Introduction to Ferroic Materials

Cover
Half Title
Title Page
Copyright Page
Contents
Foreword
Preface
Part A: GENERAL CONSIDERATIONS
	1 INTRODUCTION
		1.1 OVERVIEW
		1.2 HISTORICAL
			1.2.1 Ferromagnetic Materials
			1.2.2 Critical-Point Phenomena
			1.2.3 Ferroelectric Materials
			1.2.4 Ferroelastic Materials
			1.2.5 Secondary and Higher-Order Ferroics
			1.2.6 Ferrogyrotropic Materials
	2 CRYSTALLOGRAPHY
		2.1 GROWTH OF A CRYSTAL
			2.1.1 Nucleation
			2.1.2 The Cluster-to-Crystal Transition
			2.1.3 Growth Mechanisms
			2.1.4 Crystal Morphology
		2.2 SYMMETRY OF A CRYSTAL
			2.2.1 The Symmetry Group of a Crystal
			2.2.2 Translational and Rotational Symmetry
			2.2.3 Crystal Structure
			2.2.4 Point Space
			2.2.5 Symmetry Elements in a Crystal
			2.2.6 Orbits; Stabilizers
			2.2.7 Attributes of Space
			2.2.8 Rational and Irrational Directions
			2.2.9 The Crystallographic Restriction on Axes of Symmetry
			2.2.10 Crystal Systems and Crystal Families
			2.2.11 Primitive and Nonprimitive Bravais Lattices
			2.2.12 Screw Axes and Glide Planes
			2.2.13 Wigner-Seitz Cell
			2.2.14 The Various Types of Unit Cells
			2.2.15 Crystallographic Point Groups
			2.2.16 Simple Forms
			2.2.17 Crystallographic Space Groups
			2.2.18 Magnetic Symmetry of Crystals
			2.2.19 Limit Groups
			2.2.20 Layer Groups and Rod Groups
			2.2.21 Colour Symmetry
		2.3 CRYSTAL SYMMETRY AND THE CURIE SHUBNIKOV PRINCIPLE
			2.3.1 The Asymmetric Unit
			2.3.2 Interplay between Dissymmetrization and Symmetrization
		2.4 INCOMMENSURATELY MODULATED CRYSTALS
	3 CRYSTAL PHYSICS
		3.1 TENSOR PROPERTIES
			3.1.1 Symmetrized and Alternated Tensors
			3.1.2 Polar Tensors and Axial Tensors
			3.1.3 Matter Tensors and Field tensors
			3.1.4 Intrinsic Symmetry of Tensors; the Jahn Symbol
			3.1.5 Extrinsic Symmetry of Tensors
			3.1.6 Tensor Invariants
			3.1.7 Equilibrium Properties and Transport Properties
			3.1.8 i-Tensors and c-Tensors
			3.1.9 Special Magnetic Properties
		3.2 RESTRICTIONS IMPOSED BY CRYSTAL SYMMETRY ON TENSOR PROPERTIES
			3.2.1 Neumann Theorem
			3.2.2 Crystallographic System of Coordinates
			3.2.3 Some Consequences of the Neumann Theorem
		3.3 THE HERMANN THEOREM OF CRYSTAL PHYSICS
			3.3.1 Cyclic Coordinates
			3.3.2 Proof of the Hermann Theorem
			3.3.3 Importance of the Hermann Theorem
		3.4 REPRESENTATIONS OF CRYSTALLOGRAPHIC POINT GROUPS
		3.5 EFFECT OF FIELDS ON TENSOR PROPERTIES
	4 CRYSTALS AND THE WAVEVECTOR SPACE
		4.1 DIFFRACTION BY A CRYSTAL. THE RECIPROCAL LATTICE
			4.1.1 Diffraction by a General Distribution of Scatterers
			4.1.2 Diffraction by a Crystal
			4.1.3 The Reciprocal Lattice
			4.1.4 The Brillouin Zone
			4.1.5 Diffraction by an Incommensurately Modulated Crystal
		4.2 REPRESENTATIONS OF CRYSTALLOGRAPHIC TRANSLATION GROUPS
		4.3 THE GROUP OF THE WAVEVECTOR, AND ITS REPRESENTATIONS
		4.4 REPRESENTATIONS OF SPACE GROUPS
	5 PHASE TRANSITIONS IN CRYSTALS
		5.1 PROTOTYPE SYMMETRY
			5.1.1 Guymont\'s Nondisruption Condition
			5.1.2 Parent-Clamping Approximation
			5.1.3 Definition of Prototype Symmetry
