

                                                                                                  fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                  555 Common Pyroelectric Materials

                                                                                                  Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                                  The most common materials are tabulated below

                                                                                                  Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                                  LiTaO3 single crystal Hexagonal 665 -230

                                                                                                  075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                                  (PMN-PT) Ceramic

                                                                                                  Perovskite 150 -1300

                                                                                                  Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                                  Triglycine sulphate

                                                                                                  (NH2CH2COOH)3H2SO4

                                                                                                  Sulphate 49 -280

                                                                                                  Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                                  5551 Triglycine Sulphate (TGS)

                                                                                                  High pyroelectric coefficient

                                                                                                  Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                                  Can be modified to withstand temperatures above Curie point without depoling

                                                                                                  Used in thermal imaging cameras

                                                                                                  5552 Polyvinylidene Fluoride (PVDF)

                                                                                                  Poor pyroelectric coefficient

                                                                                                  Readily available in large areas of thin film

                                                                                                  More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                                  Low heat conductivity and low permittivity

                                                                                                  High loss tangent

                                                                                                  Commonly used for burglar alarms

                                                                                                  5553 Perovskite Ferroelectric Ceramics

                                                                                                  Generally robust and insensitive to moisture and vacuum

                                                                                                  Objectives_template

                                                                                                  fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                                  High pyroelectric coefficient and low loss

                                                                                                  Better operation near TC

                                                                                                  Strong dependence on composition

                                                                                                  As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                                  RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

                                                                                                  Objectives_template

                                                                                                  fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                  Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                  556 Common Applications

                                                                                                  5561 Burglar Alarms

                                                                                                  Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                                  Figure 532 Working of an IR intruder alarm

                                                                                                  (Courtesy copy DoITPoMS University ofCambridge)

                                                                                                  5562 Infrared or Thermal Imaging

                                                                                                  Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                                  The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                                  >

                                                                                                  Objectives_template

                                                                                                  fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                  A typical photograph generated from IR imaging looks like this

                                                                                                  Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                                  Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                                  A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                                  This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                                  Figure 534 Process of imagecreation

                                                                                                  5563 Pollutant Control

                                                                                                  The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                                  Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

                                                                                                  Objectives_template

                                                                                                  fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                  Figure 535 Gas detection using a pyroelectricdetector

                                                                                                  (Courtesy copy DoITPoMS University of Cambridge)

                                                                                                  >

                                                                                                  Objectives_template

                                                                                                  fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                                  Module 5 Nonlinear Dielectrics

                                                                                                  Summary

                                                                                                  Summary

                                                                                                  Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                                    fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                    555 Common Pyroelectric Materials

                                                                                                    Most of the inorganic pyroelectrics (including ferroelectrics) are perovskite structured For a generaldiscussion on pyroelectric materials you can refer to the review article by Roger Whatmore

                                                                                                    The most common materials are tabulated below

                                                                                                    Material Structure Tc (degC) Pyroelectric Coefficient(microCm-2K-1)

                                                                                                    LiTaO3 single crystal Hexagonal 665 -230

                                                                                                    075Pb(Mg13-Nb23)O3-025PbTiO3

                                                                                                    (PMN-PT) Ceramic

                                                                                                    Perovskite 150 -1300

                                                                                                    Ba067Sr033TiO3 (BST) Ceramic Perovskite 25 -7000

                                                                                                    Triglycine sulphate

                                                                                                    (NH2CH2COOH)3H2SO4

                                                                                                    Sulphate 49 -280

                                                                                                    Polyvinylidene fluoride (PVDF) film Polymer 80 -27

                                                                                                    5551 Triglycine Sulphate (TGS)

                                                                                                    High pyroelectric coefficient

                                                                                                    Fragile and water-soluble difficult to handle and cannot be used in devices where it would besubjected to either a hard vacuum or high humidity as it tends to decompose

