Modern Crystallography IV, Softcover reprint of the original 1st ed. 1988 Physical Properties of Crystals Coll. Springer Series in Solid-State Sciences, Vol. 37

Modern Crystallography IV is devoted to a systematic and up- to-date description of fundamental physical properties of solid and liquid crystals. These include elastic and mechanical, dielectric and ferroelectric, magnetic and optical properties, transport phenomena and spectroscopy. An important feature of the treatment is its use of the crystallographic approach, an introduction to which is given in the opening chapter of the book. The topics are treated at a level understandable to students who have two years of university physics. Researchers and engineers working on practical applications should also find the book useful, as should specialists in other fields who wish to broaden their knowledge of crystallography and materials science. The book is written by a group of leading scientists from the Institute of Crystallography of the USSR Academy of Sciences.

1. Fundamentals of Tensor and Symmetry Description of the Physical Properties of Crystals.- 1.1 Introduction.- 1.1.1 Crystal as a Continuous Homogeneous Anisotropic Medium.- 1.1.2 Cartesian Coordinate System and Its Transformations.- 1.2 Tensors and Their Transformations.- 1.2.1 Scalars, Pseudoscalars, Vectors, and Tensors.- 1.2.2 Transformation of the Components of Vectors and Second-Rank Tensors.- 1.2.3 Tensors of Different Ranks.- 1.2.4 Pseudotensors (Axial Tensors).- 1.2.5 Symmetric and Antisymmetric Tensors. Interior Symmetry of Tensors.- 1.2.6 Reciprocal Tensors.- 1.2.7 Matrix Notation.- 1.3 Geometric Interpretation of Tensors. Indicatrice Surfaces.- 1.3.1 Characteristic Surface for a Symmetric Second-Rank Tensor.- 1.3.2 Principal Axes of a Symmetric Second-Rank Tensor.- 1.3.3 Property in a Given Direction.- 1.3.4 Geometric Properties of the Characteristic Surface of a Symmetric Second-Rank Tensor.- 1.3.5 Finding the Principal Axes of a Symmetric Second-Rank Tensor.- 1.3.6 Other Indicatrice Surfaces for a Second-Rank Tensor.- 1.3.7 Indicatrice Surfaces for Higher-Than-Second-Rank Tensors.- 1.4 Proper (Exterior) Symmetry of Tensors.- 1.4.1 General Notions of the Proper Symmetry of Tensors.- 1.4.2 Limiting Groups of Symmetry.- 1.4.3 Proper Symmetry of Scalars, Pseudoscalars, and Vectors.- 1.4.4 Proper Symmetry of Second-Rank Polar Tensors.- 1.4.5 Proper Symmetry of Second-Rank Pseudotensors.- 1.4.6 Proper Symmetry of Higher-Rank Tensors.- 1.5 Symmetry of Physical Properties.- 1.5.1 Material and Field Tensors.- 1.5.2 Crystallophysical System of Coordinates.- 1.5.3 Relationship Between the Proper Symmetry of Tensors and the Symmetry of the Physical Properties Described by Them.- 1.5.4 Relationship Between the Point Symmetry of a Crystal and the Symmetry of Its Physical Properties.- 1.5.5 Form in Different Coordinate Systems of the Matrices of Tensors Describing the Physical Properties of Crystals of Different Classes.- 1.5.6 Determining the Number of Independent Components of Tensors Describing the Physical Properties of Crystals.- 1.5.7 The Curie Principle and Its Application.- 2. Mechanical Properties of Crystals.- 2.1 Elastic Properties of Crystals.- 2.1.1 Stress.- 2.1.2 Characteristic Stress Surface.- 2.1.3 Strain.- 2.1.4 Characteristic Surface and the Strain Ellipsoid.- 2.1.5 Hooke’s Law for Crystals.- 2.1.6 Matrix Notation of Coefficients of Elasticity.