(International Tables) Physical properties of crystals

International Tables for Crystallography
Volume D: Physical properties of crystals

Second online edition (2013) ISBN: 978-1-118-76229-5 doi: 10.1107/97809553602060000113

Edited by A. Authier

Preface to the second edition (p. xii) | html | pdf |
André Authier

Tensorial aspects of physical properties
- 1.1. Introduction to the properties of tensors (pp. 3-34) | html | pdf | chapter contents |
  A. Authier
  - 1.1.1. The matrix of physical properties (pp. 3-5) | html | pdf |
    - 1.1.1.1. Notion of extensive and intensive quantities (p. 3) | html | pdf |
    - 1.1.1.2. Notion of tensor in physics (pp. 3-4) | html | pdf |
    - 1.1.1.3. The matrix of physical properties (p. 4) | html | pdf |
    - 1.1.1.4. Symmetry of the matrix of physical properties (pp. 4-5) | html | pdf |
    - 1.1.1.5. Onsager relations (p. 5) | html | pdf |
  - 1.1.2. Basic properties of vector spaces (pp. 5-7) | html | pdf |
    - 1.1.2.1. Change of basis (p. 5) | html | pdf |
    - 1.1.2.2. Metric tensor (p. 5) | html | pdf |
    - 1.1.2.3. Orthonormal frames of coordinates – rotation matrix (pp. 5-6) | html | pdf |
    - 1.1.2.4. Covariant coordinates – dual or reciprocal space (pp. 6-7) | html | pdf |
      - 1.1.2.4.1. Covariant coordinates (p. 6) | html | pdf |
      - 1.1.2.4.2. Reciprocal space (p. 6) | html | pdf |
      - 1.1.2.4.3. Properties of the metric tensor (pp. 6-7) | html | pdf |
  - 1.1.3. Mathematical notion of tensor (pp. 7-10) | html | pdf |
    - 1.1.3.1. Definition of a tensor (p. 7) | html | pdf |
      - 1.1.3.1.1. Linear forms (p. 7) | html | pdf |
      - 1.1.3.1.2. Tensor product (p. 7) | html | pdf |
    - 1.1.3.2. Behaviour under a change of basis (p. 7) | html | pdf |
    - 1.1.3.3. Operations on tensors (pp. 7-8) | html | pdf |
      - 1.1.3.3.1. Addition (p. 7) | html | pdf |
      - 1.1.3.3.2. Multiplication by a scalar (p. 8) | html | pdf |
      - 1.1.3.3.3. Contracted product, contraction (p. 8) | html | pdf |
    - 1.1.3.4. Tensor nature of physical quantities (p. 8) | html | pdf |
    - 1.1.3.5. Representation surface of a tensor (pp. 8-9) | html | pdf |
      - 1.1.3.5.1. Definition (p. 8) | html | pdf |
      - 1.1.3.5.2. Representation surfaces of second-rank tensors (pp. 8-9) | html | pdf |
      - 1.1.3.5.3. Representation surfaces of higher-rank tensors (p. 9) | html | pdf |
    - 1.1.3.6. Change of variance of the components of a tensor (p. 9) | html | pdf |
      - 1.1.3.6.1. Tensor nature of the metric tensor (p. 9) | html | pdf |
      - 1.1.3.6.2. How to change the variance of the components of a tensor (p. 9) | html | pdf |
      - 1.1.3.6.3. Examples of the use in physics of different representations of the same quantity (p. 9) | html | pdf |
    - 1.1.3.7. Outer product (pp. 9-10) | html | pdf |
      - 1.1.3.7.1. Definition (p. 9) | html | pdf |
      - 1.1.3.7.2. Vector product (p. 10) | html | pdf |
      - 1.1.3.7.3. Properties of the vector product (p. 10) | html | pdf |
    - 1.1.3.8. Tensor derivatives (p. 10) | html | pdf |
      - 1.1.3.8.1. Interpretation of the coefficients of the matrix – change of coordinates (p. 10) | html | pdf |
      - 1.1.3.8.2. Generalization (p. 10) | html | pdf |
      - 1.1.3.8.3. Differential operators (p. 10) | html | pdf |
      - 1.1.3.8.4. Development of a vector function in a Taylor series (p. 10) | html | pdf |
  - 1.1.4. Symmetry properties (pp. 10-31) | html | pdf |
    - 1.1.4.1. Introduction – Neumann's principle (p. 11) | html | pdf |
    - 1.1.4.2. Curie laws (p. 11) | html | pdf |
    - 1.1.4.3. Symmetries associated with an electric field and with magnetic induction (flux density) (pp. 11-12) | html | pdf |
      - 1.1.4.3.1. Symmetry of an electric field (pp. 11-12) | html | pdf |
      - 1.1.4.3.2. Symmetry of magnetic induction (p. 12) | html | pdf |
    - 1.1.4.4. Superposition of several causes in the same medium – pyroelectricity and piezolectricity (p. 12) | html | pdf |
      - 1.1.4.4.1. Introduction (p. 12) | html | pdf |
      - 1.1.4.4.2. Pyroelectricity (p. 12) | html | pdf |
      - 1.1.4.4.3. Piezoelectricity (pp. 12-13) | html | pdf |
    - 1.1.4.5. Intrinsic symmetry of tensors (pp. 12-14) | html | pdf |
      - 1.1.4.5.1. Introduction (p. 13) | html | pdf |
      - 1.1.4.5.2. Symmetric tensors  (p. 13) | html | pdf |
        1.1.4.5.2.1. Tensors of rank 2  (p. 13) | html | pdf |
        1.1.4.5.2.2. Tensors of higher rank  (p. 13) | html | pdf |
      - 1.1.4.5.3. Antisymmetric tensors – axial tensors  (pp. 13-14) | html | pdf |
        1.1.4.5.3.1. Tensors of rank 2  (pp. 13-14) | html | pdf |
        1.1.4.5.3.2. Tensors of higher rank  (p. 14) | html | pdf |
        1.1.4.5.3.3. Properties of axial tensors  (p. 14) | html | pdf |
    - 1.1.4.6. Symmetry of tensors imposed by the crystalline medium (pp. 14-16) | html | pdf |
      - 1.1.4.6.1. Matrix method – application of Neumann's principle (p. 15) | html | pdf |
      - 1.1.4.6.2. The operator A is in diagonal form  (pp. 15-16) | html | pdf |
        1.1.4.6.2.1. Introduction  (p. 15) | html | pdf |
        1.1.4.6.2.2. Case of a centre of symmetry  (p. 15) | html | pdf |
        1.1.4.6.2.3. General case  (pp. 15-16) | html | pdf |
      - 1.1.4.6.3. The method of direct inspection (p. 16) | html | pdf |
    - 1.1.4.7. Reduction of the components of a tensor of rank 2 (pp. 16-17) | html | pdf |
      - 1.1.4.7.1. Triclinic system (p. 16) | html | pdf |
      - 1.1.4.7.2. Monoclinic system (p. 16) | html | pdf |
      - 1.1.4.7.3. Orthorhombic system (p. 16) | html | pdf |
      - 1.1.4.7.4. Trigonal, tetragonal, hexagonal and cylindrical systems  (pp. 16-17) | html | pdf |
        1.1.4.7.4.1. Groups $[{\bar 3}]$ , ; , $[{\bar 4}]$ , ; , $[{\bar 6}]$ , ; $[(A_{\infty}/M)C]$ , $[A_{\infty}]$   (pp. 16-17) | html | pdf |
        1.1.4.7.4.2. Groups $[{\bar 3}m]$ , , ; , , , $[{\bar {4}}{2}m]$ ; , , , $[{\bar{6}}{2}m]$ ; $[(A_{\infty}/M) \infty (A_{2}/M)C]$ , $[A_{\infty}\infty A_{2}]$   (p. 17) | html | pdf |
      - 1.1.4.7.5. Cubic and spherical systems (p. 17) | html | pdf |
      - 1.1.4.7.6. Symmetric tensors of rank 2  (p. 17) | html | pdf |
        1.1.4.7.6.1. Triclinic system  (p. 17) | html | pdf |
        1.1.4.7.6.2. Monoclinic system (twofold axis parallel to )  (p. 17) | html | pdf |
        1.1.4.7.6.3. Orthorhombic system  (p. 17) | html | pdf |
        1.1.4.7.6.4. Trigonal, tetragonal and hexagonal systems, isotropic groups  (p. 17) | html | pdf |
        1.1.4.7.6.5. Cubic system  (p. 17) | html | pdf |
    - 1.1.4.8. Reduction of the components of a tensor of rank 3 (pp. 17-20) | html | pdf |
      - 1.1.4.8.1. Triclinic system  (p. 17) | html | pdf |
        1.1.4.8.1.1. Group   (p. 17) | html | pdf |
        1.1.4.8.1.2. Group $[{\bar 1}]$   (p. 17) | html | pdf |
      - 1.1.4.8.2. Monoclinic system  (p. 18) | html | pdf |
        1.1.4.8.2.1. Group   (p. 18) | html | pdf |
        1.1.4.8.2.2. Group m  (p. 18) | html | pdf |
        1.1.4.8.2.3. Group   (p. 18) | html | pdf |
      - 1.1.4.8.3. Orthorhombic system  (p. 18) | html | pdf |
        1.1.4.8.3.1. Group   (p. 18) | html | pdf |
        1.1.4.8.3.2. Group   (p. 18) | html | pdf |
        1.1.4.8.3.3. Group   (p. 18) | html | pdf |
      - 1.1.4.8.4. Trigonal system  (p. 18) | html | pdf |
        1.1.4.8.4.1. Group   (p. 18) | html | pdf |
        1.1.4.8.4.2. Group with a twofold axis parallel to $[Ox_{1}]$   (p. 18) | html | pdf |
        1.1.4.8.4.3. Group with a mirror normal to $[Ox_{1}]$   (p. 18) | html | pdf |
        1.1.4.8.4.4. Groups $[\bar{3}]$ and $[\bar{3}m]$   (p. 18) | html | pdf |
      - 1.1.4.8.5. Tetragonal system  (pp. 18-19) | html | pdf |
        1.1.4.8.5.1. Group   (pp. 18-19) | html | pdf |
        1.1.4.8.5.2. Group   (p. 19) | html | pdf |
        1.1.4.8.5.3. Group   (p. 19) | html | pdf |
        1.1.4.8.5.4. Group   (p. 19) | html | pdf |
        1.1.4.8.5.5. Group $[\bar{4}]$   (p. 19) | html | pdf |
        1.1.4.8.5.6. Group $[\bar{4}2m]$   (p. 19) | html | pdf |
        1.1.4.8.5.7. Group   (p. 19) | html | pdf |
      - 1.1.4.8.6. Hexagonal and cylindrical systems  (p. 19) | html | pdf |
        1.1.4.8.6.1. Groups , $[A_{\infty}]$ , , $[A_{\infty} \infty A_{2}]$ , and $[A_{\infty} \infty M]$   (p. 19) | html | pdf |
        1.1.4.8.6.2. Group $[\bar{6} = 3/m]$   (p. 19) | html | pdf |
        1.1.4.8.6.3. Group $[\bar{6}2m]$   (p. 19) | html | pdf |
        1.1.4.8.6.4. Groups , $[(A_{\infty}/M)C]$ , and $[(A_{\infty}/M) \infty (A_{2}/M)C]$   (p. 19) | html | pdf |
      - 1.1.4.8.7. Cubic and spherical systems  (pp. 19-20) | html | pdf |
        1.1.4.8.7.1. Group   (p. 19) | html | pdf |
        1.1.4.8.7.2. Groups and $[\infty A_{\infty}/M]$   (p. 20) | html | pdf |
        1.1.4.8.7.3. Group $[{\bar 4}3m]$   (p. 20) | html | pdf |
        1.1.4.8.7.4. Groups $[m{\bar 3}]$ , $[m{\bar 3}m]$ and $[\infty(A_{\infty}/M)C]$   (p. 20) | html | pdf |
    - 1.1.4.9. Reduction of the components of a tensor of rank 4 (pp. 20-24) | html | pdf |
      - 1.1.4.9.1. Triclinic system (groups $[{\bar 1}]$ , ) (p. 20) | html | pdf |
      - 1.1.4.9.2. Monoclinic system (groups , , m) (p. 20) | html | pdf |
      - 1.1.4.9.3. Orthorhombic system (groups , , ) (p. 20) | html | pdf |
      - 1.1.4.9.4. Trigonal system  (pp. 20-21) | html | pdf |
        1.1.4.9.4.1. Groups and $[{\bar 3}]$   (p. 20) | html | pdf |
        1.1.4.9.4.2. Groups $[{\bar 3}m]$ , , , with the twofold axis parallel to $[Ox_{1}]$   (p. 21) | html | pdf |
      - 1.1.4.9.5. Tetragonal system  (p. 21) | html | pdf |
        1.1.4.9.5.1. Groups , , $[{\bar 4}]$   (p. 21) | html | pdf |
        1.1.4.9.5.2. Groups , , , $[{\bar 4}2m]$   (p. 21) | html | pdf |
      - 1.1.4.9.6. Hexagonal and cylindrical systems  (p. 21) | html | pdf |
        1.1.4.9.6.1. Groups , $[{\bar 6}]$ , ; $[(A_{\infty}/M)C]$ , $[A_{\infty}]$   (p. 21) | html | pdf |
