dielectrics_lect28

1

Dielectric MaterialsDielectric Materials

Chemistry 754Chemistry 754Solid State Chemistry Solid State Chemistry

Lecture #27Lecture #27June 4, 2002June 4, 2002

ReferencesReferencesA.R. WestA.R. West �� ��Solid State Chemistry and it�s Solid State Chemistry and it�s

ApplicationsApplications�, Wiley (1984)�, Wiley (1984)

R.H. MitchellR.H. Mitchell �� �Perovskites: Modern & Ancient �, �Perovskites: Modern & Ancient �, Almaz Almaz Press, (www.Press, (www.almazpressalmazpress.com) (2002).com) (2002)

P. P. Shiv Halasyamani Shiv Halasyamani & K.R. & K.R. PoeppelmeierPoeppelmeier �� �Non�Non--centrosymmetriccentrosymmetric Oxides�, Oxides�, Chem. MaterChem. Mater. . 1010, 2753, 2753--2769 (1998).2769 (1998).

M. Kunz & I.D. BrownM. Kunz & I.D. Brown �� �Out�Out--ofof--center Distortions center Distortions around Octahedrally Coordinated daround Octahedrally Coordinated d00 Transition Transition Metals�, Metals�, J. Solid State Chem.J. Solid State Chem. 115115, 395, 395--406 (1995).406 (1995).

A. Safari, R.K. Panda, V.F. Janas (Dept. of Ceramics, Rutgers University) http://www.rci.rutgers.edu/~ecerg/projects/ferroelectric.html

2

Dielectric ConstantDielectric ConstantIf you apply an electric field, E, across a material the chargesIf you apply an electric field, E, across a material the charges in the material in the material will respond in such a way as to reduce (shield) the field experwill respond in such a way as to reduce (shield) the field experienced within ienced within

the material, D (electric displacement)the material, D (electric displacement)

D = D = εεEE = = εε00E + P = E + P = εε00E + E + εε00χχeeE = E = εε00(1+(1+χχee)E)Ewhere where εεεεεεεε00 is the is the dielctricdielctric permitivity of free space (8.85 x 10permitivity of free space (8.85 x 101212 CC22/N/N--mm22), P is ), P is

the polarization of the material, and the polarization of the material, and χχχχχχχχee is the electric susceptibility. The is the electric susceptibility. The relative permitivity or dielectric constant of a material is defrelative permitivity or dielectric constant of a material is defined as:ined as:

εεrr = = ε/εε/ε00 = 1+= 1+χχee

When evaluating the dielectric properties of materials it is thiWhen evaluating the dielectric properties of materials it is this quantity we s quantity we will use to quantify the response of a material to an applied elwill use to quantify the response of a material to an applied electric field.ectric field.

Contributions to Contributions to PolarizabilityPolarizabilityαααααααα = = ααααααααee + + ααααααααii + + ααααααααdd + + ααααααααss

1. Electronic 1. Electronic Polarizability Polarizability ((ααee))Polarization of localized electronsPolarization of localized electrons

2. Ionic 2. Ionic PolarizabilityPolarizability ((ααii))Displacement of ionsDisplacement of ions

3. Dipolar 3. Dipolar PolarizabilityPolarizability ((ααdd))Reorientation of polar moleculesReorientation of polar molecules

4. Space Charge 4. Space Charge PolarizabilityPolarizability ((ααss))Long range charge migrationLong range charge migration

Polarizability Polarizability ((αα) increases) increases

Response Time Response Time Increases Increases

(slower (slower response)response)

3

Frequency DependenceFrequency DependenceReorientation of the dipoles in response to an electric field isReorientation of the dipoles in response to an electric field is characterized characterized by a relaxation time, by a relaxation time, ττττττττ. The relaxation time varies for each of the various . The relaxation time varies for each of the various contributions to the contributions to the polarizabilitypolarizability::

1. Electronic1. Electronic PolarizabilityPolarizability ((ααααααααee))Response is fast, Response is fast, ττ is smallis small