		5.2 A CRYSTALLOGRAPHIC CLASSIFICATION OF PHASE TRANSITIONS
			5.2.1 Disruptive Phase Transitions
			5.2.2 Nondisruptive Phase Transitions
		5.3 EXTENDED LANDAU THEORY OF CONTINUOUS PHASE TRANSITIONS
			5.3.1 Subgroup Criterion
			5.3.2 Order Parameter
			5.3.3 Isotropy Subgroups
			5.3.4 Physically Irreducible Representations
			5.3.5 Single-IR Criterion; Active IR
			5.3.6 Subduction Criterion; Subduction Frequency
			5.3.7 Chain Subduction Criterion
			5.3.8 Landau Stability Condition
			5.3.9 Lifshitz Homogeneity Condition
			5.3.10 Maximality Conjecture
			5.3.11 Tensor Field Criterion
			5.3.12 The Landau Expansion
			5.3.13 Stability Limit of a Phase
			5.3.14 Tricritical Points
		5.4 LATTICE DYNAMICS, SOFT MODES
			5.4.1 Ferrodistortive Transitions
			5.4.2 Antiferrodistortive Transitions
			5.4.3 Displacive vs. Order-Disorder Type Phase Transitions
			5.4.4 Overdamped and Under damped Soft Modes
			5.4.5 Hard Modes and Saturation Temperature for the Order Parameter
		5.5 CRITICAL-POINT PHENOMENA
			5.5.1 Critical Fluctuations
			5.5.2 Landau-Ginzburg Theory
			5.5.3 Ginzburg Criterion
			5.5.4 Critical Exponents
			5.5.5 Upper and Lower Marginal Dimensionality
			5.5.6 Models of Phase Transitions
			5.5.7 Universality Classes and Scaling
			5.5.8 Kadanoff Construction
			5.5.9 Renormalization-Group Theory
		5.6 SPONTANEOUS BREAKING OF SYMMETRY
			5.6.1 Continuous Broken Symmetries; Goldstone Modes
			5.6.2 Discrete Broken Symmetries
		5.7 DISCONTINUOUS PHASE TRANSITIONS
			5.7.1 Nondisruptive Discontinuous Transitions
			5.7.2 Disruptive Discontinuous Transitions
		5.8 TRANSITIONS TO AN INCOMMENSURATE PHASE
		5.9 INFLUENCE OF IMPURITIES ON STRUCTURAL PHASE TRANSITIONS
	6 CLASSIFICATION OF FERROIC MATERIALS. FERROGYROTROPY
		6.1 FERROIC SPECIES
			6.1.1 Aizu Symbol for Ferroic Species
			6.1.2 Orientation States
			6.1.3 F-Operations
		6.2 MACROSCOPIC CLASSIFICATION OF FERROIC MATERIALS
			6.2.1 Thermodynamic Considerations
			6.2.2 Tensor Classification of Ferroics
		6.3 FERROGYROTROPY
			6.3.1 The Optical Gyration Tensor
			6.3.2 The Hermann Theorem and Optical Gyration
			6.3.3 Optical Ferrogyrotropy as an Implicit Form of Ferroicity
			6.3.4 Optical Ferrogyrotropy vs. Ferroelasticity
			6.3.5 Partial Ferrogyrotropics
			6.3.6 The Acoustical Gyration Tensor
			6.3.7 Ferroacoustogyrotropy
			6.3.8 Acoustical Ferrogyrotropy as an Implicit Form of Ferroicity
	7 DOMAINS
		7.1 SOME SYMMETRY ASPECTS OF DOMAIN STRUCTURE
			7.1.1 Derivative Structures and Domain States
			7.1.2 Domain Pairs
			7.1.3 Single-Domain States
			7.1.4 Disorientations
			7.1.5 Antiphase Domains
			7.1.6 Orientational Twins
			7.1.7 Rotational Domains
			7.1.8 Domain Structure and the Curie Principle
			7.1.9 Symmetry of Single-Domain States
			7.1.10 Enumeration of Single-Domain States
			7.1.11 Symmetry-Labeling of Domain States and Domain Walls
		7.2 TWINNING
			7.2.1 Definition of Twinning
			7.2.2 Transformation Twins
			7.2.3 Growth Twins
			7.2.4 Mechanical Twins
			7.2.5 Friedel\'s Four Twin Types
			7.2.6 Manifestation of Twin Type in the Diffraction Pattern