        1.1.4.9.6.2. Groups , , , $[{\bar 6}2m]$ ; $[(A_{\infty}/M) \infty]$ ; $[(A_{2}/M)C]$ , $[A_{\infty}\infty A_{2}]$   (p. 21) | html | pdf |
      - 1.1.4.9.7. Cubic system  (pp. 21-22) | html | pdf |
        1.1.4.9.7.1. Groups , $[{\bar 3}m]$   (p. 21) | html | pdf |
        1.1.4.9.7.2. Groups $[m{\bar 3}m]$ , , $[{\bar 4}3m]$   (p. 22) | html | pdf |
      - 1.1.4.9.8. Spherical system (p. 22) | html | pdf |
        1.1.4.9.8.1. Groups $[\infty (A_{\infty}/M)C]$ and $[\infty A_{\infty}]$ (p. 22) | html | pdf |
      - 1.1.4.9.9. Symmetric tensors of rank 4  (pp. 22-24) | html | pdf |
        1.1.4.9.9.1. Triclinic system  (p. 22) | html | pdf |
        1.1.4.9.9.2. Monoclinic system  (p. 22) | html | pdf |
        1.1.4.9.9.3. Orthorhombic system  (p. 22) | html | pdf |
        1.1.4.9.9.4. Trigonal system  (pp. 22-23) | html | pdf |
        1.1.4.9.9.5. Tetragonal system  (p. 23) | html | pdf |
        1.1.4.9.9.6. Hexagonal and cylindrical systems  (p. 23) | html | pdf |
        1.1.4.9.9.7. Cubic system  (pp. 23-24) | html | pdf |
    - 1.1.4.10. Reduced form of polar and axial tensors – matrix representation (pp. 24-31) | html | pdf |
      - 1.1.4.10.1. Introduction (p. 24) | html | pdf |
      - 1.1.4.10.2. Stress and strain tensors – Voigt matrices (p. 24) | html | pdf |
      - 1.1.4.10.3. Reduction of the number of independent components of third-rank polar tensors due to the symmetry of the strain and stress tensors (pp. 24-25) | html | pdf |
      - 1.1.4.10.4. Independent components of the matrix associated with a third-rank polar tensor according to the following point groups  (pp. 25-26) | html | pdf |
        1.1.4.10.4.1. Triclinic system  (p. 25) | html | pdf |
        1.1.4.10.4.2. Monoclinic system  (p. 25) | html | pdf |
        1.1.4.10.4.3. Orthorhombic system  (p. 25) | html | pdf |
        1.1.4.10.4.4. Trigonal system  (p. 25) | html | pdf |
        1.1.4.10.4.5. Tetragonal, hexagonal and cylindrical systems  (pp. 25-26) | html | pdf |
        1.1.4.10.4.6. Cubic and spherical systems  (p. 26) | html | pdf |
      - 1.1.4.10.5. Reduction of the number of independent components of fourth-rank polar tensors due to the symmetry of the strain and stress tensors (pp. 26-27) | html | pdf |
      - 1.1.4.10.6. Independent components of the matrix associated with a fourth-rank tensor according to the following point groups  (pp. 27-29) | html | pdf |
        1.1.4.10.6.1. Triclinic system, groups $[{\bar 1}]$ ,   (p. 27) | html | pdf |
        1.1.4.10.6.2. Monoclinic system  (p. 27) | html | pdf |
        1.1.4.10.6.3. Orthorhombic system  (p. 27) | html | pdf |
        1.1.4.10.6.4. Trigonal system  (p. 28) | html | pdf |
        1.1.4.10.6.5. Tetragonal system  (p. 28) | html | pdf |
        1.1.4.10.6.6. Hexagonal system  (pp. 28-29) | html | pdf |
        1.1.4.10.6.7. Cubic system  (p. 29) | html | pdf |
        1.1.4.10.6.8. Spherical system  (p. 29) | html | pdf |
      - 1.1.4.10.7. Reduction of the number of independent components of axial tensors of rank 2  (pp. 29-31) | html | pdf |
        1.1.4.10.7.1. Independent components according to the following point groups  (pp. 29-30) | html | pdf |
        1.1.4.10.7.2. Independent components of symmetric axial tensors according to the following point groups  (pp. 30-31) | html | pdf |
  - 1.1.5. Thermodynamic functions and physical property tensors (pp. 31-32) | html | pdf |
    - 1.1.5.1. Isothermal study (p. 31) | html | pdf |
    - 1.1.5.2. Other forms of the piezoelectric constants (p. 32) | html | pdf |
    - 1.1.5.3. Relation between the pyroelectric coefficients at constant stress and at constant strain (p. 32) | html | pdf |
    - 1.1.5.4. Adiabatic study (p. 32) | html | pdf |
  - 1.1.6. Glossary (pp. 32-33) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.1.4.1. Symmetry of an electric field (p. 11) | html | pdf |
    - Fig. 1.1.4.2. Symmetry of magnetic induction (p. 12) | html | pdf |
  - Tables
    - Table 1.1.1.1. Extensive quantities and associated intensive parameters (p. 3) | html | pdf |
- 1.2. Representations of crystallographic groups (pp. 34-71) | html | pdf | chapter contents |
  T. Janssen
  - 1.2.1. Introduction (pp. 34-35) | html | pdf |
  - 1.2.2. Point groups (pp. 35-46) | html | pdf |
    - 1.2.2.1. Finite point groups in one, two and three dimensions (pp. 35-36) | html | pdf |
    - 1.2.2.2. Representations of finite groups (pp. 36-37) | html | pdf |
    - 1.2.2.3. General tensors (pp. 37-38) | html | pdf |
    - 1.2.2.4. Orthogonality relations (pp. 38-39) | html | pdf |
    - 1.2.2.5. Characters (pp. 39-40) | html | pdf |
    - 1.2.2.6. The representations for point groups in one, two and three dimensions (pp. 40-42) | html | pdf |
    - 1.2.2.7. Tensor representations (pp. 42-43) | html | pdf |
    - 1.2.2.8. Projective representations (pp. 43-45) | html | pdf |
    - 1.2.2.9. Double groups and their representations (pp. 45-46) | html | pdf |
  - 1.2.3. Space groups (pp. 46-51) | html | pdf |
    - 1.2.3.1. Structure of space groups (pp. 46-47) | html | pdf |
    - 1.2.3.2. Irreducible representations of lattice translation groups (p. 47) | html | pdf |
    - 1.2.3.3. Irreducible representations of space groups (pp. 47-49) | html | pdf |
    - 1.2.3.4. Characterization of space-group representations (pp. 49-50) | html | pdf |
    - 1.2.3.5. Double space groups and their representations (pp. 50-51) | html | pdf |
  - 1.2.4. Tensors (pp. 51-53) | html | pdf |
    - 1.2.4.1. Transformation properties of tensors (pp. 51-52) | html | pdf |
    - 1.2.4.2. Invariants (p. 52) | html | pdf |
    - 1.2.4.3. Clebsch–Gordan coefficients (pp. 52-53) | html | pdf |
  - 1.2.5. Magnetic symmetry (pp. 53-56) | html | pdf |
    - 1.2.5.1. Magnetic point groups (p. 53) | html | pdf |
    - 1.2.5.2. Magnetic space groups (pp. 53-54) | html | pdf |
    - 1.2.5.3. Transformation of tensors (p. 54) | html | pdf |
    - 1.2.5.4. Time-reversal operators (pp. 54-55) | html | pdf |
    - 1.2.5.5. Co-representations (pp. 55-56) | html | pdf |
  - 1.2.6. Tables (pp. 56-62) | html | pdf |
  - 1.2.7. Introduction to the accompanying software Tenχar (pp. 62-70) | html | pdf |
    M. Ephraïm, T. Janssen, A. Janner and A. Thiers
    - 1.2.7.1. Overview (pp. 62-64) | html | pdf |
    - 1.2.7.2. Tensors (pp. 64-66) | html | pdf |
    - 1.2.7.3. Characters (pp. 66-67) | html | pdf |
    - 1.2.7.4. Algorithms (pp. 67-70) | html | pdf |
      - 1.2.7.4.1. Construction of a basis (p. 67) | html | pdf |
      - 1.2.7.4.2. Action of the generators of the point group G on the basis (p. 67) | html | pdf |
      - 1.2.7.4.3. Diagonalization of the action matrix and determination of the invariant tensor (pp. 67-68) | html | pdf |
      - 1.2.7.4.4. Determination of the vector representation (p. 68) | html | pdf |
      - 1.2.7.4.5. Determination of tensor products and their decomposition (p. 68) | html | pdf |
      - 1.2.7.4.6. Invariant tensors (pp. 68-70) | html | pdf |
  - 1.2.8. Glossary (pp. 70-71) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 1.2.2.1. Character table for $[S_3\sim D_3]$ (p. 40) | html | pdf |
    - Table 1.2.2.2. Character table of $[D_{4}]$ (p. 44) | html | pdf |
    - Table 1.2.3.1. Choices of $[{\bf k}]$ in the fundamental domain of and the elements of $[K_{\bf k}]$ (p. 49) | html | pdf |
    - Table 1.2.3.2. Strata of irreducible representations of and (p. 49) | html | pdf |
    - Table 1.2.3.3. Characteristic values of $[\lambda_{i}]$ for the projective irreps of $[K_{\bf k}]$ for the point group (p. 50) | html | pdf |
    - Table 1.2.5.1. Character of the representations corresponding to the electric and magnetic fields in point groups , and (p. 54) | html | pdf |
    - Table 1.2.6.1. Finite point groups in three dimensions (p. 57) | html | pdf |
    - Table 1.2.6.2. Crystallographic point groups in three dimensions (p. 57) | html | pdf |
    - Table 1.2.6.3. Irreducible representations for cyclic groups $[C_{n}]$ (p. 57) | html | pdf |
    - Table 1.2.6.4. Irreducible representations for dihedral groups $[D_{n}]$ (p. 57) | html | pdf |
    - Table 1.2.6.5. Irreducible representations and character tables for the 32 crystallographic point groups in three dimensions (pp. 58-60) | html | pdf |
    - Table 1.2.6.6. Direct products with $[\{E,\bar{1}\}]$ and $[\{E,1'\}]$ (p. 60) | html | pdf |
    - Table 1.2.6.7. Extra representations of double point groups (p. 61) | html | pdf |
    - Table 1.2.6.8. Projective spin representations of the 32 crystallographic point groups (p. 61) | html | pdf |
    - Table 1.2.6.9. Number of free parameters of some tensors (p. 62) | html | pdf |
    - Table 1.2.6.10. Irreducible projective representations of the 32 crystallographic point groups (pp. 63-64) | html | pdf |
    - Table 1.2.6.11. Special points in the Brillouin zones in three dimensions (pp. 65-66) | html | pdf |
    - Table 1.2.6.12. Magnetic point groups (p. 66) | html | pdf |
    - Table 1.2.7.1. Data connected with the character table for point group (p. 67) | html | pdf |
    - Table 1.2.7.2. Calculation with characters (p. 69) | html | pdf |
- 1.3. Elastic properties (pp. 72-100) | html | pdf | chapter contents |
  A. Authier and A. Zarembowitch
  - 1.3.1. Strain tensor (pp. 72-76) | html | pdf |
    - 1.3.1.1. Introduction, the notion of strain field (p. 72) | html | pdf |
    - 1.3.1.2. Homogeneous deformation (pp. 72-74) | html | pdf |
      - 1.3.1.2.1. Fundamental property of the homogeneous deformation (p. 72) | html | pdf |
      - 1.3.1.2.2. Spontaneous strain (p. 72) | html | pdf |
      - 1.3.1.2.3. Cubic dilatation (pp. 72-73) | html | pdf |
      - 1.3.1.2.4. Expression of any homogeneous deformation as the product of a pure rotation and a pure deformation (p. 73) | html | pdf |
      - 1.3.1.2.5. Quadric of elongations (pp. 73-74) | html | pdf |