                                                                                                    Can be modified to withstand temperatures above Curie point without depoling

                                                                                                    Used in thermal imaging cameras

                                                                                                    5552 Polyvinylidene Fluoride (PVDF)

                                                                                                    Poor pyroelectric coefficient

                                                                                                    Readily available in large areas of thin film

                                                                                                    More stable to heat vacuum and moisture than TGS mechanically robust

                                                                                                    Low heat conductivity and low permittivity

                                                                                                    High loss tangent

                                                                                                    Commonly used for burglar alarms

                                                                                                    5553 Perovskite Ferroelectric Ceramics

                                                                                                    Generally robust and insensitive to moisture and vacuum

                                                                                                    Objectives_template

                                                                                                    fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                                    High pyroelectric coefficient and low loss

                                                                                                    Better operation near TC

                                                                                                    Strong dependence on composition

                                                                                                    As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                                    RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

                                                                                                    Objectives_template

                                                                                                    fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                    Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                    556 Common Applications

                                                                                                    5561 Burglar Alarms

                                                                                                    Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                                    Figure 532 Working of an IR intruder alarm

                                                                                                    (Courtesy copy DoITPoMS University ofCambridge)

                                                                                                    5562 Infrared or Thermal Imaging

                                                                                                    Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                                    The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                                    >

                                                                                                    Objectives_template

                                                                                                    fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                    A typical photograph generated from IR imaging looks like this

                                                                                                    Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                                    Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                                    A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                                    This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                                    Figure 534 Process of imagecreation

                                                                                                    5563 Pollutant Control

                                                                                                    The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                                    Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

                                                                                                    Objectives_template

                                                                                                    fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                    Figure 535 Gas detection using a pyroelectricdetector

                                                                                                    (Courtesy copy DoITPoMS University of Cambridge)

                                                                                                    >

                                                                                                    Objectives_template

                                                                                                    fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                                    Module 5 Nonlinear Dielectrics

                                                                                                    Summary

                                                                                                    Summary

                                                                                                    Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                                      fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_7htm[5252012 125804 PM]

                                                                                                      High pyroelectric coefficient and low loss

                                                                                                      Better operation near TC

                                                                                                      Strong dependence on composition

                                                                                                      As a very approximate guide for large area applications low dielectric constant materials such asPVDF are preferred while for small area applications materials with large dielectric constant suchas perovskite oxides are preferred

                                                                                                      RW Whatmore Pyroelectric devices and materials Reports and Progress in Physics Volume 49Page 1335 (1986)

                                                                                                      Objectives_template

                                                                                                      fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                      Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                      556 Common Applications

                                                                                                      5561 Burglar Alarms

                                                                                                      Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                                      Figure 532 Working of an IR intruder alarm

                                                                                                      (Courtesy copy DoITPoMS University ofCambridge)

                                                                                                      5562 Infrared or Thermal Imaging

                                                                                                      Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                                      The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                                      >

                                                                                                      Objectives_template

                                                                                                      fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                      A typical photograph generated from IR imaging looks like this

                                                                                                      Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                                      Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                                      A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                                      This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                                      Figure 534 Process of imagecreation

                                                                                                      5563 Pollutant Control

                                                                                                      The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                                      Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

                                                                                                      Objectives_template

                                                                                                      fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                      Figure 535 Gas detection using a pyroelectricdetector

                                                                                                      (Courtesy copy DoITPoMS University of Cambridge)

                                                                                                      >

                                                                                                      Objectives_template

                                                                                                      fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                                      Module 5 Nonlinear Dielectrics

                                                                                                      Summary

                                                                                                      Summary

                                                                                                      Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                                        Objectives_template

                                                                                                        fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                        Module 5 Nonlinear Dielectrics Pyroelectric Ceramics

                                                                                                        556 Common Applications

                                                                                                        5561 Burglar Alarms

                                                                                                        Change in temperature of detector against the ambient temperature when an intruder comes in thevicinity of the alarm leads to a voltage which can be used to trigger an alarm To avoid the effectsdue to thermal expansion one needs to use a reference identical material to counter theseextraneous effects Such detectors can sense the objects presence up to about 100 m

                                                                                                        Figure 532 Working of an IR intruder alarm

                                                                                                        (Courtesy copy DoITPoMS University ofCambridge)