			7.2.7 Hypertwins
			7.2.8 Hermann\'s Space-Group Decomposition Theorem
		7.3 BICRYSTALLOGRAPHY
			7.3.1 General Methodology
			7.3.2 Dichromatic Pattern
			7.3.3 Coincidence Lattice
			7.3.4 Dichromatic Complex
			7.3.5 Unrelaxed or Ideal Bicrystal
			7.3.6 Relaxed Bicrystal
			7.3.7 The Six Bicrystal Systems
			7.3.8 Bicrystallographic Variants
		7.4 A TENSOR CLASSIFICATION OF TWINNING
			7.4.1 S-TWINS
			7.4.2 N-Twins
			7.4.3 B-Twins
			7.4.4 T-Twins
			7.4.5 A Symbol for Twinning
		7.5 THE GROUP-TREE FORMALISM
	8 DOMAIN WALLS
		8.1 ORIENTATIONAL DEPENDENCE OF PROPERTIES OF INTERFACES
			8.1.1 Morphology of Crystals Grown from Crystalline Matrices
			8.1.2 Homophase Interfaces
			8.1.3 Symmetry-Dictated Extrema
		8.2 STRUCTURAL EXTENDED DEFECTS
			8.2.1 Aristotype and Hettotype Structures
			8.2.2 Antiphase Boundaries
			8.2.3 Stacking Faults
			8.2.4 General Twin Walls
			8.2.5 Grain Boundaries
		8.3 COMPOSITIONAL EXTENDED DEFECTS
			8.3.1 Crystallographic Shear Planes
			8.3.2 Irrational Shear Planes
			8.3.3 Chemical Twin Planes
		8.4 ATOMIC DISPLACEMENTS UNDERLYING THE MOVEMENT OF DOMAIN WALLS
		8.5 DOMAIN STRUCTURE OF INCOMMENSURATE PHASES
Part B: CLASSES OF FERROICS, MICROSTRUCTURE, NANOSTRUCTURE, APPLICATIONS
	9 FERROMAGNETIC CRYSTALS
		9.1 SOME MAGNETIC PROPERTIES OF ORDERED CRYSTALS
			9.1.1 Magnetic Moment and Exchange Interaction
			9.1.2 Magnetic Ions in Solids
			9.1.3 Coupling Between Magnetic Moments
			9.1.4 Diamagnetism and Paramagnetism
			9.1.5 Ferromagnetism, Antiferromagnetism, and Ferrimagnetism
			9.1.6 Molecular Ferromagnets
			9.1.7 Metamagnetism and Incipient Ferromagnetism
			9.1.8 Helimagnetism
		9.2 SPIN GLASSES AND CLUSTER GLASSES
			9.2.1 Giant-Moment Ferromagnetism
			9.2.2 Characteristics of Spin Glasses
			9.2.3 The Glassy Phase and the Glass Transition
			9.2.4 Two-Level Model for Tunneling or Thermal Hopping in Glasses
			9.2.5 Broken Ergodicity
			9.2.6 Frustration
			9.2.7 Edwards Anderson Model and Sherrington Kirkpatrick Model
			9.2.8 Breaking of Replica Permutation Symmetry
			9.2.9 Thouless-Anderson-Palmer Theory
			9.2.10 Cluster Glasses, Mictomagnets, Superparamagnets
			9.2.11 Percolation-Related Magnetic Order
			9.2.12 Speromagnets and Sperimagnets
			9.2.13 Nonexponential Relaxation in Materials
		9.3 FERROMAGNETIC PHASE TRANSITIONS
			9.3.1 Prototype Symmetry for a Ferromagnetic Transition
			9.3.2 Ferromagnetic Species of Crystals
			9.3.3 Proper Ferromagnetic Transitions and Critical Phenomena
			9.3.4 Colour Symmetry and the Landau Potential
			9.3.5 Incommensurate Ferromagnetic Transitions
		9.4 DOMAIN STRUCTURE OF FERROMAGNETIC CRYSTALS
			9.4.1 The Various Contributions to the Internal Energy
			9.4.2 Orientations of Walls between Ferromagnetic Domain Pairs
			9.4.3 Thickness of Walls Separating Ferromagnetic Domain Pairs
			9.4.4 The Ferromagnetic Hysteresis Loop
		9.5 DYNAMICS OF FERROMAGNETIC BEHAVIOUR
	10 FERROELECTRIC CRYSTALS
		10.1 SOME DIELECTRIC PROPERTIES OF ORDERED CRYSTALS
			10.1.1 Polarization
			10.1.2 Pyroelectric Effect
			10.1.3 Effect of Static Electric Field