    - 1.3.1.3. Arbitrary but small deformations (pp. 74-75) | html | pdf |
      - 1.3.1.3.1. Definition of the strain tensor (pp. 74-75) | html | pdf |
      - 1.3.1.3.2. Geometrical interpretation of the coefficients of the strain tensor (p. 75) | html | pdf |
    - 1.3.1.4. Particular components of the deformation (pp. 75-76) | html | pdf |
      - 1.3.1.4.1. Simple elongation (p. 75) | html | pdf |
      - 1.3.1.4.2. Pure shear (p. 76) | html | pdf |
      - 1.3.1.4.3. Simple shear (p. 76) | html | pdf |
  - 1.3.2. Stress tensor (pp. 76-80) | html | pdf |
    - 1.3.2.1. General conditions of equilibrium of a solid (p. 76) | html | pdf |
    - 1.3.2.2. Definition of the stress tensor (pp. 76-77) | html | pdf |
    - 1.3.2.3. Condition of continuity (p. 77) | html | pdf |
    - 1.3.2.4. Symmetry of the stress tensor (pp. 77-78) | html | pdf |
    - 1.3.2.5. Voigt's notation – interpretation of the components of the stress tensor (p. 78) | html | pdf |
      - 1.3.2.5.1. Voigt's notation, reduced form of the stress tensor (p. 78) | html | pdf |
      - 1.3.2.5.2. Interpretation of the components of the stress tensor – special forms of the stress tensor (p. 78) | html | pdf |
    - 1.3.2.6. Boundary conditions (pp. 78-79) | html | pdf |
    - 1.3.2.7. Local properties of the stress tensor (p. 79) | html | pdf |
    - 1.3.2.8. Energy density in a deformed medium (pp. 79-80) | html | pdf |
  - 1.3.3. Linear elasticity (pp. 80-85) | html | pdf |
    - 1.3.3.1. Hooke's law (pp. 80-81) | html | pdf |
    - 1.3.3.2. Elastic constants (pp. 81-82) | html | pdf |
      - 1.3.3.2.1. Definition (p. 81) | html | pdf |
      - 1.3.3.2.2. Matrix notation – reduction of the number of independent components (pp. 81-82) | html | pdf |
      - 1.3.3.2.3. Passage from elastic compliances $[s_{\alpha \beta}]$ to elastic stiffnesses $[c_{\alpha \beta}]$ (p. 82) | html | pdf |
    - 1.3.3.3. Elastic strain energy (pp. 82-83) | html | pdf |
    - 1.3.3.4. Particular elastic constants (pp. 83-84) | html | pdf |
      - 1.3.3.4.1. Volume compressibility (p. 83) | html | pdf |
      - 1.3.3.4.2. Linear compressibility (p. 83) | html | pdf |
      - 1.3.3.4.3. Young's modulus, Poisson's ratio (p. 83) | html | pdf |
      - 1.3.3.4.4. Variation of Young's modulus with orientation (p. 84) | html | pdf |
    - 1.3.3.5. Isotropic materials (pp. 84-85) | html | pdf |
    - 1.3.3.6. Equilibrium conditions of elasticity for isotropic media (pp. 85-86) | html | pdf |
  - 1.3.4. Propagation of elastic waves in continuous media – dynamic elasticity (pp. 86-89) | html | pdf |
    - 1.3.4.1. Introduction (p. 86) | html | pdf |
    - 1.3.4.2. Equation of propagation of a wave in a material (p. 86) | html | pdf |
    - 1.3.4.3. Dynamic elastic stiffnesses (pp. 86-87) | html | pdf |
    - 1.3.4.4. Polarization of the elastic waves (p. 87) | html | pdf |
    - 1.3.4.5. Relation between velocity of propagation and elastic stiffnesses (pp. 87-88) | html | pdf |
      - 1.3.4.5.1. Cubic crystals (p. 87) | html | pdf |
      - 1.3.4.5.2. Hexagonal crystals (p. 87) | html | pdf |
      - 1.3.4.5.3. Tetragonal crystals (classes , $[\bar{4}2m]$ , ) (pp. 87-88) | html | pdf |
    - 1.3.4.6. Experimental determination of elastic constants (pp. 88-89) | html | pdf |
      - 1.3.4.6.1. Introduction (p. 88) | html | pdf |
      - 1.3.4.6.2. Resonance technique (p. 88) | html | pdf |
      - 1.3.4.6.3. Pulse-echo techniques (pp. 88-89) | html | pdf |
  - 1.3.5. Pressure dependence and temperature dependence of the elastic constants (pp. 89-91) | html | pdf |
    - 1.3.5.1. Introduction (pp. 89-90) | html | pdf |
    - 1.3.5.2. Temperature dependence of the elastic constants (pp. 90-91) | html | pdf |
    - 1.3.5.3. Pressure dependence of the elastic constants (p. 91) | html | pdf |
  - 1.3.6. Nonlinear elasticity (pp. 92-95) | html | pdf |
    - 1.3.6.1. Introduction (p. 92) | html | pdf |
    - 1.3.6.2. Lagrangian and Eulerian descriptions (p. 92) | html | pdf |
    - 1.3.6.3. Strain and stress tensors (pp. 92-93) | html | pdf |
    - 1.3.6.4. Second-order and higher-order elastic stiffnesses (p. 93) | html | pdf |
    - 1.3.6.5. Expansion of elastic constants for small initial stress (pp. 93-94) | html | pdf |
    - 1.3.6.6. Elastic strain-energy density (pp. 94-95) | html | pdf |
  - 1.3.7. Nonlinear dynamic elasticity (pp. 95-98) | html | pdf |
    - 1.3.7.1. Introduction (p. 95) | html | pdf |
    - 1.3.7.2. Equation of motion for elastic waves (p. 95) | html | pdf |
    - 1.3.7.3. Wave propagation in a nonlinear elastic medium (pp. 95-97) | html | pdf |
      - 1.3.7.3.1. Isotropic media (p. 96) | html | pdf |
      - 1.3.7.3.2. Cubic media (most symmetrical groups) (pp. 96-97) | html | pdf |
    - 1.3.7.4. Harmonic generation (p. 97) | html | pdf |
    - 1.3.7.5. Small-amplitude waves in a strained medium (p. 97) | html | pdf |
    - 1.3.7.6. Experimental determination of third- and higher-order elastic constants (pp. 97-98) | html | pdf |
  - 1.3.8. Glossary (p. 98) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.3.1.1. Displacement vector, $[{\bf u}({\bf r})]$ (p. 72) | html | pdf |
    - Fig. 1.3.1.2. Elongation, $[u_{r}/r]$ (p. 73) | html | pdf |
    - Fig. 1.3.1.3. Quadric of elongations (p. 74) | html | pdf |
    - Fig. 1.3.1.4. Geometrical interpretation of the components of the strain tensor (p. 75) | html | pdf |
    - Fig. 1.3.1.5. Special deformations (p. 75) | html | pdf |
    - Fig. 1.3.2.1. Definition of stress (p. 76) | html | pdf |
    - Fig. 1.3.2.2. Stress, $[{\bf T}_{n}]$ , applied to the surface of an internal volume (p. 76) | html | pdf |
    - Fig. 1.3.2.3. Equilibrium of a small volume element (p. 77) | html | pdf |
    - Fig. 1.3.2.4. Symmetry of the stress tensor (p. 78) | html | pdf |
    - Fig. 1.3.2.5. Special forms of the stress tensor (p. 79) | html | pdf |
    - Fig. 1.3.2.6. Normal ( $[\boldnu]$ ) and shearing ( $[\boldtau]$ ) stress (p. 79) | html | pdf |
    - Fig. 1.3.2.7. The stress quadric (p. 80) | html | pdf |
    - Fig. 1.3.2.8. Determination of the energy density in a deformed medium (p. 80) | html | pdf |
    - Fig. 1.3.3.1. Bar loaded in pure tension (p. 80) | html | pdf |
    - Fig. 1.3.3.2. Schematic stress–strain curve (p. 81) | html | pdf |
    - Fig. 1.3.3.3. Spherical coordinates (p. 84) | html | pdf |
    - Fig. 1.3.3.4. Representation surface of the inverse of Young's modulus (p. 85) | html | pdf |
    - Fig. 1.3.4.1. Resonance technique: standing waves excited in a parallelepiped (p. 89) | html | pdf |
    - Fig. 1.3.4.2. Block diagram of the pulse-echo technique (p. 89) | html | pdf |
    - Fig. 1.3.5.1. Temperature dependence of the elastic stiffnesses of an aluminium single crystal (p. 90) | html | pdf |
    - Fig. 1.3.5.2. Pressure dependence of the elastic stiffness $[c_{11} ]$ of a KZnF₃ crystal (p. 91) | html | pdf |
    - Fig. 1.3.5.3. Temperature dependence of the elastic constant $[c_{44}]$ in RbCdF₃, CsCdF₃ and TlCdF₃ crystals (p. 91) | html | pdf |
    - Fig. 1.3.5.4. Temperature dependence of the elastic constant $[c_{11}]$ in KNiF₃ (p. 91) | html | pdf |
    - Fig. 1.3.5.5. Temperature dependence of $[(c_{11} - c_{12})/2]$ in DyVO₄ (p. 91) | html | pdf |
    - Fig. 1.3.5.6. Pressure dependence of the elastic constants $[(c_{11} - c_{12})/2]$ in TlCdF₃ (p. 91) | html | pdf |
  - Tables
    - Table 1.3.2.1. Stresses applied to the faces surrounding a volume element (p. 77) | html | pdf |
    - Table 1.3.3.1. Number of independent components of the elastic compliances and stiffnesses for each Laue class (p. 82) | html | pdf |
    - Table 1.3.3.2. Elastic compliances of some cubic materials in (GPa)⁻¹ (after Every & McCurdy, 1992) (p. 83) | html | pdf |
    - Table 1.3.3.3. Relations between elastic coefficients in isotropic media (p. 85) | html | pdf |
    - Table 1.3.4.1. Velocity of propagation when the wavevector is parallel to [100] (cubic crystals) (p. 87) | html | pdf |
    - Table 1.3.4.2. Velocity of propagation when the wavevector is parallel to [110] (cubic crystals) (p. 87) | html | pdf |
    - Table 1.3.4.3. Velocity of propagation when the wavevector is parallel to [111] (cubic crystals) (p. 87) | html | pdf |
    - Table 1.3.4.4. Velocity of propagation when the wavevector is parallel to [001] (hexagonal crystals) (p. 87) | html | pdf |
    - Table 1.3.4.5. Velocity of propagation when the wavevector is parallel to [100] (hexagonal crystals) (p. 87) | html | pdf |
    - Table 1.3.4.6. Velocity of propagation when the wavevector is parallel to [001] (tetragonal crystals) (p. 87) | html | pdf |
    - Table 1.3.4.7. Velocity of propagation when the wavevector is parallel to [100] (tetragonal crystals) (p. 87) | html | pdf |
    - Table 1.3.5.1. Temperature dependence of the elastic stiffnesses for some cubic crystals (p. 90) | html | pdf |
    - Table 1.3.5.2. Order of magnitude of the temperature dependence of the elastic stiffnesses for different types of crystals (p. 91) | html | pdf |
    - Table 1.3.6.1. Number of independent third-order elastic stiffnesses for each Laue class (p. 93) | html | pdf |
    - Table 1.3.6.2. Third-order elastic stiffnesses of some materials in (GPa)⁻¹ (after Every & McCurdy, 1992) (p. 94) | html | pdf |
    - Table 1.3.7.1. Relationships between $[\rho W^{2}]$ , its pressure derivatives and the second- and third-order elastic constants (p. 98) | html | pdf |
- 1.4. Thermal expansion (pp. 100-105) | html | pdf | chapter contents |
  H. Küppers
  - 1.4.1. Definition, symmetry and representation surfaces (pp. 100-101) | html | pdf |
  - 1.4.2. Grüneisen relation (pp. 101-102) | html | pdf |
  - 1.4.3. Experimental methods (pp. 102-104) | html | pdf |
    - 1.4.3.1. General remarks (pp. 102-103) | html | pdf |
    - 1.4.3.2. Diffraction (p. 103) | html | pdf |