- 2.1.7 Effect of the Crystal Symmetry on the Tensor of Coefficients of Elasticity.- 2.1.8 Hooke’s Law for an Isotropic Body.- 2.1.9 Young’s Modulus in an Arbitrary Direction and the Characteristic Surfaces of Elastic Properties.- 2.1.10 Adiabatic and Isothermal Values of Elasticity Coefficients.- 2.1.11 Volume Compressibility of Crystals.- 2.1.12 Born Theory.- 2.1.13 Cauchy Ratio.- 2.1.14 Elastic Waves in Crystals.- 2.2 Plastic Glide Deformation.- 2.2.1 Elastic Deformation in Crystals.- 2.2.2 Translational Glide.- 2.2.3 Plastic Strain Tensor.- 2.2.4 Glide Elements.- 2.2.5 Slip Lines.- 2.2.6 Polar Glide.- 2.2.7 Critical Shear Stress Law.- 2.2.8 Independent Glide Systems.- 2.2.9 Cases of Complex Slipping.- 2.2.10 Stages of Glide Deformation.- 2.2.11 Theoretical Shear Strength.- 2.3 Dislocation Description of Plastic Deformation by Glide.- 2.3.1 Dislocations as the Result of Shear Strain.- 2.3.2 Dislocation Structure of Slip Lines and the Movement of Dislocations.- 2.3.3 Force Acting on a Dislocation.- 2.3.4 Dislocation Velocity.- 2.3.5 Lattice Resistance to the Dislocation Movement.- 2.3.6 Multiplication of Dislocations.- 2.3.7 Interaction Between Dislocations.- 2.3.8 Dislocation Reactions.- 2.3.9 Interaction of Dislocations with Point Defects.- 2.3.10 Types of Interaction of Dislocations with Impurities.- 2.3.11 Precipitation Particles.- 2.3.12 Internal Friction.- 2.3.13 Anisotropy of the Internal Friction.- 2.3.14 Theories of Dislocation Internal Friction.- 2.3.15 Mechanisms of Overcoming Impurity Obstacles.- 2.4 Diffusion Mechanisms of Plastic Deformation.- 2.4.1 Gorsky Effect.- 2.4.2 Diffusion Creep.- 2.4.3 Climb of the Edge Dislocations.- 2.4.4 Diffusion-Dislocation Creep.- 2.4.5 Creep Stages.- 2.4.6 Radiation-Induced Diffusion Creep.- 2.4.7 Stress Relaxation.- 2.5 Mechanical Twinning of Crystals.- 2.5.1 Twinning of Crystals.- 2.5.2 Representation of Twinning with a Change in Shape as a Uniform Shear.- 2.5.3 Polarity of Twinning.- 2.5.4 Twinning Elements.- 2.5.5 Types of Twinning.- 2.5.6 Transformation of Indices of Planes and Directions in Twinning.- 2.5.7 Energy Conditions for the Formation of Twins Causing a Change in the Shape of Crystals.- 2.5.8 Twin Nucleation.- 2.5.9 Twinning Without a Change in Crystal Shape.- 2.5.10 Behavior of Crystals with Polysynthetic Twins.- 2.5.11 Martensitic Transformations.- 2.6 Fracture.- 2.6.1 Theoretical and Actual Strength.- 2.6.2 Cleavage Plane.- 2.6.3 Fracture Surface.- 2.6.4 Law of Critical Normal Stress.- 2.6.5 Role of Plastic Deformation in the Preparation of Failure Nuclei.- 2.6.6 Griffith’s and Orowan’s Criteria of Growth of Nucleus Cracks.- 2.6.7 “Viscous” and “Brittle” Cracks.- 2.6.8 Joffe Effect.- 2.6.9 Rebinder Effect.- 2.7 Methods for Studying the Mechanical Properties of Crystals.- 2.7.1 Hardness Measurement.- 2.7.2 Investigating the Elastic Properties of Crystals.- 2.7.3 Investigating the Plastic Properties of Crystals.- 2.7.4 Studying the Ability of Crystals to Undergo Failure.- 2.7.5 Long-Term Strength.- 3. Electrical Properties of Crystals.- 3.1 Polarization, Electrical Conductivity, and Dielectric Losses.- 3.1.1 General.- 3.1.2 Main Types of Polarization.- 3.1.3 Electrical Conductivity.- 3.1.4 Dielectric Losses.- 3.2 Pyroelectric Phenomena.- 3.2.1 General.- 3.2.2 Pyroelectric Effect.- 3.2.3 Electrocaloric Effect.- 3.3 Piezoelectric Effect and Electrostriction.- 3.3.1 Piezoelectric Effect.