2. Ionic2. Ionic PolarizabilityPolarizability ((ααααααααii))Response is slowerResponse is slower

3. Dipolar3. Dipolar PolarizabilityPolarizability ((ααααααααdd))Response is still slowerResponse is still slower

4. Space Charge4. Space Charge PolarizabilityPolarizability ((ααααααααss))Response is quite slow, Response is quite slow, ττττττττ is largeis large

AudiofrequenciesAudiofrequencies (~ 10(~ 1033 Hz)Hz) αααααααα = = ααααααααee++ααααααααii++ααααααααdd++ααααααααssRadiofrequenciesRadiofrequencies (~ 10(~ 1066 Hz)Hz) ((ααααααααss →→ 0)0) αααααααα = = ααααααααee++ααααααααii++ααααααααddMicrowave frequenciesMicrowave frequencies (~ 10(~ 1099 Hz)Hz) ((ααααααααss, , ααααααααdd →→ 0)0) αααααααα = = ααααααααee++ααααααααiiVisible/UV frequenciesVisible/UV frequencies (~ 10(~ 101212 Hz)Hz) ((ααααααααss, , ααααααααdd, , ααααααααii →→ 0)0) αααααααα = = ααααααααee

Dielectric LossDielectric Loss

When the relaxation time is much When the relaxation time is much fasterfaster than the than the frequency of the applied electric field, frequency of the applied electric field, polarization polarization occurs instantaneouslyoccurs instantaneously..

When the relaxation time is much When the relaxation time is much slowerslower than the than the frequency of the applied electric field, frequency of the applied electric field, no polarization no polarization (of that type) occurs(of that type) occurs..

When the relaxation time and the frequency of the When the relaxation time and the frequency of the applied field are similar, a phase lag occurs and energy applied field are similar, a phase lag occurs and energy is absorbed. This is called dielectric loss, it is normally is absorbed. This is called dielectric loss, it is normally quantified by the relationshipquantified by the relationship

tan tan δδδδδδδδ = = εεεεεεεεrr�/�/εεεεεεεεrr��where where εεrr� � is the real part of the dielectric constant and is the real part of the dielectric constant and εεrr� is the � is the imaginary part of the dielectric constant.imaginary part of the dielectric constant.

4

Frequency DependenceFrequency Dependenceεεεε(ωωωω)

εεεε∞∞∞∞

εεεε0

log(ωωωω)

Microwaves

IR

UV

ααααd++++ααααi++++ααααe

ααααi++++ααααe

ααααe only

tan δ(Loss)

εεεεr (Dielectric Const.)

Ionic Polarization and FerroelectricityIonic Polarization and FerroelectricityMost dielectric materials are insulating (no conductivity of eitMost dielectric materials are insulating (no conductivity of either her electrons or ions) dense solids (no molecules that can reorient)electrons or ions) dense solids (no molecules that can reorient). . Therefore, the Therefore, the polarizability polarizability must come from either ionic and must come from either ionic and electronic electronic polarizabilitypolarizability. Of these two ionic . Of these two ionic polarizability polarizability can make can make the largest contribution, particularly in a class of solids callthe largest contribution, particularly in a class of solids called ed ferroelectrics. The ionic ferroelectrics. The ionic polarizability polarizability will be large, and a will be large, and a ferroelectric material will result, when the following two condiferroelectric material will result, when the following two conditions tions are met:are met:

1.1. Certain ions in the structure displace in response to the Certain ions in the structure displace in response to the application of an external electric field. Typically this application of an external electric field. Typically this requires the presence of certain types of ions such as drequires the presence of certain types of ions such as d00

or sor s22pp00 cations.cations.

2.2. The displacements line up in the same direction (or at The displacements line up in the same direction (or at least they do not cancel out). This cannot happen if the least they do not cancel out). This cannot happen if the crystal structure has an inversion center.crystal structure has an inversion center.

3.3. The displacements do not disappear when the electric The displacements do not disappear when the electric field is removed.field is removed.