    - 1.4.3.3. Optical methods (interferometry) (pp. 103-104) | html | pdf |
    - 1.4.3.4. Electrical methods (p. 104) | html | pdf |
      - 1.4.3.4.1. Inductance changes (pushrod dilatometry) (p. 104) | html | pdf |
      - 1.4.3.4.2. Capacitance methods (p. 104) | html | pdf |
  - 1.4.4. Relation to crystal structure (pp. 104-105) | html | pdf |
  - 1.4.5. Glossary (p. 105) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.4.1.1. Sections (ac plane) of representation surfaces for a trigonal (or tetragonal or hexagonal) crystal (p. 100) | html | pdf |
    - Fig. 1.4.3.1. Schematic diagram of a Fizeau interferometer (p. 104) | html | pdf |
    - Fig. 1.4.3.2. Schematic diagram of a Michelson interferometer (p. 104) | html | pdf |
  - Tables
    - Table 1.4.1.1. Shape of the quadric and symmetry restrictions (p. 101) | html | pdf |
- 1.5. Magnetic properties (pp. 106-153) | html | pdf | chapter contents |
  A. S. Borovik-Romanov, H. Grimmer and M. Kenzelmann
  - 1.5.1. Introduction (pp. 106-110) | html | pdf |
    - 1.5.1.1. Magnetically disordered materials (pp. 107-108) | html | pdf |
    - 1.5.1.2. Magnetically ordered materials (pp. 108-110) | html | pdf |
      - 1.5.1.2.1. Ferromagnets (including ferrimagnets) (pp. 108-109) | html | pdf |
      - 1.5.1.2.2. Antiferromagnets (pp. 109-110) | html | pdf |
      - 1.5.1.2.3. Helical and sinusoidal magnetic order (p. 110) | html | pdf |
  - 1.5.2. Magnetic symmetry (pp. 110-117) | html | pdf |
    - 1.5.2.1. Magnetic point groups (pp. 110-114) | html | pdf |
    - 1.5.2.2. Magnetic lattices (pp. 114-117) | html | pdf |
    - 1.5.2.3. Magnetic space groups (p. 117) | html | pdf |
    - 1.5.2.4. Exchange symmetry (p. 117) | html | pdf |
  - 1.5.3. Phase transitions into a magnetically ordered state (pp. 117-126) | html | pdf |
    - 1.5.3.1. Magnetic structures in rhombohedral crystals (pp. 118-120) | html | pdf |
    - 1.5.3.2. Exchange and magnetic anisotropy energies (pp. 120-121) | html | pdf |
    - 1.5.3.3. The thermodynamic theory of transitions into a magnetically ordered state (pp. 121-126) | html | pdf |
      - 1.5.3.3.1. Uniaxial ferromagnet (pp. 124-125) | html | pdf |
      - 1.5.3.3.2. Uniaxial antiferromagnet (pp. 125-126) | html | pdf |
  - 1.5.4. Domain structure (pp. 126-128) | html | pdf |
    - 1.5.4.1. 180° domains (pp. 126-128) | html | pdf |
    - 1.5.4.2. Twin domains (p. 128) | html | pdf |
    - 1.5.4.3. Ferroic domains (p. 128) | html | pdf |
  - 1.5.5. Weakly non-collinear magnetic structures (pp. 128-132) | html | pdf |
    - 1.5.5.1. Weak ferromagnetism (pp. 128-132) | html | pdf |
    - 1.5.5.2. Other weakly non-collinear magnetic structures (p. 132) | html | pdf |
  - 1.5.6. Reorientation transitions (pp. 132-133) | html | pdf |
  - 1.5.7. Piezomagnetism (pp. 133-139) | html | pdf |
    - 1.5.7.1. Piezomagnetic effect (pp. 134-137) | html | pdf |
    - 1.5.7.2. Linear magnetostriction (pp. 137-138) | html | pdf |
    - 1.5.7.3. Linear magnetic birefringence (pp. 138-139) | html | pdf |
  - 1.5.8. Magnetoelectric effect (pp. 139-145) | html | pdf |
    - 1.5.8.1. Linear magnetoelectric effect (pp. 140-141) | html | pdf |
    - 1.5.8.2. Nonlinear magnetoelectric effects (pp. 142-143) | html | pdf |
    - 1.5.8.3. Multiferroics (pp. 143-145) | html | pdf |
  - 1.5.9. Magnetostriction (pp. 145-148) | html | pdf |
    - 1.5.9.1. Spontaneous magnetostriction (pp. 145-147) | html | pdf |
    - 1.5.9.2. Magnetostriction in an external magnetic field (pp. 147-148) | html | pdf |
    - 1.5.9.3. The difference between the magnetic anisotropies at zero strain and zero stress (p. 148) | html | pdf |
  - 1.5.10. Connection between Gaussian and SI units (p. 148) | html | pdf |
  - 1.5.11. Glossary (p. 149) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.5.1.1. Temperature dependence of $[1/\chi]$ at high temperatures for different types of materials (p. 108) | html | pdf |
    - Fig. 1.5.1.2. Ordered arrangements of magnetic moments $[{\boldmu}_{i}]$ in: (a) an ordinary ferromagnet $[{\bf M}_s = N{\boldmu}_1]$ ; (b) a ferrimagnet $[{\bf M}_s =]$ $[(N/3)({\boldmu}_1 +]$ $[{\boldmu}_2 +]$ $[{\boldmu}_3)]$ ; (c) a weak ferromagnet $[{\bf M} =]$ $[{\bf M}_D =]$ $[(N/2)({\boldmu}_1 +]$ $[{\boldmu}_2)]$ , $[{\bf L} =]$ $[(N/2)({\boldmu}_1]$ $[- {\boldmu}_2)]$ , $[L_x \gg M_y]$ ; (p. 109) | html | pdf |
    - Fig. 1.5.1.3. Ordered arrangements of magnetic moments $[{\boldmu}_{i}]$ in: (a) an ordinary two-sublattice antiferromagnet $[{\bf L} =]$ $[(N/2)({\boldmu}_1 -]$ $[{\boldmu}_2)]$ ; (b) a weakly non-collinear four-sublattice antiferromagnet $[{\bf L}_1(x) =]$ $[(N/4)({\boldmu}_1]$ − $[{\boldmu}_2]$ − $[{\boldmu}_3]$ + $[{\boldmu}_4)]$ , $[{\bf L}_2(y) =]$ $[(N/4)({\boldmu}_1]$ − $[{\boldmu}_2]$ + $[{\boldmu}_3]$ − $[{\boldmu}_4)]$ ; (c) a strongly non-collinear three-sublattice antiferromagnet $[{\bf L}_1 =]$ $[(N/3)(3)^{1/2}({\boldmu}_2]$ − $[{\boldmu}_1)]$ , $[{\bf L}_2 =]$ $[(N/3)({\boldmu}_1]$ + $[{\boldmu}_2]$ − $[{\boldmu}_3)]$ (p. 109) | html | pdf |
    - Fig. 1.5.1.4. Helical and sinusoidal magnetic structures (p. 110) | html | pdf |
    - Fig. 1.5.2.1. Magnetic lattices of the triclinic system (p. 114) | html | pdf |
    - Fig. 1.5.2.2. Magnetic lattices of the monoclinic system (p. 114) | html | pdf |
    - Fig. 1.5.2.3. Magnetic lattices of the orthorhombic system (p. 115) | html | pdf |
    - Fig. 1.5.2.4. Magnetic lattices of the tetragonal system (p. 116) | html | pdf |
    - Fig. 1.5.2.5. Magnetic lattices of the rhombohedral system (p. 116) | html | pdf |
    - Fig. 1.5.2.6. Magnetic lattices of the hexagonal system (p. 116) | html | pdf |
    - Fig. 1.5.2.7. Magnetic lattices of the cubic system (p. 117) | html | pdf |
    - Fig. 1.5.3.1. Arrangement of the symmetry elements of the group $[\widetilde{{\bi D}}^6_{3d}]$ (p. 118) | html | pdf |
    - Fig. 1.5.3.2. Crystallographic structure of transition-metal oxides of the type $[\alpha]$ -Fe₂O₃ (p. 118) | html | pdf |
    - Fig. 1.5.3.3. Crystallographic structure of transition-metal carbonates of the type MnCO₃ (p. 119) | html | pdf |
    - Fig. 1.5.3.4. Four types of magnetic structures of rhombohedral oxides of transition metals (p. 119) | html | pdf |
    - Fig. 1.5.3.5. The conventional unit cell of UO₂ (p. 122) | html | pdf |
    - Fig. 1.5.3.6. Temperature dependence of the mass susceptibility $[\chi_{g}]$ for a uniaxial antiferromagnet along ( $[{\chi}_{ \parallel }]$ ) and perpendicular ( $[{\chi}_{\perp}]$ ) to the axis of antiferromagnetism (p. 125) | html | pdf |
    - Fig. 1.5.3.7. Dependence of the relative magnetization $[M/M_{\rm max}]$ on the magnetic field at (p. 126) | html | pdf |
    - Fig. 1.5.3.8. Magnetic phase diagram for a uniaxial antiferromagnet in a magnetic field applied parallel to the axis (p. 126) | html | pdf |
    - Fig. 1.5.3.9. Phase diagram for a uniaxial antiferromagnet in the proximity of , calculated for MnCl₂·4H₂O (p. 126) | html | pdf |
    - Fig. 1.5.4.1. Magnetization curves of hexagonal cobalt (p. 127) | html | pdf |
    - Fig. 1.5.4.2. Magnetization curves of two cubic crystals (iron and nickel) for three crystallographic directions (p. 127) | html | pdf |
    - Fig. 1.5.4.3. Schematic display of the magnetization: (a) H along the easy axis; (b) H at an arbitrary angle to the easy axis; (c) H perpendicular to the easy axis (p. 127) | html | pdf |
    - Fig. 1.5.4.4. A 180° domain wall in an antiferromagnet (p. 128) | html | pdf |
    - Fig. 1.5.5.1. Diagrams demonstrating two weakly ferromagnetic structures in rhombohedral crystals with two magnetic ions in the primitive cell (p. 129) | html | pdf |
    - Fig. 1.5.5.2. Dependence of magnetization $[M_{\perp}]$ and $[M_{ \parallel }]$ on the magnetic field H for the weak ferromagnet MnCO₃ at 4.2 K (p. 129) | html | pdf |
    - Fig. 1.5.5.3. Magnetic structures of fluorides of transition metals (p. 130) | html | pdf |
    - Fig. 1.5.5.4. Magnetic structures of orthoferrites and orthochromites RMO₃ (p. 131) | html | pdf |
    - Fig. 1.5.5.5. Temperature dependence of the susceptibility for CoCO₃ (p. 131) | html | pdf |
    - Fig. 1.5.5.6. A weakly non-collinear magnetic structure corresponding to (1.5.5.12) (p. 132) | html | pdf |
    - Fig. 1.5.6.1. Schematic representation of the rotation of the vectors $[\bf G]$ and $[\bf F]$ (in the xz plane) at a reorientation transition in orthoferrites (p. 133) | html | pdf |
    - Fig. 1.5.6.2. Schematic representation of the rotation of the vector $[\bf L]$ under the action of a magnetic field applied to CoF₂ perpendicular to the fourfold axis z (reorientation transition) (p. 133) | html | pdf |
    - Fig. 1.5.7.1. The dependence of the magnetic moment of CoF₂ on the magnetic field (p. 136) | html | pdf |
    - Fig. 1.5.7.2. Linear magnetostriction of CoF₂ (p. 137) | html | pdf |
    - Fig. 1.5.7.3. Variation of symmetry of the crystal field in the presence of the piezomagnetic effect in CoF₂ (p. 139) | html | pdf |
    - Fig. 1.5.8.1. Temperature dependence of the components $[\alpha_{ \parallel }]$ and $[\alpha_{\perp}]$ in Cr₂O₃ (p. 141) | html | pdf |
    - Fig. 1.5.8.2. The hysteresis loop of the linear magnetoelectric effect in ferroelectric and weakly ferromagnetic Ni₃B₇O₁₃I at 46 K (p. 144) | html | pdf |
    - Fig. 1.5.9.1. Diagram explaining the occurrence of magnetostrictive strains in the demagnetized and saturated states of a cube-shaped crystal with a cubic prototype (p. 147) | html | pdf |
  - Tables
    - Table 1.5.2.1. Comparison of different symbols for magnetic point groups (p. 110) | html | pdf |
    - Table 1.5.2.2. Comparison of different symbols for the elements of magnetic point groups (p. 110) | html | pdf |
    - Table 1.5.2.3. The 90 magnetic point groups of types 2 and 3 (pp. 111-112) | html | pdf |
    - Table 1.5.2.4. List of the magnetic classes in which ferromagnetism is admitted (p. 113) | html | pdf |
