В. А. Strukov А. Р. Levanyuk Ferroelectric Phenomena in Crystals Physical Foundations With 153 Figures and 14 Tables Springer
Contents 1. General Characteristics of Structural Phase Transitions in Crystals 1 1.1 First- and Second-Order Structural Phase Transitions 1 1.2 Structural Phase Transitions of Displacive and Order-Disorder Types 5 1.3 The Domain Structure 9 1.4 Ferroelectric Phase Transitions 12 1.5 Basic Types of Ferroelectric Crystals 19 2. Phenomenological Theory of Second-Order Structural Transitions in Crystals 31 2.1 The Incomplete Thermodynamic Potential 31 2.2 Structural Phase Transitions Described by a One-Component Order Parameter 35 2.3 Structural Phase Transitions Described by Two- and Three-Component Order Parameters 40 3. Proper Ferroelectrics: Anomalies of Physical Properties in Phase Transitions... 49 3.1 Anomalies of Thermal and Electrical Properties (One-Component Order Parameter) 49 3.2 Anomalies of Electrical Properties (Multicomponent Order Parameter) 58 3.3 First-Order Phase Transitions Close to Second-Order Transitions 61 3.4 The Tricritical Point 65 4. Dielectric Anomalies in Structural Nonferroelectric and Improper Ferroelectric Phase Transitions 73 4.1 Nonferroelectric Phase Transitions: Dielectric Anomalies 73 4.2 Improper Ferroelectric Phase Transitions: Dielectric Anomalies 81
VIII Contents 5. Anomalies of Elastic and Electromechanical Characteristics of Crystals in Second-Order Phase Transitions 89 5.1 One-Component Order Parameter: Elastic Properties of an Isotropic Liquid 89 5.2 One-Component Order Parameter: Elastic Properties of an Anisotropic Crystal 94 5.3 Ferroelectric-Ferroelastics: One-Component Order Parameter with Transformation Properties of the Component of a Second-Rank Tensor and the Polar Vector 99 5.4 Temperature Dependences of "Morphic" Moduli of Elasticity 102 5.5 Two-Component Order Parameter: Elastic Properties of Crystals 104 5.6 Piezoelectric Effect and Electrostriction in the Case of One-Component Order Parameter and Centrosymmetric Paraelectric Phase 110 5.7 Piezoelectric Effect in the Case of One-Component Order Parameter and Noncentrosymmetric Paraelectric Phase 114 6. Fluctuations of the Order Parameter in Phenomenological Theory 119 6.1 Spatially Inhomogeneous Fluctuations of the Order Parameter in the Incomplete Thermodynamic Potential 119 6.2 Applicability of Landau Theory to Nonferroelectric Structural Phase Transitions 124 6.3 Applicability of Landau Theory to Phase Transitions in Uniaxial Ferroelectrics 128 6.4 Fluctuational Phenomena in Ferroelectric-Ferroelastics and in Phase Transitions in Multiaxial Ferroelectrics 133 7. Structural Phase Transitions in the Single-Ion Model 135 7.1 Problems of the Microscopic Theory 135 7.2 The Single-Ion Model of a Diatomic Crystal 137 7.3 Phase Transitions of Displacive and Order-Disorder Types in the Single-Ion Model 145 7.4 Applicability of the Landau Theory to Phase Transitions of Displacive and Order-Disorder Types 147
Contents IX 8. Statistical Theory of Ferroelectric Phase Transitions of the Order Disorder Type 151 8.1 The Hamiltonian of a Uniaxial Ferroelectric with an Order-Disorder Phase Transition 151 8.2 The Free Energy of an Order-Disorder Crystal in the Self-Consistent Molecular Field Approximation 154 8.3 Tunneling Effects in Hydrogen-Containing Ferroelectrics 160 8.4 The Cluster Approximation: Crystals of the KH 2 P0 4 Group 166 9. Dynamics of Displacive and Order Disorder Phase Transitions 175 9.1 The Equation of Motion of the Order Parameter 175 9.2 Dynamic Dielectric Constant: Order-Disorder Phase Transitions 177 9.3 Dynamic Dielectric Constant: Displacive Phase Transitions 179 9.4 Microscopic Theory of Dynamic Processes in Displacive Phase Transitions 181 9.5 Microscopic Theory of Dynamic Processes in Order-Disorder Phase Transitions 187 9.6 Dielectric Constant and Soft Mode: The Lyddane-Sachs-Teller Relation: 189 10. Domain Structure and Defects 193 10.1 Nucleation of Domains in a Structural Phase Transition 193 10.2 Domain Wall Structure: One-Component Order Parameter 194 10.3 Domain Wall Structure: Two-Component Order Parameter 199 10.4 Motion of the Domain Wall in an Ideal and a Real Crystal 201 10.5 Motion of the Domain Wall: Account of the Discreteness of the Crystal 206 10.6 Domain Walls and Defects 210 10.7 Defects in the Symmetrical Phase 214 10.8 Domains in Proper Ferroelectrics 216 10.9 Domains in Ferroelastics 222 10.10 Domains in Polyaxial Ferroelectrics 224 11. Ferroelectrics with an Incommensurate Phase 227 11.1 Phase Transitions into an Incommensurate Phase 227
X Contents 11.2 Phenomenological Theory of Phase Transitions into an Incommensurate Phase 231 11.3 Specific Features of Crystal Lattice Vibrations in an Incommensurate Phase 235 11.4 The Incommensurate Phase in a Real Crystal 238 11.5 The Commensurate-Incommensurate Phase Transition: A Special Type of Phase Transition 241 11.6 Evolution of the Structure of the Incommensurate Phase (General Picture) 250 11.7 Evolution of the Structure of the Incommensurate Phase (the Continuum Approximation) 254 12. Ferroelectric Liquid Crystals 267 12.1 Basic Types of Orientational Ordering in Liquid Crystals... 267 12.2 Conditions for Existence of Dipolar Ordering in Liquid Crystals 270 12.3 Phenomenological Theory of Phase Transition SmA* -> SmC* 274 12.4 The Behavior of a Ferroelectric Smectic Liquid Crystal in an External Electric Field 281 13. Crystallochemical Aspects of the Theory of Ferroelectric Phenomena 289 13.1 Calculation of the Constants of the Hamiltonians of Some Crystals 289 13.2 An Approach Based on the Classical Theory of Ionic Crystals 294 14. Recommended Literature 299 References 301 Index 303