5

What is a FerroelectricWhat is a FerroelectricA ferroelectric material develops a spontaneous polarization A ferroelectric material develops a spontaneous polarization (builds up a charge) in response to an external electric field. (builds up a charge) in response to an external electric field.

��The polarization does not The polarization does not go away when the go away when the external field is removed.external field is removed.

��The direction of the The direction of the polarization is reversible.polarization is reversible.

Applications of Applications of Ferroelectric Ferroelectric MaterialsMaterials��MultilayerMultilayer capacitorscapacitors��NonNon--volatile FRAM (volatile FRAM (FerroelectricFerroelectric Random Access Memory)Random Access Memory)

22ndnd Order JahnOrder Jahn--Teller DistortionsTeller DistortionsOccurs when the HOMOOccurs when the HOMO--LUMO gap is small and there is a symmetry allowed LUMO gap is small and there is a symmetry allowed distortion which gives rise to mixing between the two. This disdistortion which gives rise to mixing between the two. This distortion is tortion is favored because it stabilizes the HOMO, while destabilizing the favored because it stabilizes the HOMO, while destabilizing the LUMO. LUMO. Second order JahnSecond order Jahn--Teller Distortions are typically observed for two classes Teller Distortions are typically observed for two classes of cations.of cations.

1.1. Octahedrally coordinated high Octahedrally coordinated high valent valent dd00 cations (i.e. Tications (i.e. Ti4+4+, Nb, Nb5+5+, , WW6+6+, Mo, Mo6+6+). ).

�� BaTiOBaTiO33, KNbO, KNbO33, WO, WO33

�� Increasingly favored as the HOMOIncreasingly favored as the HOMO--LUMO splitting LUMO splitting decreases (covalency of the Mdecreases (covalency of the M--O bonds increases)O bonds increases)

2.2. Cations containing filled valence s shells (SnCations containing filled valence s shells (Sn2+2+, Sb, Sb3+3+, Pb, Pb2+2+, Bi, Bi3+3+))�� Red Red PbOPbO, , TlITlI, , SnOSnO, Bi, Bi44TiTi33OO1212, Ba, Ba33BiBi22TeOTeO99

�� SOJT Distortion leads to development of a SOJT Distortion leads to development of a stereoactive stereoactive electronelectron--lone pair.lone pair.

6

Octahedral dOctahedral d00 CationCation

ΓΓΓΓ point(kx=ky=0)

non-bonding

In the cubic perovskite structure the In the cubic perovskite structure the bottom of the conduction band is nonbottom of the conduction band is non--

bonding M tbonding M t2g2g, and the top of the , and the top of the valence band is nonvalence band is non--bonding O 2p. If bonding O 2p. If

the symmetry is lowered the two the symmetry is lowered the two states can mix, lowering the energy of states can mix, lowering the energy of

the occupied VB states and raising the occupied VB states and raising the energy of the empty CB states. the energy of the empty CB states.

This is a 2This is a 2ndnd order JT dist.order JT dist.

22ndnd Order JT Distortion Order JT Distortion Band PictureBand Picture

M t2g(ππππ*)

EF

DOS

O 2p

M t2g(ππππ*)

EF

DOS

Overlap at Overlap at ΓΓ is is nonnon--bonding by bonding by

symmetrysymmetry

Overlap at Overlap at ΓΓ is is slightly slightly

antibonding antibonding in the in the CB & slightly CB & slightly

bonding in the VB.bonding in the VB.

The 2The 2ndnd order JT distortion reduces the order JT distortion reduces the symmetry and widens the band gap. It is the symmetry and widens the band gap. It is the driving force for stabilizing ionic shifts. The driving force for stabilizing ionic shifts. The stabilization disappears by the time you get stabilization disappears by the time you get

to a dto a d11 TM ion. Hence, ReOTM ion. Hence, ReO33 is cubic.is cubic.See Wheeler et al. J. Amer. Chem. Soc. 108, 2222 (1986), and/or

T. Hughbanks, J. Am. Chem. Soc. 107, 6851-6859 (1985).

7

What Determines the Orientation What Determines the Orientation of the Cation Displacements?of the Cation Displacements?