    - Table 1.5.3.1. Two types of symbols for collinear antiferromagnetic and ferromagnetic structures (p. 119) | html | pdf |
    - Table 1.5.3.2. Sign variation of the components of antiferromagnetic and ferromagnetic vectors during transformations of the group $[\widetilde{\bi D}_{3d}^6]$ in rhombohedral crystals with four magnetic ions (p. 120) | html | pdf |
    - Table 1.5.3.3. Magnetic groups of symmetry in rhombohedral oxides of trivalent transition-metal ions (p. 120) | html | pdf |
    - Table 1.5.3.4. Magnetic point groups in rhombohedral oxides of transition metals (p. 120) | html | pdf |
    - Table 1.5.3.5. The signs of $[{\boldmu}_i({\bf k}_j)]$ for four sites $[{\bf t}_i]$ of the conventional unit cell (the corners of a primitive cell) (p. 123) | html | pdf |
    - Table 1.5.3.6. Characters of the irreducible representations of the group $[{\bi D}_{3d}=\bar{3}m]$ and corresponding magnetic structures (p. 123) | html | pdf |
    - Table 1.5.5.1. The numbers of the crystallographic space groups that allow a phase transition into a weakly ferromagnetic state and the invariants of lowest order that are responsible for weak ferromagnetism (p. 130) | html | pdf |
    - Table 1.5.5.2. Magnetic point groups that allow weak ferromagnetism (p. 131) | html | pdf |
    - Table 1.5.7.1. The forms of the matrix characterizing the piezomagnetic effect (p. 135) | html | pdf |
    - Table 1.5.7.2. Experimental data for the piezomagnetic effect (PM) and for linear magnetostriction (LM) (p. 138) | html | pdf |
    - Table 1.5.8.1. The forms of the tensor characterizing the linear magnetoelectric effect (p. 139) | html | pdf |
    - Table 1.5.8.2. A list of some magnetoelectrics (p. 141) | html | pdf |
    - Table 1.5.8.3. Classification of the 122 magnetic point groups according to magnetoelectric types (p. 142) | html | pdf |
    - Table 1.5.8.4. List of the magnetic point groups of the ferromagnetoelectrics (p. 143) | html | pdf |
    - Table 1.5.8.5. Irreducible representations of the group G_k for TbMnO₃ (Kenzelmann et al., 2005) (p. 144) | html | pdf |
    - Table 1.5.9.1. Correspondence between matrix indices $[\alpha]$ , A and tensor indices of the tensors describing spontaneous magnetostriction (p. 146) | html | pdf |
    - Table 1.5.9.2. Magnetostriction data for ferromagnets with prototype symmetry $[m\bar{3}m1']$ (p. 147) | html | pdf |
    - Table 1.5.10.1. Conversion of non-rationalized (except for α) Gaussian units to SI units (p. 148) | html | pdf |
- 1.6. Classical linear crystal optics (pp. 153-180) | html | pdf | chapter contents |
  A. M. Glazer and K. G. Cox
  - 1.6.1. Introduction (p. 153) | html | pdf |
  - 1.6.2. Generalized optical, electro-optic and magneto-optic effects (pp. 153-155) | html | pdf |
    - 1.6.2.1. Spontaneous polarization (pp. 153-154) | html | pdf |
    - 1.6.2.2. Dielectric polarization $[\varepsilon_o \chi_{ij}E_j^\omega]$ (p. 154) | html | pdf |
    - 1.6.2.3. Optical rotation (gyration) $[\varepsilon_o\chi_{ij\ell}\nabla_{\ell}E_j^{\omega}]$ (p. 154) | html | pdf |
    - 1.6.2.4. Quadratic electric effect $[\varepsilon_o\chi_{ijk}E_j^{\omega_1}E_k^{\omega_2}]$ (p. 154) | html | pdf |
    - 1.6.2.5. Linear electro-optic effect $[\varepsilon_o\chi_{ijk}E_j^{\omega_1}E_k^{\omega_2}]$ (p. 154) | html | pdf |
    - 1.6.2.6. Sum/difference frequency generation (two-wave mixing) $[\varepsilon_o\chi_{ijk}E_j^{\omega_1}E_k^{\omega_2}]$ (p. 154) | html | pdf |
    - 1.6.2.7. Quadratic electro-optic effect $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}E_k^{\omega_2}E_\ell^{\omega_3}]$ (p. 154) | html | pdf |
    - 1.6.2.8. Electric-field induced second harmonic generation $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}E_k^{\omega_2}E_\ell^{\omega_3}]$ (p. 154) | html | pdf |
    - 1.6.2.9. Four-wave mixing $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}E_k^{\omega_2}E_\ell^{\omega_3}]$ (pp. 154-155) | html | pdf |
    - 1.6.2.10. Faraday rotation $[\varepsilon_o\chi_{ijk}E_j^{\omega_1}B_k^{\omega_2}]$ (p. 155) | html | pdf |
    - 1.6.2.11. Quadratic magneto-optic effect $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}B_k^{\omega_2}B_\ell^{\omega_3}]$ (p. 155) | html | pdf |
    - 1.6.2.12. Linear photoelastic effect $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}T_{k\ell}^{\omega_2}]$ (p. 155) | html | pdf |
    - 1.6.2.13. Linear acousto-optic effect $[\varepsilon_o\chi_{ijk\ell}E_j^{\omega_1}T_{k\ell}^{\omega_2}]$ (p. 155) | html | pdf |
  - 1.6.3. Linear optics (pp. 155-157) | html | pdf |
    - 1.6.3.1. The fundamental equation of crystal optics (pp. 155-156) | html | pdf |
    - 1.6.3.2. The optical indicatrix (pp. 156-157) | html | pdf |
    - 1.6.3.3. The dielectric impermeability tensor (p. 157) | html | pdf |
  - 1.6.4. Practical observation of crystals (pp. 157-169) | html | pdf |
    - 1.6.4.1. The polarizing microscope (pp. 157-158) | html | pdf |
    - 1.6.4.2. Specimen preparation (p. 158) | html | pdf |
    - 1.6.4.3. The indicatrix as an aid to practical microscopy (p. 158) | html | pdf |
    - 1.6.4.4. Vibration directions (pp. 158-159) | html | pdf |
    - 1.6.4.5. Measuring refractive indices (pp. 159-160) | html | pdf |
    - 1.6.4.6. Determination of linear birefringence (pp. 160-161) | html | pdf |
    - 1.6.4.7. Identification of polarization colours (p. 161) | html | pdf |
    - 1.6.4.8. Fringe counting (pp. 161-162) | html | pdf |
    - 1.6.4.9. Fast and slow vibration directions (pp. 162-163) | html | pdf |
    - 1.6.4.10. Other methods of measuring birefringence (p. 163) | html | pdf |
    - 1.6.4.11. Interference figures (pp. 163-164) | html | pdf |
    - 1.6.4.12. Uniaxial figures (pp. 164-165) | html | pdf |
    - 1.6.4.13. Biaxial figures (pp. 165-168) | html | pdf |
    - 1.6.4.14. Orientation studies (pp. 168-169) | html | pdf |
    - 1.6.4.15. Absorption colours (p. 169) | html | pdf |
    - 1.6.4.16. Dispersion (p. 169) | html | pdf |
  - 1.6.5. Optical rotation (pp. 169-175) | html | pdf |
    - 1.6.5.1. Introduction (pp. 169-170) | html | pdf |
    - 1.6.5.2. The dielectric tensor and spatial dispersion (pp. 170-171) | html | pdf |
    - 1.6.5.3. Symmetry of effective dielectric tensor (p. 171) | html | pdf |
    - 1.6.5.4. Gyration tensor (p. 171) | html | pdf |
    - 1.6.5.5. Optical rotation along the optic axis of a uniaxial crystal (pp. 171-173) | html | pdf |
    - 1.6.5.6. Optical rotation perpendicular to the optic axis of a uniaxial crystal (pp. 173-175) | html | pdf |
  - 1.6.6. Linear electro-optic effect (pp. 175-176) | html | pdf |
    - 1.6.6.1. Primary and secondary effects (p. 175) | html | pdf |
    - 1.6.6.2. Example of LiNbO₃ (pp. 175-176) | html | pdf |
  - 1.6.7. The linear photoelastic effect (pp. 176-179) | html | pdf |
    - 1.6.7.1. Introduction (pp. 176-177) | html | pdf |
    - 1.6.7.2. Spontaneous strain in BaTiO₃ (pp. 177-178) | html | pdf |
    - 1.6.7.3. The acousto-optic effect (pp. 178-179) | html | pdf |
  - 1.6.8. Glossary (p. 179) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.6.3.1. The optical indicatrix (p. 156) | html | pdf |
    - Fig. 1.6.3.2. Positive and negative uniaxial indicatrix (p. 156) | html | pdf |
    - Fig. 1.6.3.3. Biaxial indicatrix, showing the two optic axes and corresponding circular cross sections (p. 157) | html | pdf |
    - Fig. 1.6.4.1. A thin section of a rock containing the minerals aegirine (elongated crystals) and eudyalite (the matrix) viewed in plane-polarized light in two positions at right angles to each other (p. 158) | html | pdf |
    - Fig. 1.6.4.2. Successive sections across the optical path of the microscope (p. 160) | html | pdf |
    - Fig. 1.6.4.3. Plot of retardation, R, versus wavelength, showing how polarization colours are formed (p. 160) | html | pdf |
    - Fig. 1.6.4.4. A quartz wedge between crossed Nicols (p. 161) | html | pdf |
    - Fig. 1.6.4.5. (a) Photomicrograph between crossed polars of a thin section of rock containing large olivine crystals set in a fine-grained matrix (p. 161) | html | pdf |
    - Fig. 1.6.4.6. Polarization colours versus thickness (p. 162) | html | pdf |
    - Fig. 1.6.4.7. Three birefringence images of industrial diamond viewed along [111] taken with the rotating analyser system (p. 164) | html | pdf |
    - Fig. 1.6.4.8. Formation of the interference figure (p. 164) | html | pdf |
    - Fig. 1.6.4.9. (a) Centred uniaxial optic axis figure of a crystal with low birefringence (p. 165) | html | pdf |
    - Fig. 1.6.4.10. (a) Vibration directions of an oblique ray passing through calcite, viewed relative to the indicatrix (p. 165) | html | pdf |
    - Fig. 1.6.4.11. (a) Centred optic axis figure of quartz (uniaxial) (p. 166) | html | pdf |
    - Fig. 1.6.4.12. (a) The Biot–Fresnel construction illustrated on the stereographic projection (p. 166) | html | pdf |
    - Fig. 1.6.4.13. (a) Illustration of the formation of crossed isogyres when the optic axial plane of a biaxial figure lies N–S (p. 166) | html | pdf |
    - Fig. 1.6.4.14. (a) Drawing of biaxial optic axis figures set in the 45° position with the optic axial plane set NW–SE (p. 167) | html | pdf |
    - Fig. 1.6.4.15. (a) Acute bisectrix figure of a biaxial crystal with $[2V \simeq 40]$ ° (p. 167) | html | pdf |
    - Fig. 1.6.5.1. Fresnel's explanation of optical rotation (p. 170) | html | pdf |
    - Fig. 1.6.5.2. Real and imaginary birefringence as a function of wavelength (p. 170) | html | pdf |
    - Fig. 1.6.5.3. The principle of superposition (p. 173) | html | pdf |
    - Fig. 1.6.6.1. (a) Symmetry elements of point group 3m (p. 176) | html | pdf |
    - Fig. 1.6.7.1. (a) Symmetry elements of point group $[{\bar 4}3m]$ (p. 177) | html | pdf |
  - Tables
    - Table 1.6.2.1. Summary of linear and nonlinear optical properties (p. 153) | html | pdf |