- 3.3.2 Electromechanical Transformation.- 3.3.3 Piezoelectric Properties of Linear Dielectrics.- 3.3.4 Electrostriction.- 3.3.5 Piezoelectric Textures.- 3.4 Domain Structure and Peculiarities of the Electrical Properties of Ferroelectrics and Antiferroelectrics.- 3.4.1 General.- 3.4.2 Domains.- 3.4.3 Polarization, Electrical Conductivity, and Dielectric Losses.- 3.4.4 Piezoelectric Properties.- 3.4.5 Antiferroelectrics.- 3.5 Structure and Properties of Some Ferroelectrics and Antiferroelectrics.- 3.5.1 Barium Titanate.- 3.5.2 Potassium Dihydrophosphate.- 3.5.3 RochelleSalt.- 3.5.4 Triglycinesulphate.- 3.5.5 Antiferroelectries.- 3.6 Phase Transition in Ferroelectrics. Fundamentals of Spontaneous Polarization Theory.- 3.6.1 General.- 3.6.2 Thermodynamic Theory of Phase Transitions in Ferroelectrics.- 3.6.3 Macroscopic Models.- 3.6.4 Sublattice Polarization and Phase Transitions in Antiferroelectrics.- 3.6.5 Crystal Lattice Dynamics and Phase Transitions in Ferroelectrics.- 3.6.6 Incommensurate Phase Transitions in Ferroelectrics.- 4. Magnetic Properties of Crystals.- 4.1 Disordered Magnetics.- 4.1.1 Basic Relations Characterizing the Behavior of a Substance in a Magnetic Field.- 4.1.2 Tensors of Diamagnetic and Paramagnetic Susceptibility.- 4.1.3 Classification of Magnetic Substances.- 4.1.4 Diamagnetism.- 4.1.5 Paramagnetism.- 4.2 Ordered Magnetics.- 4.2.1 Different Types of Magnetic Structures in Crystals. Ferromagnetism, Antiferromagnetism, and Ferrimagnetism.- 4.2.2 Magnetic Symmetry.- 4.2.3 Basic Types of Interaction in Ordered Magnetics.- 4.2.4 Molecular Field Theory. The Curie and Néel Points.- 4.3 Domain Structure of Ferromagnetic Crystals and Magnetization Processes.- 4.3.1 Change of Symmetry at the Curie Point. Symmetry Aspects of Splitting of a Ferromagnetic into Domains.- 4.3.2 Spontaneous Magnetostriction. Magnetoelastic Energy.- 4.3.3 Energy Aspects of Domain Structure. Domain Walls.- 4.3.4 Methods for Observing the Domain Structure. Examples of Domain Structures.- 4.3.5 Magnetization Processes.- 4.3.6 Magnetic Hysteresis.- 4.4 Anisotropy of Ferromagnetic Crystals.- 4.4.1 Peculiarities of the Tensor Description of Ferromagnetic Crystals.- 4.4.2 Magnetostriction Anisotropy in Ferromagnetics of Different Symmetry.- 4.4.3 Magnetic Anisotropy Energy Corresponding to Zero Strains and Zero Stresses.- 4.4.4 Equilibrium Directions of Spontaneous Magnetization.- 4.4.5 Magnetic Anisotropy Measurement.- 4.5 Structure of Some Magnetically Ordered Crystals and Reorientation Transitions.- 4.5.1 Ferrites.- 4.5.2 Weakly Ferromagnetic Crystals (Canted Antiferromagnetics).- 4.5.3 Reorientation Transitions.- 4.6 Piezomagnetic and Magnetoelectric Effects.- 5. Semiconducting Crystals.- 5.1 Basic Properties of Semiconductors.- 5.1.1 Metals, Semiconductors, and Insulators.- 5.1.2 Intrinsic and Extrinsic Conductivity.- 5.1.3 Electrical Conductivity of Semiconductors.- 5.1.4 Hall Effect.- 5.1.5 Photoconductivity.- 5.2 Electron-Hole Junctions.- 5.2.1 Electron Energy Distribution.- 5.2.2 Semiconductor-Metal Contact.- 5.2.3 Semiconductor Diodes with p-n Junctions.- 5.2.4 SemiconductorTriode(Transistor).- 5.2.5 Semiconductor Laser.- 5.2.6 Photocells with a p-n Junction.- 6. Transport Phenomena in Crystals.- 6.1 Electrical Conductivity of Crystals.- 6.1.1 Electrical Conductivity and Resistivity Tensors.- 6.1.2 Crystal Conductivity in a Given Direction.