			10.1.4 Thermodynamics and Symmetry of Dielectric Properties
			10.1.5 A Crystallophysical Perspective for Ferroelectrics
			10.1.6 Dielectric Response and Relaxation
			10.1.7 Absolute and Relative Spontaneous Polarization
		10.2 STRUCTURAL CLASSIFICATION OF FERROELECTRICS
			10.2.1 Hydrogen-Bonded Ferroelectrics
			10.2.2 Non-Hydrogen-Bonded Ferroelectrics
		10.3 FERROELECTRIC PHASE TRANSITIONS
			10.3.1 Proper Ferroelectric Phase Transitions
			10.3.2 Improper or Faint Ferroelectric Phase Transitions
			10.3.3 Pseudoproper Ferroelectric Phase Transitions
			10.3.4 Ferroelectric Diffuse Transitions
		10.4 DIPOLAR GLASSES. RELAXOR FERROELECTRICS
			10.4.1 Classes of Glassy, Compositionally Modified, Ferroelectrics with Perovskite Type Structure
			10.4.2 Salient Features of Ferroelectric Crystals with a Dipolar-Glass Transition
			10.4.3 Spin Glasses vs. Dipolar Glasses
			10.4.4 Dipolar-Glass Transitions vs. Ferroelectric Phase Transitions
			10.4.5 Relaxor Ferroelectrics
			10.4.6 Field-Induced Phase Transitions in Relaxor Ferroelectrics
		10.5 QUANTUM FERROELECTRICS
			10.5.1 Displacive Limit of a Structural Phase Transition
			10.5.2 Modern Approach to Quantum Ferroelectrics
			10.5.3 Strontium Calcium Titanate
			10.5.4 Potassium Tantalate Niobate
			10.5.5 Potassium Dihydrogen Phosphate
		10.6 DOMAIN STRUCTURE OF FERROELECTRIC CRYSTALS
			10.6.1 Domains in a Ferroelectric Crystal
			10.6.2 Orientation of Walls Between Ferroelectric Domain Pairs
			10.6.3 Thickness of Walls Between Ferroelectric Domain Pairs
		10.7 FERROELECTRIC DOMAIN SWITCHING
			10.7.1 Kinetics of Domain Switching in Ferroelectrics
			10.7.2 The Ferroelectric Hysteresis Loop
	11 FERROELASTIC CRYSTALS
		11.1 SOME ELASTIC PROPERTIES OF ORDERED CRYSTALS
			11.1.1 Strain, Stress, Compliance
			11.1.2 Absolute Spontaneous Strain
			11.1.3 Relative Spontaneous Strain
			11.1.4 Anelasticity
		11.2 STRUCTURAL CLASSIFICATION OF FERROELASTICS
		11.3 FERROELASTIC PHASE TRANSITIONS
			11.3.1 True-Proper and Pseudoproper Ferroelastic Phase Transitions
			11.3.2 Improper Ferroelastic Phase Transitions
		11.4 QUADRUPOLAR GLASSES
		11.5 MARTENSITIC PHASE TRANSITIONS
			11.5.1 General Features
			11.5.2 Pseudoelasticity and Pseudoplasticity
			11.5.3 Crystallographic Reversibility of a Phase Transition
			11.5.4 Shape-Memory Effect
			11.5.5 Falk\'s Universal Model for Shape-Memory Alloys
		11.6 DOMAIN STRUCTURE OF FERROELASTIC CRYSTALS
			11.6.1 Domains in Ferroelastic Crystals
			11.6.2 Suborientation States
			11.6.3 Double Ferroelasticity
			11.6.4 Orientation of Walls Between Ferroelastic Domain Pairs
			11.6.5 Phase Boundaries and Poly domain Phases in Ferroelastics
			11.6.6 Some Further Aspects of the Effect of Long Ranged Elastic Interaction on Domain Structure
			11.6.7 Ferrielastics and Their Domain Structure
		11.7 FERROELASTIC DOMAIN SWITCHING
			11.7.1 The Optimum Switching Configuration
			11.7.2 Plasticity Related to Ferroelastic Domain Switching
			11.7.3 Mobility and Thickness of Domain Boundaries in Ferroelastics
			11.7.4 The Ferroelastic Hysteresis Loop