    - Table 1.6.3.1. Symmetry constraints on the optical indicatrix (p. 157) | html | pdf |
    - Table 1.6.5.1. Symmetry constraints (see Section 1.1.4.10 ) on the gyration tensor $[g_{ij}]$ (p. 172) | html | pdf |
    - Table 1.6.6.1. Symmetry constraints (see Section 1.1.4.10 ) on the linear electro-optic tensor $[r_{ij}]$ (contracted notation) (p. 174) | html | pdf |
    - Table 1.6.7.1. Symmetry constraints on the linear elasto-optic (strain-optic) tensor $[p_{ij}]$ (contracted notation) (see Section 1.1.4.10.6 ) (p. 178) | html | pdf |
- 1.7. Nonlinear optical properties (pp. 181-222) | html | pdf | chapter contents |
  B. Boulanger and J. Zyss
  - 1.7.1. Introduction (p. 181) | html | pdf |
  - 1.7.2. Origin and symmetry of optical nonlinearities (pp. 181-186) | html | pdf |
    - 1.7.2.1. Induced polarization and susceptibility (pp. 181-184) | html | pdf |
      - 1.7.2.1.1. Linear and nonlinear responses  (p. 182) | html | pdf |
        1.7.2.1.1.1. Linear response  (p. 182) | html | pdf |
        1.7.2.1.1.2. Quadratic response  (p. 182) | html | pdf |
        1.7.2.1.1.3. Higher-order response  (p. 182) | html | pdf |
      - 1.7.2.1.2. Linear and nonlinear susceptibilities  (pp. 182-183) | html | pdf |
        1.7.2.1.2.1. Linear susceptibility  (p. 183) | html | pdf |
        1.7.2.1.2.2. Second-order susceptibility  (p. 183) | html | pdf |
        1.7.2.1.2.3. nth-order susceptibility  (p. 183) | html | pdf |
      - 1.7.2.1.3. Superposition of monochromatic waves (p. 183) | html | pdf |
      - 1.7.2.1.4. Conventions for nonlinear susceptibilities  (pp. 183-184) | html | pdf |
        1.7.2.1.4.1. Classical convention  (pp. 183-184) | html | pdf |
        1.7.2.1.4.2. Convention used in this chapter  (p. 184) | html | pdf |
    - 1.7.2.2. Symmetry properties (pp. 184-186) | html | pdf |
      - 1.7.2.2.1. Intrinsic permutation symmetry  (pp. 184-185) | html | pdf |
        1.7.2.2.1.1. ABDP and Kleinman symmetries  (pp. 184-185) | html | pdf |
        1.7.2.2.1.2. Manley–Rowe relations  (p. 185) | html | pdf |
        1.7.2.2.1.3. Contracted notation for susceptibility tensors  (p. 185) | html | pdf |
      - 1.7.2.2.2. Implications of spatial symmetry on the susceptibility tensors (pp. 185-186) | html | pdf |
  - 1.7.3. Propagation phenomena (pp. 186-215) | html | pdf |
    - 1.7.3.1. Crystalline linear optical properties (pp. 186-190) | html | pdf |
      - 1.7.3.1.1. Index surface and electric field vectors (pp. 186-188) | html | pdf |
      - 1.7.3.1.2. Isotropic class (p. 188) | html | pdf |
      - 1.7.3.1.3. Uniaxial class (pp. 188-189) | html | pdf |
      - 1.7.3.1.4. Biaxial class  (pp. 189-190) | html | pdf |
        1.7.3.1.4.1. Propagation in the principal planes  (pp. 189-190) | html | pdf |
        1.7.3.1.4.2. Propagation out of the principal planes  (p. 190) | html | pdf |
    - 1.7.3.2. Equations of propagation of three-wave and four-wave interactions (pp. 190-199) | html | pdf |
      - 1.7.3.2.1. Coupled electric fields amplitudes equations (pp. 190-191) | html | pdf |
      - 1.7.3.2.2. Phase matching  (pp. 191-195) | html | pdf |
        1.7.3.2.2.1. Cubic crystals  (p. 192) | html | pdf |
        1.7.3.2.2.2. Uniaxial crystals  (p. 192) | html | pdf |
        1.7.3.2.2.3. Biaxial crystals  (pp. 192-195) | html | pdf |
      - 1.7.3.2.3. Quasi phase matching (pp. 195-196) | html | pdf |
      - 1.7.3.2.4. Effective coefficient and field tensor  (pp. 196-199) | html | pdf |
        1.7.3.2.4.1. Definitions and symmetry properties  (pp. 196-197) | html | pdf |
        1.7.3.2.4.2. Uniaxial class  (pp. 197-199) | html | pdf |
        1.7.3.2.4.3. Biaxial class  (p. 199) | html | pdf |
    - 1.7.3.3. Integration of the propagation equations (pp. 199-215) | html | pdf |
      - 1.7.3.3.1. Spatial and temporal profiles (pp. 199-200) | html | pdf |
      - 1.7.3.3.2. Second harmonic generation (SHG)  (pp. 200-209) | html | pdf |
        1.7.3.3.2.1. Non-resonant SHG with undepleted pump in the parallel-beam limit with a Gaussian transverse profile  (pp. 200-205) | html | pdf |
        1.7.3.3.2.2. Non-resonant SHG with undepleted pump and transverse and longitudinal Gaussian beams  (pp. 205-206) | html | pdf |
        1.7.3.3.2.3. Non-resonant SHG with depleted pump in the parallel-beam limit  (pp. 206-208) | html | pdf |
        1.7.3.3.2.4. Resonant SHG  (pp. 208-209) | html | pdf |
      - 1.7.3.3.3. Third harmonic generation (THG)  (pp. 209-210) | html | pdf |
        1.7.3.3.3.1. SHG ( $[\omega+\omega=2\omega]$ ) and SFG ( $[\omega+2\omega=3\omega]$ ) in different crystals  (pp. 209-210) | html | pdf |
        1.7.3.3.3.2. SHG ( $[\omega+\omega=2\omega]$ ) and SFG ( $[\omega+2\omega=3\omega]$ ) in the same crystal  (p. 210) | html | pdf |
        1.7.3.3.3.3. Direct THG ( $[\omega+\omega+\omega=3\omega]$ )  (p. 210) | html | pdf |
      - 1.7.3.3.4. Sum-frequency generation (SFG)  (pp. 210-211) | html | pdf |
        1.7.3.3.4.1. SFG ( $[\omega_1+\omega_2=\omega_3]$ ) with undepletion at $[\omega_1]$ and $[\omega_2]$   (p. 211) | html | pdf |
        1.7.3.3.4.2. SFG ( $[\omega_s+\omega_p=\omega_i]$ ) with undepletion at $[\omega_p]$   (p. 211) | html | pdf |
      - 1.7.3.3.5. Difference-frequency generation (DFG)  (pp. 211-215) | html | pdf |
        1.7.3.3.5.1. DFG ( $[\omega_p-\omega_s=\omega_i]$ ) with undepletion at $[\omega_p]$ and $[\omega_s]$   (p. 211) | html | pdf |
        1.7.3.3.5.2. DFG ( $[\omega_s-\omega_p=\omega_i]$ ) with undepletion at $[\omega_p]$   (p. 211) | html | pdf |
        1.7.3.3.5.3. DFG ( $[\omega_p-\omega_s=\omega_i]$ ) with undepletion at $[\omega_p]$ – optical parametric amplification (OPA), optical parametric oscillation (OPO)  (pp. 211-215) | html | pdf |
  - 1.7.4. Determination of basic nonlinear parameters (pp. 215-217) | html | pdf |
    - 1.7.4.1. Phase-matching directions and associated acceptance bandwidths (p. 215) | html | pdf |
    - 1.7.4.2. Nonlinear coefficients (pp. 215-217) | html | pdf |
      - 1.7.4.2.1. Non-phase-matched interaction method (pp. 215-217) | html | pdf |
      - 1.7.4.2.2. Phase-matched interaction method (p. 217) | html | pdf |
  - 1.7.5. The main nonlinear crystals (pp. 217-219) | html | pdf |
  - 1.7.6. Glossary (p. 219) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.7.3.1. Field vectors of a plane wave propagating in an anisotropic medium (p. 186) | html | pdf |
    - Fig. 1.7.3.2. Index surfaces of the negative and positive uniaxial classes (p. 189) | html | pdf |
    - Fig. 1.7.3.3. Index surfaces of the negative and positive biaxial classes (p. 189) | html | pdf |
    - Fig. 1.7.3.4. Index surface sections in a plane containing the optic axis z of a negative uniaxial crystal (p. 192) | html | pdf |
    - Fig. 1.7.3.5. Stereographic projection on the optical frame of the possible loci of phase-matching directions in the principal planes of a biaxial crystal (p. 196) | html | pdf |
    - Fig. 1.7.3.6. Schematic configurations for second harmonic generation (p. 199) | html | pdf |
    - Fig. 1.7.3.7. Spatial growth evolution of second harmonic conversion efficiency (p. 201) | html | pdf |
    - Fig. 1.7.3.8. Conversion efficiency evolution as a function of ξ for a given crystal length (p. 201) | html | pdf |
    - Fig. 1.7.3.9. Beam separation in the particular case of type-II (oeo) SHG out of the xy plane of a positive uniaxial crystal or in the xz and yz planes of a positive biaxial crystal (p. 204) | html | pdf |
    - Fig. 1.7.3.10. Twin-crystal device allowing walk-off compensation for a direction of propagation θ_PM in the yz plane of a positive uniaxial crystal (p. 204) | html | pdf |
    - Fig. 1.7.3.11. Comparison between (a) collinear and (b) special non-collinear phase matching for (oeo) type-II SHG (p. 205) | html | pdf |
    - Fig. 1.7.3.12. Position f_opt of the beam waist for different values of walk-off angles and , leading to an optimum SHG conversion efficiency (p. 206) | html | pdf |
    - Fig. 1.7.3.13. Optimum walk-off function as a function of for various values of $[B=(1/2)\rho\{[(k_o^\omega+k_e^\omega)/2]L\}^{1/2}]$ (p. 206) | html | pdf |
    - Fig. 1.7.3.14. Type-I and -II conversion efficiencies calculated as a function of for different typical walk-off angles ρ (p. 207) | html | pdf |
    - Fig. 1.7.3.15. Schematic SHG conversion efficiency for different situations of pump depletion and dephasing (p. 208) | html | pdf |
    - Fig. 1.7.3.16. Configurations for third harmonic generation (p. 209) | html | pdf |
    - Fig. 1.7.3.17. Frequency up-conversion process $[\omega_1+\omega_2=\omega_3]$ (p. 210) | html | pdf |
    - Fig. 1.7.3.18. Schematic OPO configurations (p. 212) | html | pdf |
    - Fig. 1.7.3.19. Calculated angular tuning curves (p. 214) | html | pdf |
    - Fig. 1.7.3.20. Calculated pump wavelength tuning curve (p. 214) | html | pdf |
    - Fig. 1.7.4.1. (a) The Maker-fringes technique; (b) the wedge-fringes technique (p. 217) | html | pdf |
  - Tables
    - Table 1.7.2.1. The most common nonlinear effects and the corresponding susceptibility tensors in the frequency domain (p. 184) | html | pdf |
    - Table 1.7.2.2. Nonzero χ⁽²⁾ coefficients and equalities between them in the general case (p. 185) | html | pdf |
    - Table 1.7.2.3. Nonzero χ⁽²⁾ coefficients and equalities between them under the Kleinman symmetry assumption (p. 186) | html | pdf |
    - Table 1.7.2.4. Nonzero χ⁽³⁾ coefficients and equalities between them in the general case (p. 187) | html | pdf |
    - Table 1.7.2.5. Nonzero χ⁽³⁾ coefficients and equalities between them under the Kleinman symmetry assumption (p. 188) | html | pdf |
    - Table 1.7.3.1. Correspondence between the phase-matching relations, the configurations of polarization and the types according to the sum- and difference-frequency generation processes SFG ( $[\omega_3=\omega_1+\omega_2]$ ), DFG ( $[\omega_1=\omega_3-\omega_2]$ ) and DFG ( $[\omega_2=\omega_3-\omega_1]$ ) (p. 191) | html | pdf |