Tetragonal Tetragonal BaTiOBaTiO33

d=2.21d=2.21ÅÅs = 0.34s = 0.34

d=1.83d=1.83ÅÅs = 0.96s = 0.96

MoOMoO33

d=1.67d=1.67ÅÅs = 1.90s = 1.90

d=2.33d=2.33ÅÅs = 0.32s = 0.32

d=1.95d=1.95ÅÅs = 0.90s = 0.90

The 2The 2ndnd Order JT effect at the Order JT effect at the metal only dictates that a distortion metal only dictates that a distortion should occur. It doesn�t tell how the should occur. It doesn�t tell how the

displacements will order. That displacements will order. That depends upon: depends upon:

(i)(i) the valence requirements at the valence requirements at the anion the anion (i.e. 2 short or 2 long (i.e. 2 short or 2 long

bonds to same anion is unfavorable),bonds to same anion is unfavorable),(ii)(ii) cationcation--cation repulsions cation repulsions (high (high

oxidation state cations prefer to oxidation state cations prefer to move away from each other)move away from each other)

See Kunz & Brown J. Solid State Chem.J. Solid State Chem. 115115, 395, 395--406 (1995).406 (1995).

Why is BaTiOWhy is BaTiO33 FerroelectricFerroelectric

��BaBa2+2+ is larger than the vacancy in the is larger than the vacancy in the octahedral network tolerance factor > 1.octahedral network tolerance factor > 1.

��This expands the octahedron, which leads to This expands the octahedron, which leads to a shift of Tia shift of Ti4+4+ toward one of the corners of toward one of the corners of the octahedron.the octahedron.

��The direction of the shift can be altered The direction of the shift can be altered through application of an electric field.through application of an electric field.

8

BaTiOBaTiO33 Phase Phase TransitionsTransitions

Cubic (Pm3m)Cubic (Pm3m)T > 393 KT > 393 K

TiTi--O Distances (Å)O Distances (Å)66××××××××2.002.00

Tetragonal (P4mm)Tetragonal (P4mm)273 K < T < 393 K273 K < T < 393 KTiTi--O Distances (Å)O Distances (Å)1.83, 41.83, 4××××××××2.00, 2.212.00, 2.21

Toward a cornerToward a cornerOrthorhombic (Amm2)Orthorhombic (Amm2)183 K < T < 273 K183 K < T < 273 KTiTi--O Distances (Å)O Distances (Å)

22××××××××1.87, 21.87, 2××××××××2.00, 22.00, 2××××××××2.172.17Toward an edgeToward an edge

RhombohedralRhombohedral (R3m)(R3m)183 K < T < 273 K183 K < T < 273 KTiTi--O Distances (Å)O Distances (Å)

33××××××××1.88, 31.88, 3××××××××2.132.13Toward a faceToward a face

In the cubic structure BaTiOIn the cubic structure BaTiO33 is is paraelectricparaelectric. That is to say that the . That is to say that the

orientations of the ionic orientations of the ionic displacements are not ordered and displacements are not ordered and

dynamic.dynamic.

Below 393 K BaTiOBelow 393 K BaTiO33 becomes becomes ferroelectric ferroelectric and the displacement and the displacement

of the Tiof the Ti4+4+ ions progressively ions progressively displace upon cooling.displace upon cooling.

See Kwei et al. J. Phys. Chem. 97, 2368 (1993),

Structure, Bonding and PropertiesStructure, Bonding and PropertiesGiven what you know about 2Given what you know about 2ndnd order JT distortions and ferroelectric order JT distortions and ferroelectric distortions can you explain the following physical properties.distortions can you explain the following physical properties.