	12 SECONDARY AND HIGHER-ORDER FERROICS
		12.1 SECONDARY AND HIGHER ORDER FERROIC PHASE TRANSITIONS
		12.2 FERROBIELECTRICS AND FERROBIMAGNETICS
		12.3 FERROBIELASTICS
		12.4 FERROELASTOELECTRICS
		12.5 FERROMAGNETOELASTICS
		12.6 FERROMAGNETOELECTRICS
		12.7 TERTIARY FERROICS
	13 POLYCRYSTAL FERROICS AND COMPOSITE FERROICS
		13.1 SIZE EFFECTS IN FERROIC MATERIALS
			13.1.1 General Considerations
			13.1.2 Size Effects in Ferromagnetic Powders
			13.1.3 Size Effects in Ferroelectric Powders
			13.1.4 Size Effects in Ferroelastic Powders
		13.2 POLYCRYSTAL FERROICS
			13.2.1 Polycrystal Ferromagnetics
			13.2.2 Polycrystal Ferroelectrics
			13.2.3 Polycrystal Ferroelastics
		13.3 COMPOSITES WITH AT LEAST ONE FERROIC CONSTITUENT
			13.3.1 General Considerations
			13.3.2 Sum, Combination, and Product Properties of Composites
			13.3.3 Symmetry of Composites
			13.3.4 Connectivity of Composites
			13.3.5 Transitions in Composites
			13.3.6 Ferroic Nanocomposites
	14 APPLICATIONS OF FERROIC MATERIALS
		14.1 SALIENT FEATURES OF FERROIC MATERIALS
			14.1.1 Existence of the Ferroic Orientation State
			14.1.2 Mobility of Domain Boundaries and Phase Boundaries
			14.1.3 Enhancement of Certain Macroscopic Properties Near a Ferroic Phase Transition
			14.1.4 A Comparative Analysis of the Properties of Ferroic Materials
		14.2 APPLICATIONS
			14.2.1 Applications Related to the Existence of the Ferroic Orientation State
			14.2.2 Applications Exploiting the Mobility of Domain Boundaries and Phase Boundaries
			14.2.3 Applications Using Enhanced Macroscopic Properties near the Ferroic Phase Transition
			14.2.4 Applications Involving Field-Induced Phase Transitions
			14.2.5 Applications Involving Transport Properties
		14.3 FERROIC MATERIALS IN SMART STRUCTURES
			14.3.1 Smart Systems, Structures, and Materials
			14.3.2 Passively Smart Structures
			14.3.3 Actively Smart Structures
			14.3.4 Tuning of Properties of Ferroics by External Fields
			14.3.5 Applications of Ferroic Materials in Smart Structures
	15 EPILOGUE
APPENDICES
	APPENDIX A: SET THEORY
	APPENDIX B: GROUP THEORY
		B.1 ABSTRACT GROUP THEORY
		B.2 LINEAR SPACES AND OPERATORS
		B.3 REPRESENTATIONS OF FINITE GROUPS
		B.4 SOME CONTINUOUS GROUPS
	APPENDIX C: THE CURIE SHUBNIKOV PRINCIPLE
		C.1 THE CURIE PRINCIPLE. DISSYMMETRIZATION
		C.2 THE CURIE SHUBNIKOV PRINCIPLE. SYMMETRIZATION
		C.3 LATENT SYMMETRY
	APPENDIX D: THE FOURIER TRANSFORM
	APPENDIX E: THERMODYNAMICS AND STATISTICAL MECHANICS
		E.1 THERMODYNAMICS
			E.1.1 Thermodynamic Potentials
			E.1.2 Homogeneous Functions
		E.2 EQUILIBRIUM STATISTICAL MECHANICS
			E.2.1 Microcanonical Ensemble
			E.2.2 Canonical Ensemble
			E.2.3 Partition Function
			E.2.4 Quantum Statistical Mechanics
			E.2.5 Fluctuations
			E.2.6 Correlation Functions
		E.3 NONEQUILIBRIUM STATISTICAL MECHANICS
			E.3.1 Linear Response Theory
			E.3.2 Time Correlation Functions
			E.3.3 Fluctuation Dissipation Theorem
			E.3.4 Response Function
			E.3.5 Relaxation
			E.3.6 Generalized Susceptibility
References Cited
Author Index
Subject Index