    - Table 1.7.3.2. Correspondence between the phase-matching relations, the configurations of polarization and the types according to SFG ( $[\omega_4=\omega_1+\omega_2+\omega_3]$ ), DFG ( $[\omega_1=\omega_4-\omega_2-\omega_3]$ ), DFG ( $[\omega_2=\omega_4-\omega_1-\omega_3]$ ) and DFG ( $[\omega_3=\omega_4-\omega_1-\omega_2]$ ) (Boulanger et al., 1993) (p. 192) | html | pdf |
    - Table 1.7.3.3. Classes of refractive-index inequalities for collinear phase matching of three-wave interactions in positive and negative uniaxial crystals (p. 193) | html | pdf |
    - Table 1.7.3.4. Classes of refractive-index inequalities for collinear phase matching of four-wave interactions in positive () and negative () uniaxial crystals with $[(n_{b4}/\lambda_4)\,\lt\,(n_{a1}/\lambda_1)+(n_{a2}/\lambda_2)+(n_{a3}/\lambda_3)]$ (p. 193) | html | pdf |
    - Table 1.7.3.5. Refractive-index conditions that determine collinear phase-matching loci in the principal planes of positive and negative biaxial crystals for three-wave SFG (p. 194) | html | pdf |
    - Table 1.7.3.6. Refractive-index conditions that determine collinear phase-matching loci in the principal planes of positive and negative biaxial crystals for four-wave SFG (pp. 195-196) | html | pdf |
    - Table 1.7.3.7. Matrix representations of the (oee) and (eoo) field tensors of the uniaxial class and of the biaxial class in the principal planes xz and yz, with $[\omega_1\ne \omega_2]$ (Boulanger & Marnier, 1991) (p. 198) | html | pdf |
    - Table 1.7.3.8. Matrix representations of the (oeee), (eooo) and (ooee) field tensors of the uniaxial class and of the biaxial class in the principal planes xz and yz, with $[\omega_1\ne\omega_2\ne\omega_3]$ (Boulanger et al., 1993) (p. 198) | html | pdf |
    - Table 1.7.3.9. Field-tensor components specifically nil in the principal planes of uniaxial and biaxial crystals for three-wave and four-wave interactions (p. 199) | html | pdf |
    - Table 1.7.5.1. Mineral nonlinear crystals (pp. 216-217) | html | pdf |
    - Table 1.7.5.2. Organic and organo-mineral crystals (pp. 218-219) | html | pdf |
- 1.8. Transport properties (pp. 223-230) | html | pdf | chapter contents |
  G. D. Mahan
  - 1.8.1. Introduction (p. 223) | html | pdf |
  - 1.8.2. Macroscopic equations (p. 223) | html | pdf |
  - 1.8.3. Electrical resistivity (pp. 223-227) | html | pdf |
    - 1.8.3.1. Properties of the electrical resistivity (pp. 223-225) | html | pdf |
    - 1.8.3.2. Metal alloys (p. 225) | html | pdf |
    - 1.8.3.3. Semiconductors (pp. 225-226) | html | pdf |
    - 1.8.3.4. The Hall effect (pp. 226-227) | html | pdf |
    - 1.8.3.5. Insulators (p. 227) | html | pdf |
    - 1.8.3.6. Ionic conductors (p. 227) | html | pdf |
  - 1.8.4. Thermal conductivity (pp. 227-229) | html | pdf |
    - 1.8.4.1. Introduction (p. 227) | html | pdf |
    - 1.8.4.2. Boundary scattering (p. 227) | html | pdf |
    - 1.8.4.3. Impurity scattering (p. 227) | html | pdf |
    - 1.8.4.4. Isotope scattering (p. 228) | html | pdf |
    - 1.8.4.5. Alloy scattering (p. 228) | html | pdf |
    - 1.8.4.6. Anharmonic interactions (p. 228) | html | pdf |
    - 1.8.4.7. Thermal conductivity of metals (pp. 228-229) | html | pdf |
  - 1.8.5. Seebeck coefficient (pp. 229-230) | html | pdf |
  - 1.8.6. Glossary (p. 230) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.8.3.1. The temperature dependence of the intrinsic electrical resistivity of sodium at constant density (p. 224) | html | pdf |
    - Fig. 1.8.3.2. The temperature coefficient of resistance versus resistivity for alloys according to Mooij (1973) (p. 225) | html | pdf |
    - Fig. 1.8.3.3. The intrinsic mobility of electrons in silicon (p. 225) | html | pdf |
    - Fig. 1.8.5.1. The Seebeck coefficient in units of for $[\Sigma(\varepsilon)]$ containing a Lorentzian peak (p. 229) | html | pdf |
- 1.9. Atomic displacement parameters (pp. 231-245) | html | pdf | chapter contents |
  W. F. Kuhs
  - 1.9.1. Introduction (p. 231) | html | pdf |
  - 1.9.2. The atomic displacement parameters (ADPs) (pp. 231-235) | html | pdf |
    - 1.9.2.1. Tensorial properties of (quasi)moments and cumulants (p. 232) | html | pdf |
    - 1.9.2.2. Contraction, expansion and invariants of atomic displacement tensors (pp. 232-235) | html | pdf |
  - 1.9.3. Site-symmetry restrictions (p. 235) | html | pdf |
    - 1.9.3.1. Calculation procedures (p. 235) | html | pdf |
    - 1.9.3.2. Key to tables (p. 235) | html | pdf |
  - 1.9.4. Graphical representation (pp. 235-245) | html | pdf |
    - 1.9.4.1. Representation surfaces of second-order ADTs (pp. 235-242) | html | pdf |
    - 1.9.4.2. Higher-order representations (pp. 242-245) | html | pdf |
  - 1.9.5. Glossary (p. 245) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.9.4.1. A selection of graphical representations of density modulations due to higher-order terms in the Gram–Charlier series expansion of a Gaussian atomic probability density function (pp. 243-244) | html | pdf |
  - Tables
    - Table 1.9.3.1. Site-symmetry table giving key to Tables 1.9.3.2 to 1.9.3.6 for restrictions on the symmetry of various thermal-motion tensors (pp. 233-234) | html | pdf |
    - Table 1.9.3.2. Symmetry restrictions on coefficients in second-order tensors (p. 235) | html | pdf |
    - Table 1.9.3.3. Symmetry restrictions on coefficients in third-rank symmetric polar tensors (p. 236) | html | pdf |
    - Table 1.9.3.4. Symmetry restrictions on coefficients in fourth-rank symmetric polar tensors (pp. 237-238) | html | pdf |
    - Table 1.9.3.5. Symmetry restrictions on coefficients in fifth-rank symmetric polar tensors (pp. 238-240) | html | pdf |
    - Table 1.9.3.6. Symmetry restrictions on coefficients in sixth-rank symmetric polar tensors (pp. 241-242) | html | pdf |
- 1.10. Tensors in quasiperiodic structures (pp. 246-270) | html | pdf | chapter contents |
  T. Janssen
  - 1.10.1. Quasiperiodic structures (pp. 246-248) | html | pdf |
    - 1.10.1.1. Introduction (p. 246) | html | pdf |
    - 1.10.1.2. Types of quasiperiodic crystals (pp. 246-247) | html | pdf |
    - 1.10.1.3. Embedding in superspace (pp. 247-248) | html | pdf |
  - 1.10.2. Symmetry (pp. 248-252) | html | pdf |
    - 1.10.2.1. Symmetry transformations (pp. 248-249) | html | pdf |
    - 1.10.2.2. Point groups (pp. 249-250) | html | pdf |
    - 1.10.2.3. Superspace groups (p. 250) | html | pdf |
    - 1.10.2.4. Magnetic superspace groups (pp. 250-251) | html | pdf |
    - 1.10.2.5. Pseudotensors (pp. 251-252) | html | pdf |
  - 1.10.3. Action of the symmetry group (pp. 252-253) | html | pdf |
    - 1.10.3.1. Action of superspace groups (p. 252) | html | pdf |
    - 1.10.3.2. Compensating gauge transformations (p. 252) | html | pdf |
    - 1.10.3.3. Irreducible representations of three-dimensional space groups (pp. 252-253) | html | pdf |
  - 1.10.4. Tensors (pp. 253-262) | html | pdf |
    - 1.10.4.1. Tensors in higher-dimensional spaces (p. 253) | html | pdf |
    - 1.10.4.2. Tensors in superspace (p. 254) | html | pdf |
    - 1.10.4.3. Inhomogeneous tensors (pp. 254-255) | html | pdf |
    - 1.10.4.4. Irreducible representations (p. 255) | html | pdf |
    - 1.10.4.5. Determining the number of independent tensor elements (pp. 255-257) | html | pdf |
      - 1.10.4.5.1. Piezoelectric tensor (pp. 255-256) | html | pdf |
      - 1.10.4.5.2. Elasticity tensor (p. 256) | html | pdf |
      - 1.10.4.5.3. Electric field gradient tensor (pp. 256-257) | html | pdf |
    - 1.10.4.6. Determining the independent tensor elements (pp. 257-262) | html | pdf |
      - 1.10.4.6.1. Metric tensor for an octagonal three-dimensional quasicrystal (p. 257) | html | pdf |
      - 1.10.4.6.2. EFG tensor for Pcmn (p. 257) | html | pdf |
      - 1.10.4.6.3. Elasticity tensor for a two-dimensional octagonal quasicrystal (pp. 257-258) | html | pdf |
      - 1.10.4.6.4. Piezoelectric tensor for a three-dimensional octagonal quasicrystal (pp. 258-259) | html | pdf |
      - 1.10.4.6.5. Elasticity tensor for an icosahedral quasicrystal (p. 259) | html | pdf |
      - 1.10.4.6.6. Coupling to magnetism (pp. 259-262) | html | pdf |
  - 1.10.5. Tables (pp. 262-268) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 1.10.2.1. Allowable three-dimensional point groups for systems up to rank six (p. 251) | html | pdf |
    - Table 1.10.4.1. Characters of the point group $[10\,mm(10^3\,mm)]$ for representations relevant for elasticity (p. 256) | html | pdf |
    - Table 1.10.4.2. Sign change of $[\partial_iE_j]$ under the generators A, B, C (p. 257) | html | pdf |
    - Table 1.10.4.3. Elastic constants for icosahedral quasicrystals (p. 260) | html | pdf |
    - Table 1.10.5.1. Character tables of some point groups for quasicrystals (pp. 260-261) | html | pdf |
    - Table 1.10.5.2. Matrices of the irreducible representations of dimension $[d \geq 2]$ corresponding to the irreps of Table 1.10.5.1 (pp. 262-267) | html | pdf |
    - Table 1.10.5.3. The representation matrices for $[\Gamma_3]$ (p. 268) | html | pdf |
    - Table 1.10.5.4. Number of free parameters for some tensors and their symmetry groups (p. 268) | html | pdf |
- 1.11. Tensorial properties of local crystal susceptibilities (pp. 269-283) | html | pdf | chapter contents |
  V. E. Dmitrienko, A. Kirfel and E. N. Ovchinnikova
  - 1.11.1. Introduction (pp. 269-270) | html | pdf |
  - 1.11.2. Symmetry restrictions on local tensorial susceptibility and forbidden reflections (pp. 270-272) | html | pdf |
    - 1.11.2.1. General symmetry restrictions (p. 270) | html | pdf |
    - 1.11.2.2. Tensorial structure factors and forbidden reflections (pp. 270-271) | html | pdf |
      - 1.11.2.2.1. Glide-plane forbidden reflections (pp. 270-271) | html | pdf |
      - 1.11.2.2.2. Screw-axis forbidden reflections (p. 271) | html | pdf |
