An Introduction to the Phenomenological Theory of Ferroelectricity

Preface

Chapter 1 Ferroelectricity

1.1 Ferroelectricity

1.1.1 Ferroelectricity

1.1.2 Dielectric Hysteresis

1.2 Potassium Dihydrogen Phosphate

1.3 Rochelle Salt

1.4 Barium Titanate

1.5 Mueller's Theory

Bibliography

Chapter 2 The Linear Elastic Dielectric

2.1 Introduction

2.2 Infinitesimal Strain

2.2.1 Deformation

2.2.2 Physical Significance of the Sij

2.2.3 Compatibility Relations

2.3 Stress

2.3.1 Stress and Body Forces

2.3.2 Conservation of Momentum

2.3.3 Stress Tensor

2.3.4 Boundary Conditions

2.3.5 Mechanical Work

2.3.6 Inequivalence of Body Forces and Stresses

2.4 Electric and Displacement Fields

2.4.1 Electric Field

2.4.2 Field Equations and Boundary Conditions

2.4.3 Electrostatic Work

2.4.4 Depolarization Factor

2.5 The Linear Elastic Dielectric

2.5.1 Assumptions

2.5.2 Field Equations and Boundary Conditions

2.5.3 Equations of State I

2.5.4 Equations of State II

2.5.5 Quasi-Linear Theory

2.5.6 Summary

Bibliography

Chapter 3 Thermodynamics of the Elastic Dielectric

3.1 Thermodynamic Identities

3.1.1 The First Law

3.1.2 Thermodynamic Potentials

3.1.3 Thermodynamic Identities I

3.1.4 Thermodynamic Identities II

3.1.5 Change of Initial State

3.2 Stability

3.2.1 Stable Equilibrium

3.2.2 Stability Conditions

3.2.3 Phase Transitions I

3.2.4 Phase Transitions II

3.2.5 Ehrenfest Classification

3.3 Equations of State

3.3.1 Equations of State

3.3.2 Compliances

3.3.3 Identities

3.3.4 Linear Equations of State I

3.3.5 Linear Equations of State II

3.3.6 Transformation of Axes

3.3.7 Material Symmetry

3.3.8 Quasi-Linear Theory

3.3.9 D or P

3.4 Neighborhood Temperature

3.4.1 Neighborhood Temperature

3.4.2 Ehrenfest Relations

3.4.3 The Cylindrical Approximation

3.4.4 General Case

3.4.5 TGS

Bibliography

Chapter 4 The Non-linear Elastic Dielectric

4.1 The Non-linear Elastic Dielectric

4.1.1 Finite Deformation

4.1.2 Variational Principle

4.1.3 Field Equations and Boundary Conditions

4.1.4 Work and Energy

4.1.5 Conservation of Momentum

4.1.6 Invariance I

4.1.7 Invariance II

4.1.8 Summary

4.1.9 Linear Theory

4.2 Approximation

4.2.1 Equations of State

4.2.2 Approximation

4.2.3 Maxwell Stress

4.2.4 m3m Material Symmetry

4.3 Dielectric Slab

4.3.1 Introduction

4.3.2 Boundary Conditions

4.3.3 Comparison with the Quasi-linear Theory

4.3.4 Barium Titanate

Bibliography

Chapter 5 Phenomenological Models for Ferroelectricity

5.1 Dielectric Properties

5.1.1 Stability and Constraints

5.1.2 Dielectric Equation of State

5.1.3 Phase Transition, ξ > 0

5.1.4 Phase Transition, ξ < 0

5.1.5 Dielectric Hysteresis

5.1.6 Numerics

5.1.7 Ε = 0, ξ ≥ 0

5.1.8 E = 0, ξ < 0

5.1.9 Field Dependent Permeability θ >< θ

5.1.10 The Critical Point

5.2 Electrocaloric Coupling

5.2.1 Entropy and Specific Heats

5.2.2 E = 0

5.2.3 Field Dependence of Entropy and Specific Heats

5.2.4 Transition Heat and Transition Entropy

5.2.5 Electrocaloric Effect

5.3 Electroelastic Coupling

5.3.1 Introduction

5.3.2 Spontaneous Strain

5.3.3 The Free Crystal and the Clamped Crystal (A)

5.3.4 The Free Crystal and the Clamped Crystal (B)

5.3.5 Hydrostatic Pressure

5.4 Phase Transition

Part I. Model (A)

Part II. Model (B)

5.5 A Multi-Axial Ferroelectric Model

5.5.1 Equations of State

5.5.2 Stability Conditions

References

Glossary of Symbols

Index

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