                                                                                                        5562 Infrared or Thermal Imaging

                                                                                                        Just like we use visible light to make a photograph infrared (IR) radiation emitted by objects atdifferent temperatures is focused onto a sensitive plate to create thermal image of the object The atmospheric window typically used in IR imaging is from 8 to 14 microm and co-incidentally thepower radiated from a black body at 300K peaks around 10 microm making it a perfect match

                                                                                                        The pyroelectric elements used in the devices are typically square plates with sides about a mmlong and thicknesses around 30 microm Because entire scenes are focused onto the plates in thermalimaging they have to be larger typically squares of side about 1 cm the thicknesses are the sameas for the simpler devices

                                                                                                        >

                                                                                                        Objectives_template

                                                                                                        fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                        A typical photograph generated from IR imaging looks like this

                                                                                                        Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                                        Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                                        A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                                        This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                                        Figure 534 Process of imagecreation

                                                                                                        5563 Pollutant Control

                                                                                                        The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                                        Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

                                                                                                        Objectives_template

                                                                                                        fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                        Figure 535 Gas detection using a pyroelectricdetector

                                                                                                        (Courtesy copy DoITPoMS University of Cambridge)

                                                                                                        >

                                                                                                        Objectives_template

                                                                                                        fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                                        Module 5 Nonlinear Dielectrics

                                                                                                        Summary

                                                                                                        Summary

                                                                                                        Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                                          fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                          A typical photograph generated from IR imaging looks like this

                                                                                                          Figure 533 IR image of a dog (Ref Wikipedia) Bar onthe right shows the temperature-colour relation

                                                                                                          Here is a simple explanation of how IT imaging using pyroelectrics works

                                                                                                          A special lens focuses the infrared light emitted by all of the objects in viewThe focused light is scanned by a phased array of pyroelectric elements which create a very detailedtemperature pattern called a thermogram It only takes about one-thirtieth of a second for thedetector array to obtain to create a thermogram This information is obtained from several thousandpoints in the field of view of the detector array

                                                                                                          This thermogram is translated into electrical signals which are sent to a signal-processing unit whichthen translates the information from the elements into data for the displayThe signal-processing unit sends the information to the display where it appears as various colorsdepending on the intensity of the infrared emission The combination of all the signals from all of theelements creates the image

                                                                                                          Figure 534 Process of imagecreation

                                                                                                          5563 Pollutant Control

                                                                                                          The reduction of pollution and greenhouse gases has become a major priority for our country as weprogress This requires us to monitor the levels of pollution We can use pyroelectric materials forthese purposes as well

                                                                                                          Pyroelectrics being excellent detectors of IR radiation can easily detect the level of IR radiationwhich passes through a gas sample Since each gas has a characteristic wavelength which itabsorbs we can measure it easily

                                                                                                          Objectives_template

                                                                                                          fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                          Figure 535 Gas detection using a pyroelectricdetector

                                                                                                          (Courtesy copy DoITPoMS University of Cambridge)

                                                                                                          >

                                                                                                          Objectives_template

                                                                                                          fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                                          Module 5 Nonlinear Dielectrics

                                                                                                          Summary

                                                                                                          Summary

                                                                                                          Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_8htm[5252012 125804 PM]

                                                                                                            Figure 535 Gas detection using a pyroelectricdetector

                                                                                                            (Courtesy copy DoITPoMS University of Cambridge)

                                                                                                            >

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                                                                                                            fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                                            Module 5 Nonlinear Dielectrics

                                                                                                            Summary

                                                                                                            Summary

                                                                                                            Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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                                                                                                              fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture30(33)30_9htm[5252012 125804 PM]

                                                                                                              Module 5 Nonlinear Dielectrics

                                                                                                              Summary

                                                                                                              Summary

                                                                                                              Pyroelectric materials are different from the ferroelectric materials in the sense that in the former thepolarization direction cannot be reserved by changing the direction of applied electric field Thesematerials are of immense use because of their ability to demonstrate surface voltage by subjecting tochanging temperature These have found applications in burglar alarms and in infrared imaging

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