BaTiOBaTiO33 : : Ferroelectric (TFerroelectric (TCC ~ 130~ 130°°C, C, εεεεεεεεrr > 1000)> 1000)��

SrTiOSrTiO33 : : Insulator, Normal dielectric (Insulator, Normal dielectric (εεεεεεεεrr ~ x)~ x)��

PbTiOPbTiO33 : : Ferroelectric (TFerroelectric (TCC ~ 490~ 490°°C)C)��

BaSnOBaSnO3 3 :: Insulator, Normal dielectric (Insulator, Normal dielectric (εεεεεεεεrr ~ x)~ x)��

KNbOKNbO33 : : Ferroelectric (TFerroelectric (TCC ~ x)~ x)��

KTaOKTaO33 : : Insulator, Normal dielectric (Insulator, Normal dielectric (εεεεεεεεrr ~ x)~ x)��

9

Structure, Bonding and PropertiesStructure, Bonding and PropertiesBaTiOBaTiO33 : : Ferroelectric (TFerroelectric (TCC ~ 130~ 130°°C, C, εεεεεεεεrr > 1000)> 1000)

�� BaBa2+2+ ion stretches the octahedra (Tiion stretches the octahedra (Ti--O dist. ~ 2.00Å), this lowers energy O dist. ~ 2.00Å), this lowers energy of CB (LUMO) and stabilizes SOJT dist.of CB (LUMO) and stabilizes SOJT dist.

SrTiOSrTiO33 : : Insulator, Normal dielectric (Insulator, Normal dielectric (εεεεεεεεrr ~ x)~ x)�� SrSr2+2+ ion is a good fit (Tiion is a good fit (Ti--O dist. ~ 1.95O dist. ~ 1.95ÅÅ), this compound is close to a ), this compound is close to a

ferroelectric instability and is called a quantum paraelectric.ferroelectric instability and is called a quantum paraelectric.PbTiOPbTiO33 : : Ferroelectric (TFerroelectric (TCC ~ 490~ 490°°C)C)

�� Displacements of both TiDisplacements of both Ti4+4+ and Pband Pb2+2+ (6s(6s226p6p00 cation) stabilize cation) stabilize ferroelectricityferroelectricity

BaSnOBaSnO3 3 :: Insulator, Normal dielectric (Insulator, Normal dielectric (εεεεεεεεrr ~ x)~ x)�� Main group SnMain group Sn4+4+ has no low lying thas no low lying t2g2g orbitals orbitals and no tendency toward SOJT and no tendency toward SOJT

dist.dist.KNbOKNbO33 : : Ferroelectric (TFerroelectric (TCC ~ x)~ x)

�� Behavior is very similar to BaTiOBehavior is very similar to BaTiO33

KTaOKTaO33 : : Insulator, Normal dielectric (Insulator, Normal dielectric (εεεεεεεεrr ~ x)~ x)�� Ta 5dTa 5d orbitalsorbitals are more electropositive and have a larger spatial extent are more electropositive and have a larger spatial extent

than than Nb Nb 4d 4d orbitalsorbitals (greater spatial overlap with O 2p), both effects raise (greater spatial overlap with O 2p), both effects raise the energy of the tthe energy of the t2g2g LUMO, diminishing the driving force for a SOJT dist.LUMO, diminishing the driving force for a SOJT dist.

22ndnd Order JahnOrder Jahn--Teller Distortions Teller Distortions with swith s22pp00 Main Group CationsMain Group Cations

FactFact: : Main group cations that retain 2 valence electrons (i.e. Main group cations that retain 2 valence electrons (i.e. TlTl++, Pb, Pb2+2+, Bi, Bi3+3+, , SnSn2+2+, Sb, Sb3+3+, Te, Te4+4+, Ge, Ge2+2+, As, As3+3+, Se, Se4+4+, , ectect.) tend to prefer distorted environments. .) tend to prefer distorted environments.

MM--X Bonding:X Bonding: The occupied cation s The occupied cation s orbitals orbitals have an have an antibonding antibonding interaction interaction with the surrounding with the surrounding ligandsligands. .

