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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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fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture25(28)25_2htm[5252012 125757 PM]

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

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture25(28)25_4html[5252012 125757 PM]

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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fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture25(28)25_5htm[5252012 125757 PM]

Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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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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fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture25(28)25_4html[5252012 125757 PM]

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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fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture25(28)25_5htm[5252012 125757 PM]

Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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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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fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture25(28)25_5htm[5252012 125757 PM]

Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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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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fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture25(28)25_5htm[5252012 125757 PM]

Figure 55 Schematic of Ferroelectric to Paraelectrictransition

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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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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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(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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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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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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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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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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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

Objectives_template

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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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture28(31)28_4htm[5252012 125800 PM]

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)

>

Objectives_template

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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

Objectives_template

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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

Objectives_template

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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

Objectives_template

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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

Objectives_template

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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

Objectives_template

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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

Objectives_template

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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

Objectives_template

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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

Objectives_template

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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

Objectives_template

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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

Objectives_template

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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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture28(31)28_6htm[5252012 125800 PM]

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

Objectives_template

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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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture28(31)28_7htm[5252012 125800 PM]

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

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

Objectives_template

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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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_12htm[5252012 125801 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_12htm[5252012 125801 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_2htm[5252012 125801 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_8htm[5252012 125802 PM]

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)

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_4htm[5252012 125801 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_4htm[5252012 125801 PM]

Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_5htm[5252012 125802 PM]

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)

>

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_8htm[5252012 125802 PM]

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)

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_4htm[5252012 125801 PM]

Figure 521 Poling of ferroelectrics and application of stress on poledmaterial

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_5htm[5252012 125802 PM]

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)

>

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_8htm[5252012 125802 PM]

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)

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_5htm[5252012 125802 PM]

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)

>

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_8htm[5252012 125802 PM]

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)

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_8htm[5252012 125802 PM]

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)

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_6htm[5252012 125802 PM]

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

Objectives_template

fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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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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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fileC|Documents20and20Settingsiitkrana1Desktopnew_electroceramics_14may2012lecture29(32)29_7htm[5252012 125802 PM]

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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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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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 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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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

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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

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 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

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

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

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

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

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

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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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

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)

>

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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

Objectives_template

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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