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Electrical conductivity very small; insulators They are, however, affected by an electric field. Capacitance of a parallel plate capacitor
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−−− −−−
d
Parallel plate capacitor with platesof area A and separation d. When adielectric material is placedbetween the plates, the dielectricbecomes polarized.
The HCl molecule and variation of the dielectric constant εr with temperature T for HCl.The abrupt change corresponds to the temperature at which the molecules are no longerable to align themselves with the external electric field.
Usually, the static dielectric constant is higher. Electrons can quickly follow the alternating electric field. However, the ionic contribution to the polarization becomes much
smaller. The ions cannot follow the quick change of the field. At high frequencies, only the induced polarization remains.
Polarization mechanisms inmaterials: (a) electronic, (b)ionic, (c) high-frequencydipolar or orientation(present in ferroelectrics), (d)low-frequency dipolar(present in linear dielectricsand glasses), (e) interfacialspace charge at electrodes,and (f) interfacial spacecharge at heterogeneitiessuch as grain boundaries.E
When any material undergoes polarization, its ions and electronicclouds are displaced, causing the development of a mechanical strainin the material. This effect is seen in all materials subjected to anelectric field and is known as the electrostriction.
Piezoelectrics – materials that develop voltage upon the applicationof a stress and develop strain when an electric field is applied.
Pyroelectric – the ability of a material to spontaneously polarize andproduce a voltage due to changes in temperature.
Ferroelectric – a material that shows spontaneous and reversibledielectric polarization.
When a stress is applied to a crystal structure with three-fold symmetry and zeropolarization, the symmetry is altered and the material acquires a non-zeropolarization even without an electric field.
Example: A PZT spark igniter is made using a disk that has a 5 mm diameter and 20 mm height. Calculate the voltage generated if the g coefficient for PZT used is 35 mV m/N. Assume thata compressive force of 10 kN is applied on the circular face.
Solution:
Definition of the g coefficientStress σ = F/A = 5.09 MN/m2
Therefore, the electric field is E = gσ =1.78·105 V/mU = E d = 3565 V.
Hysteresis curve as the polarization versus the electric field. Characteristic values arethe saturation polarization Ps, the remanent polarization Pr, and the coercive field Ec.
Neighboring dipoles are aligned in mutual interaction. Arranged dipoles form domains
(compare the magnetic domains in ferromagnets). Characteristic transition temperature, where the alignment of the
dipoles is destroyed (ferroelectric Curie temperature) Typically, material with complicated crystal structure of low
symmetry Finite polarization even without external electric field All ferroelectrics are also piezoelectric materials Ferroelectric materials have a very high dielectric constant
(as large as several thousand). Permanent polarization can be used to store non-volatile digital
The effect of temperature and grain size on thedielectric constant in barium titanate. Abovethe Curie temperature, the spontaneouspolarization is lost due to a change in crystalstructure and barium titanate is in theparaelectric state. The grain size dependenceshows that the dielectric constant is amicrostructure sensitive property.
Tetragonal perovskite phase:each titanium atom is bonded tosix nearest-neighbor oxygenatoms, but is not exactly in thecentre of the octahedron. Thisoffset means that tetragonalBaTiO3 is ferroelectric. Theelectrical polarization may bereversed by applying an externalelectric field.
Single crystals of BaTiO3 generallycontain many domains,corresponding to differentdirections of Ti off-centering. Thenet effect of the different domainorientations is to cancel out anymacroscopic polarisation.
Example: A multi-layer capacitor is to be designed using a BaTiO3-based formulation containing SrTiO3. The dielectric constant of the material is 3000. Calculate the capacitance of a multi-layer capacitor consisting of 100 layers connected in parallel using Ni electrodes. The sides of the capacitor are 10 mm × 5 mm and the thickness of each layer is 10 µm. What is the role of SrTiO3? What processing technique will be used to make these?
Solution:
Capacitance
Capacitance of one layer: 13.27 µFTotal capacitance of 100 layers connected in parallel:
At a critical (high) field, the dielectric material becomes a conductor. Increasing number of electrons by an avalanche process
Con
duct
ivity
Electrical fieldEb
Conductivity against the applied electricfield. If the field is below the breakdownfield then no current flows.
e−
e− e−
e− e− e− e−
e− e− e− e− e− e− e− e−
Scheme of the avalanche process. Theaccelerated electrons are able to exciteother electrons into the conductionband. Each of these electrons thenexcites another electron, and so on.
A dielectric placed in a electric field becomes polarized. 3 factors which can contribute to polarization: induced
polarization, ionic, and permanent dipole contributions Specific frequency dependence of these contributions Requirement to control the dielectric constant in modern devices
Read about this lecture:R. Turton: The physics of solids. Oxford University Press 2000,chapter 10.
References to pictures and data used are given in the fileReferences.pdf