- 6.2 Thermal Conductivity of Crystals.- 6.2.1 Tensors of the Thermal Conductivity and Thermal Resistivity Coefficients.- 6.2.2 Onsager’s Principle.- 6.3 Thermoelectric Effects.- 6.3.1 Definition of Thermal Effects.- 6.3.2 Thermoelectric Effects in an Isotropic Medium.- 6.3.3 Thermoelectric Effects in Crystals.- 6.3.4 Dependence of the Tensor of the Thermoelectric Coefficients on the Crystal Symmetry.- 6.3.5 Peltier, Thomson, and BridgmanEffects.- 6.3.6 Thermoelectric Effects in Technology.- 6.4 Galvano-and Thermomagnetic Effects.- 6.4.1 Onsager’s Principle in the Presence of a Magnetic Field.- 6.4.2 Hall, Righi-Leduc, Nernst, and Ettingshausen Effects.- 6.4.3 Tensors of the Hall, Righi-Leduc, Nernst, and Ettingshausen Coefficients and of Magnetoresistance for Crystals of Different Classes.- 7. Optical Properties of Crystals.- 7.1 Plane Electromagnetic Waves in an Anisotropic Medium.- 7.1.1 Dielectric Constants of Crystals.- 7.1.2 Plane Waves in Transparent Crystals.- 7.1.3 Optical Surfaces.- 7.2 Uniaxial and Biaxial Crystals.- 7.2.1 Uniaxial Crystals.- 7.2.2 Biaxial Crystals.- 7.3 Birefringence in Crystals.- 7.3.1 Birefringence of Plane Waves at the Interface of Two Media.- 7.3.2 Light Reflection from Transparent Crystals.- 7.4 Light Interference in Crystals.- 7.4.1 Elliptical Polarization.- 7.4.2 Light Interference in Parallel Beams.- 7.4.3 Conoscopic Patterns in Uniaxial Crystals.- 7.4.4 Conoscopic Patterns in Biaxial Crystals.- 7.4.5 Measurements of Refractive Indices of Crystals.- 7.5 Light Absorption in Crystals.- 7.6 Optical Activity of Crystals.- 7.7 Electro-optical Properties of Crystals.- 7.8 Magneto-optical Properties of Crystals.- 7.9 Piezo-optical Properties of Crystals.- 7.10 Light Scattering in Crystals.- 7.11 Nonlinear Optical Properties of Crystals.- 7.12 Essentials of the Crystal-Field Theory.- 7.12.1 Crystal-Field Model.- 7.12.2 A Single d Electron in a Cubic Field.- 7.12.3 Ion with Configuration 3d2 in a Weak Cubic Field.- 7.12.4 Strong Crystal Field.- 7.12.5 Calculating the Spin-Orbital Interaction of Configuration d2 in a Cubic Field.- 7.13 Laser Crystals.- 7.14 Polarized Luminescence in Crystals.- 7.15 Electron Paramagnetic Resonance of Impurity Ions in Crystals.- 8. Liquid Crystals.- 8.1 Basic Characteristics of Liquid Crystals.- 8.2 Texture and Optical Properties of Liquid Crystals.- 8.2.1 Smectic Liquid Crystals.- 8.2.2 Nematic Liquid Crystals.- 8.2.3 Cholesteric Liquid Crystals.- 8.2.4 Lyotropic Liquid Crystals.- 8.3 Theory of Liquid-Crystal State.- 8.3.1 Thermodynamic States of Liquid Crystals.- 8.3.2 Supercooled Liquid-Crystal Phases.- 8.3.3 Two-Dimensional Ordering and Plastic SLC.- 8.3.4 Orientational Distortions of Liquid Crystals.- 8.3.5 Polarized States of Liquid Crystals.- 8.3.6 Electrohydrodynamic Phenomena in Liquid Crystals.- 8.4 Magnetic Properties of Liquid Crystals.- 8.5 Electrical Properties of Liquid Crystals.- 8.5.1 Dielectric Properties of Liquid Crystals.- 8.5.2 Transverse Domains in Nematics with a Negative Dielectric Anisotropy.- 8.5.3 Effect of Dynamic Light Scattering.- 8.5.4 Effect of Deformation of a Nematic Liquid-Crystal Layer.- 8.5.5 Longitudinal Domains in Substances with a Negative Dielectric Anisotropy.- 8.5.6 Domains in Liquid Crystals with a Positive Dielectric Anisotropy.- 8.5.7 Behavior of Cholesteric and Smectic Liquid Crystals in an Electric Field.- 8.6 Thermal Properties of Liquid Crystals.- References.