Symmetric CoordinationSymmetric Coordination: The occupied M s and empty M p : The occupied M s and empty M p orbitals orbitals are not are not allowed by symmetry to mix.allowed by symmetry to mix.

Distorted CoordinationDistorted Coordination: : The lower symmetry allows mixing of s and at least The lower symmetry allows mixing of s and at least one p orbital on the metal. This lowers the energy of the occupone p orbital on the metal. This lowers the energy of the occupied orbital, ied orbital, which now forms an orbital which is largely nonwhich now forms an orbital which is largely non--bonding and has strong mixed bonding and has strong mixed sp character. It is generally referred to as a sp character. It is generally referred to as a stereoactive stereoactive electron lone pair electron lone pair (for example as seen in NH(for example as seen in NH33).).

Tetrahedral CoordinationTetrahedral Coordination (T(Tdd): s): s--orbital = orbital = aa11, p, p--orbitalsorbitals = = tt22TrigonalTrigonal Pyramidal Pyramidal CoordCoord.. (C(C3v3v): s): s--orbital = orbital = aa11, p, p--orbitalsorbitals = = e,e,aa11Octahedral CoordinationOctahedral Coordination (O(Ohh): s): s--orbital = orbital = aa1g1g, p, p--orbitalsorbitals = = tt1u1uSquare Pyramidal Square Pyramidal CoordCoord.. (C(C4v4v): s): s--orbital = orbital = aa11, p, p--orbitalsorbitals = = e,e,aa11

10

Some Examples sSome Examples s22pp00 SOJTSOJT

Red Red PbOPbODistorted Distorted CsClCsCl

CsGeBrCsGeBr33

Distorted Distorted PerovskitePerovskite

SbClSbCl33Trig. Pyramidal Trig. Pyramidal

SbSb3+3+

Cooperative SOJT DistortionsCooperative SOJT Distortions

Tetragonal PbTiOTetragonal PbTiO33TTCC = 490°C= 490°C

Ti displacement = 0.323 ÅTi displacement = 0.323 ÅTiTi--O short = 1.77 ÅO short = 1.77 ÅTiTi--O long = 2.39 ÅO long = 2.39 Å

PbPb2+2+ displacement = 0.48 Ådisplacement = 0.48 Å

Tetragonal BaTiOTetragonal BaTiO33TTCC = 120°C= 120°C

Ti displacement = 0.125 ÅTi displacement = 0.125 ÅTiTi--O short = 1.83 ÅO short = 1.83 ÅTiTi--O long = 2.21 ÅO long = 2.21 Å

BaBa2+2+ displacement = 0.067 Ådisplacement = 0.067 Å

11

Related Dielectric PhenomenaRelated Dielectric Phenomena

PyroelectricityPyroelectricity �� Similar to ferroelectricity, but the Similar to ferroelectricity, but the ionic shifts which give rise to spontaneous polarization ionic shifts which give rise to spontaneous polarization cannot be reversed by an external field (i.e. cannot be reversed by an external field (i.e. ZnOZnO). ). Called a pyroelectric because the polarization changes Called a pyroelectric because the polarization changes gradually as you increase the temperature.gradually as you increase the temperature.

AntiferroelectrictyAntiferroelectricty �� Each ion which shifts in a given Each ion which shifts in a given direction is accompanied by a shift of an ion of the direction is accompanied by a shift of an ion of the same type in the opposite direction (i.e. PbZrOsame type in the opposite direction (i.e. PbZrO33))

Piezoelectricity Piezoelectricity �� A spontaneous polarization develops A spontaneous polarization develops under the application of a mechanical stress, and viceunder the application of a mechanical stress, and vice--versa (i.e. quartz)versa (i.e. quartz)

PZT Phase DiagramPZT Phase DiagramPb(ZrPb(Zr11--xxTiTixx)O)O33 (PZT) is probably the most important piezoelectric (PZT) is probably the most important piezoelectric material. The piezoelectric properties are optimal near x = 0.5material. The piezoelectric properties are optimal near x = 0.5, This , This composition is near the composition is near the morphotropicmorphotropic phase boundary, which separates phase boundary, which separates the tetragonal and rhombohedral phases.the tetragonal and rhombohedral phases.

12

Hysteresis Hysteresis Loops in PbZrLoops in PbZr11--xxTiTixxOO33

PbTiOPbTiO33

FerroelectricFerroelectricTetragonalTetragonal

PbZrPbZr11--xxTiTixxOO33

x ~ 0.3x ~ 0.3FerroelectricFerroelectricRhombohedralRhombohedral

PbZrOPbZrO33

AntiferroelectricAntiferroelectricMonoclinicMonoclinic

PbZrPbZr11--xxTiTixxOO33

ParaelectricParaelectricCubicCubic

An An antiferroelectic antiferroelectic material does not polarize much for low applied fields, but material does not polarize much for low applied fields, but higher applied fields can lead to a polarization loop reminiscenhigher applied fields can lead to a polarization loop reminiscent of a t of a ferroelectricferroelectric. The combination gives split . The combination gives split hysteresis hysteresis loops as shown above. loops as shown above.

What is PiezoelectricityWhat is Piezoelectricity

A piezoelectric material converts mechanical (strain) A piezoelectric material converts mechanical (strain) energy to electrical energy and viceenergy to electrical energy and vice--versa. versa.

Voltage InVoltage In

Mechanical Signal OutMechanical Signal Out

i.e. Speakeri.e. Speaker

Mechanical Signal InMechanical Signal In

Voltage OutVoltage Out

i.e. Microphonei.e. Microphone

13

Applications of Applications of PiezoelectricsPiezoelectrics

•• PiezoPiezo--ignition systemsignition systems•• Pressure gauges and transducersPressure gauges and transducers•• Ultrasonic imaging Ceramic phonographic Ultrasonic imaging Ceramic phonographic

cartridgecartridge•• Small, sensitive microphonesSmall, sensitive microphones•• Piezoelectric actuators for precisely Piezoelectric actuators for precisely

controlling movements (as in an AFM)controlling movements (as in an AFM)•• Powerful sonarPowerful sonar

Symmetry Constraints and Symmetry Constraints and Dielectric PropertiesDielectric Properties

Dielectric properties can only be found with certain crystal symDielectric properties can only be found with certain crystal symmetries metries

PiezoelectricPiezoelectricDo not posses an inversion center (Do not posses an inversion center (noncentrosymmetricnoncentrosymmetric))

Ferroelectric/PyroelectricFerroelectric/PyroelectricDo not posses an inversion center (Do not posses an inversion center (noncentrosymmetricnoncentrosymmetric))Posses a Unique Polar AxisPosses a Unique Polar Axis

The 32 point groups can be divided up in the following manner (cThe 32 point groups can be divided up in the following manner (color olor coded according to crystal system: triclinic, monoclinic, etc.).coded according to crystal system: triclinic, monoclinic, etc.).PiezoelectricPiezoelectric

1, 1, 2, m,2, m, 222, mm2,222, mm2, 4, 4, --4, 422, 4mm, 42m, 4, 422, 4mm, 42m, 3, 32, 3m,3, 32, 3m,6, 6, --6, 6, 622, 6mm, 6m2, 622, 6mm, 6m2, 23, 43m23, 43m

Ferroelectric/PyroelectricFerroelectric/Pyroelectric1, 1, 2, m,2, m, mm2,mm2, 4, 4mm, 4, 4mm, 3, 3m,3, 3m, 6, 6mm6, 6mm

Centrosymmetric Centrosymmetric (Neither)(Neither)--11, , 2/m2/m, , mmmmmm, , 4/m, 4/4/m, 4/mmmmmm, , --3, 3/m3, 3/m, 6/m, 6/, 6/m, 6/mmmmmm, , m3, m3mm3, m3m

14

Electronic Electronic PolarizabilityPolarizabilityLet�s limit our discussion to insulating extended solids. In thLet�s limit our discussion to insulating extended solids. In the e absence of charge carriers (ions or electrons) or molecules, we absence of charge carriers (ions or electrons) or molecules, we only need to consider the electronic and ionic only need to consider the electronic and ionic polarizabilitiespolarizabilities..

The presence of an electric field polarizes the electron The presence of an electric field polarizes the electron distribution about an atom creating a dipole moment, distribution about an atom creating a dipole moment,

µµµµµµµµ==qxqxThe dipole moment per unit volume, P, is then given byThe dipole moment per unit volume, P, is then given by

P = P = nnmmµµµµµµµµwhere nwhere nmm is the number of atoms per unit volume. is the number of atoms per unit volume.

- qq

+ qq

EEwithout without fieldfield

with with fieldfield xx

Microwave DielectricsMicrowave DielectricsWere not talking microwave ovens here, rather Were not talking microwave ovens here, rather

communication systems which operate in the microwave communication systems which operate in the microwave region:region:

�� Ultra high frequency TV (470Ultra high frequency TV (470--870 MHz)870 MHz)�� Satellite TV (4 GHz)Satellite TV (4 GHz)�� Mobile (Cellular) Phones (900Mobile (Cellular) Phones (900--1800 MHz)1800 MHz)

All such systems depend upon a All such systems depend upon a bandpass bandpass filter that filter that selects a narrow frequency range and blocks all others. selects a narrow frequency range and blocks all others.

These filters are constructed from ceramics with These filters are constructed from ceramics with desirable dielectric properties.desirable dielectric properties.

15

Microwave DielectricsMicrowave Dielectrics--PropertiesProperties

The following dielectric properties are intimately related to itThe following dielectric properties are intimately related to it�s �s performanceperformance

Dielectric Constant (Permitivity)Dielectric Constant (Permitivity)�� A high dielectric constant allows components to be A high dielectric constant allows components to be

miniaturizedminiaturizedDielectric LossDielectric Loss

�� A low dielectric loss is needed to prevent energy A low dielectric loss is needed to prevent energy dissipation and minimize the dissipation and minimize the bandpass bandpass of the filterof the filter

Temperature CoefficientTemperature Coefficient�� For device stability the dielectric properties should be For device stability the dielectric properties should be

relatively insensitive to temperaturerelatively insensitive to temperature

Microwave DielectricsMicrowave DielectricsMaterials by DesignMaterials by Design

The the required properties it is possible to apply some conceptThe the required properties it is possible to apply some concepts of s of rational design to the search for materials. rational design to the search for materials.

High Dielectric ConstantHigh Dielectric Constant�� High electron density (dense structure type, High electron density (dense structure type, polarizablepolarizable cations, i.e. cations, i.e.

TaTa5+5+).).Low Dielectric LossLow Dielectric Loss

�� Ionic Ionic polarizabilitypolarizability comes with large losses in the microwave region. comes with large losses in the microwave region. Therefore, one needs to avoid ferroelectrics, disorder and Therefore, one needs to avoid ferroelectrics, disorder and impurities. Ions should not be able to rattle around too much.impurities. Ions should not be able to rattle around too much.

Temperature CoefficientTemperature Coefficient�� Very sensitive to rotations of Very sensitive to rotations of polyhedrapolyhedra, vibrations of atoms, as well , vibrations of atoms, as well

as thermal expansion. In perovskites the temperature coefficientas thermal expansion. In perovskites the temperature coefficient is is linked to octahedral tilting distortions. Tolerance factors justlinked to octahedral tilting distortions. Tolerance factors just below below 1 tend to have very low temperature coefficients1 tend to have very low temperature coefficients..

16

Commercial Microwave DielectricsCommercial Microwave Dielectrics

See Dr. Rick See Dr. Rick Ubic�s Ubic�s (University of Sheffield) site for a more detailed (University of Sheffield) site for a more detailed treatment of microwave dielectrics.treatment of microwave dielectrics.

http://www.http://www.qmulqmul.ac..ac.ukuk/~ugez644/index.html#microwave/~ugez644/index.html#microwave