    - 1.11.2.3. Local tensorial susceptibility of cubic crystals (pp. 271-272) | html | pdf |
  - 1.11.3. Polarization properties and azimuthal dependence (pp. 272-274) | html | pdf |
  - 1.11.4. Physical mechanisms for the anisotropy of atomic X-ray susceptibility (p. 274) | html | pdf |
  - 1.11.5. Non-resonant magnetic scattering (p. 275) | html | pdf |
  - 1.11.6. Resonant atomic factors: multipole expansion (pp. 275-280) | html | pdf |
    - 1.11.6.1. Tensor atomic factors: internal symmetry (pp. 275-276) | html | pdf |
    - 1.11.6.2. Tensor atomic factors (non-magnetic case) (pp. 276-277) | html | pdf |
    - 1.11.6.3. Hidden internal symmetry of the dipole–quadrupole tensors in resonant atomic factors (pp. 277-278) | html | pdf |
    - 1.11.6.4. Tensor structure factors (p. 278) | html | pdf |
    - 1.11.6.5. Tensor atomic factors (magnetic case) (pp. 278-279) | html | pdf |
    - 1.11.6.6. Tensor atomic factors (spherical tensor representation) (pp. 279-280) | html | pdf |
  - 1.11.7. Glossary (p. 281) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 1.11.2.1. The indices $[\ell]$ of the screw-axis/glide-plane forbidden reflections ( $[n = 0, \pm 1, \pm 2,\ldots]$ ) and independent components of their tensorial structure factors $[F^{{\bf H}}_{jk}]$ (p. 271) | html | pdf |
    - Table 1.11.2.2. The indices of the forbidden reflections and corresponding tensors of structure factors $[F_{jk}(hk\ell)]$ for the cubic space groups ( $[n = 0, \pm 1, \pm 2,\ldots]$ ) (p. 272) | html | pdf |
    - Table 1.11.6.1. Coefficients $[\gamma]$ corresponding to various kinds of tensor symmetry with respect to space inversion $[{\bar 1}]$ , rotations , and time reversal $[1^{\prime}]$ (p. 275) | html | pdf |
    - Table 1.11.6.2. Identification of properties under time inversion and space inversion of tensors associated with multipole expansion (p. 280) | html | pdf |

Symmetry aspects of excitations
- 2.1. Phonons (pp. 286-313) | html | pdf | chapter contents |
  G. Eckold
  - 2.1.1. Introduction (p. 286) | html | pdf |
  - 2.1.2. Fundamentals of lattice dynamics in the harmonic approximation (pp. 286-294) | html | pdf |
    - 2.1.2.1. Hamiltonian and equations of motion (pp. 286-287) | html | pdf |
    - 2.1.2.2. Stability conditions (p. 287) | html | pdf |
    - 2.1.2.3. The dynamical matrix (pp. 287-288) | html | pdf |
    - 2.1.2.4. Eigenvalues and phonon dispersion, acoustic modes (pp. 288-290) | html | pdf |
    - 2.1.2.5. Eigenvectors and normal coordinates (p. 290) | html | pdf |
    - 2.1.2.6. Amplitudes of lattice vibrations (pp. 290-291) | html | pdf |
    - 2.1.2.7. Density of states and the lattice heat capacity (pp. 291-292) | html | pdf |
    - 2.1.2.8. Thermal expansion, compressibility and Grüneisen parameters (pp. 292-294) | html | pdf |
  - 2.1.3. Symmetry of lattice vibrations (pp. 294-311) | html | pdf |
    - 2.1.3.1. Symmetry constraints for the dynamical matrix (pp. 294-301) | html | pdf |
      - 2.1.3.1.1. Example (pp. 297-301) | html | pdf |
    - 2.1.3.2. Symmetry of dispersion planes (p. 301) | html | pdf |
    - 2.1.3.3. Symmetry properties of eigenvectors (pp. 301-303) | html | pdf |
      - 2.1.3.3.1. Example (p. 303) | html | pdf |
    - 2.1.3.4. Symmetry coordinates (pp. 303-306) | html | pdf |
      - 2.1.3.4.1. Example (pp. 304-306) | html | pdf |
    - 2.1.3.5. Degeneracy of lattice vibrations (pp. 306-309) | html | pdf |
      - 2.1.3.5.1. Accidental degeneracy (p. 306) | html | pdf |
      - 2.1.3.5.2. Time-reversal degeneracy (pp. 306-308) | html | pdf |
      - 2.1.3.5.3. Example (pp. 308-309) | html | pdf |
    - 2.1.3.6. Compatibility relations (pp. 309-310) | html | pdf |
      - 2.1.3.6.1. Example (pp. 309-310) | html | pdf |
    - 2.1.3.7. Optical selection rules (pp. 310-311) | html | pdf |
      - 2.1.3.7.1. Example (p. 311) | html | pdf |
  - 2.1.4. Conclusion (p. 311) | html | pdf |
  - 2.1.5. Glossary (pp. 311-312) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.1.2.1. Definition of position vectors (p. 286) | html | pdf |
    - Fig. 2.1.2.2. Definition of the force acting on atom ( $[\kappa l]$ ) when atom ( $[\kappa' l']$ ) is displaced by $[{\bf u}_{\kappa'l'}]$ (p. 287) | html | pdf |
    - Fig. 2.1.2.3. Phonon dispersion of b.c.c. hafnium for wavevectors along the main symmetry directions of the cubic structure (p. 288) | html | pdf |
    - Fig. 2.1.2.4. Phonon dispersion of Nd₂CuO₄ along the main symmetry directions of the tetragonal structure (p. 289) | html | pdf |
    - Fig. 2.1.2.5. Low-frequency part of the phonon dispersion of deuterated naphthalene at 6 K (p. 289) | html | pdf |
    - Fig. 2.1.2.6. Energy levels of a quantum-mechanical harmonic oscillator (p. 291) | html | pdf |
    - Fig. 2.1.2.7. Phonon dispersion and density of states for GaAs (p. 291) | html | pdf |
    - Fig. 2.1.2.8. Schematic representation of the true phonon density of states (solid line) along with the Debye approximation (dotted line) (p. 292) | html | pdf |
    - Fig. 2.1.2.9. Temperature dependence of the heat capacity at constant volume according to the Debye model (p. 292) | html | pdf |
    - Fig. 2.1.3.1. Transformation of atomic displacements by a symmetry operation (p. 295) | html | pdf |
    - Fig. 2.1.3.2. Relation between interaction of symmetry-related atoms (p. 295) | html | pdf |
    - Fig. 2.1.3.3. Symmetry-related atoms in different primitive cells (p. 296) | html | pdf |
    - Fig. 2.1.3.4. Projection along the tetragonal z axis of the example structure given in Table 2.1.3.1 (p. 298) | html | pdf |
    - Fig. 2.1.3.5. Symmetry of the dispersion surface (p. 301) | html | pdf |
    - Fig. 2.1.3.6. The dispersion relation is an even function of q (p. 301) | html | pdf |
    - Fig. 2.1.3.7. Matrix of symmetry coordinates at $[{\bf q}={\bf 0}]$ for the example structure given in Fig. 2.1.3.4 and Table 2.1.3.1 (p. 307) | html | pdf |
    - Fig. 2.1.3.8. (a) Accidental degeneracy of phonons with different symmetry (p. 307) | html | pdf |
    - Fig. 2.1.3.9. Low-frequency part of the phonon dispersion of KLiSO₄ at room temperature (space group P6₃) (p. 309) | html | pdf |
    - Fig. 2.1.3.10. Illustration of the compatibility relations for phonons in a tetragonal crystal with space group for wavevectors along [ $[\xi 00 ]$ ] (p. 310) | html | pdf |
    - Fig. 2.1.3.11. Principle of infrared absorption (p. 310) | html | pdf |
    - Fig. 2.1.3.12. Principle of Raman spectroscopy (p. 310) | html | pdf |
  - Tables
    - Table 2.1.3.1. Example structure in space group (p. 298) | html | pdf |
    - Table 2.1.3.2. Atom transformation table (p. 298) | html | pdf |
    - Table 2.1.3.3. Character table of the point group (p. 303) | html | pdf |
    - Table 2.1.3.4. Irreducible representations of the point group (p. 308) | html | pdf |
    - Table 2.1.3.5. Irreducible representations of the space group for $[{\bf q}={\bf 0}]$ (the $[\Gamma]$ point) (p. 309) | html | pdf |
    - Table 2.1.3.6. Irreducible representations of the space group for $[{\bf q}={\bf c}^*/2]$ (the A point) (p. 309) | html | pdf |
    - Table 2.1.3.7. Irreducible representations of the space group for $[{\bf q}={\bf 0}]$ (the $[\Gamma]$ point) (p. 310) | html | pdf |
    - Table 2.1.3.8. Character table of the space group for $[{\bf q}={\bf 0}]$ (the $[\Gamma]$ point) (p. 311) | html | pdf |
- 2.2. Electrons (pp. 314-333) | html | pdf | chapter contents |
  K. Schwarz
  - 2.2.1. Introduction (p. 314) | html | pdf |
  - 2.2.2. The lattice (p. 314) | html | pdf |
    - 2.2.2.1. The direct lattice and the Wigner–Seitz cell (p. 314) | html | pdf |
    - 2.2.2.2. The reciprocal lattice and the Brillouin zone (p. 314) | html | pdf |
  - 2.2.3. Symmetry operators (pp. 314-315) | html | pdf |
    - 2.2.3.1. Transformation of functions (pp. 314-315) | html | pdf |
    - 2.2.3.2. Transformation of operators (p. 315) | html | pdf |
    - 2.2.3.3. The Seitz operators (p. 315) | html | pdf |
    - 2.2.3.4. The important groups and their first classification (p. 315) | html | pdf |
  - 2.2.4. The Bloch theorem (pp. 315-316) | html | pdf |
    - 2.2.4.1. A simple quantum-mechanical derivation (pp. 315-316) | html | pdf |
    - 2.2.4.2. Periodic boundary conditions (p. 316) | html | pdf |
    - 2.2.4.3. A simple group-theoretical approach (p. 316) | html | pdf |
  - 2.2.5. The free-electron (Sommerfeld) model (p. 317) | html | pdf |
  - 2.2.6. Space-group symmetry (pp. 317-318) | html | pdf |
    - 2.2.6.1. Representations and bases of the space group (pp. 317-318) | html | pdf |
    - 2.2.6.2. Energy bands (p. 318) | html | pdf |
  - 2.2.7. The vector and the Brillouin zone (p. 318) | html | pdf |
    - 2.2.7.1. Various aspects of the $[{\bf k}]$ vector (p. 318) | html | pdf |
    - 2.2.7.2. The Brillouin zone (BZ) (p. 318) | html | pdf |
    - 2.2.7.3. The symmetry of the Brillouin zone (p. 318) | html | pdf |
  - 2.2.8. Bloch functions (p. 319) | html | pdf |
  - 2.2.9. Quantum-mechanical treatment (pp. 319-320) | html | pdf |
    - 2.2.9.1. Exchange and correlation treatment (p. 319) | html | pdf |
    - 2.2.9.2. The choice of basis sets and wavefunctions (p. 319) | html | pdf |
    - 2.2.9.3. The form of the potential (p. 319) | html | pdf |
    - 2.2.9.4. Relativistic effects (p. 320) | html | pdf |
  - 2.2.10. Density functional theory (pp. 320-321) | html | pdf |
  - 2.2.11. Band-theory methods (pp. 321-323) | html | pdf |
    - 2.2.11.1. LCAO (linear combination of atomic orbitals) (p. 321) | html | pdf |
    - 2.2.11.2. TB (tight binding) (pp. 321-322) | html | pdf |
    - 2.2.11.3. The pseudo-potential schemes (p. 322) | html | pdf |
    - 2.2.11.4. APW (augmented plane wave) and LAPW methods (p. 322) | html | pdf |
    - 2.2.11.5. KKR (Korringa–Kohn–Rostocker) method (p. 322) | html | pdf |
    - 2.2.11.6. LMTO (linear combination of muffin-tin orbitals) method (p. 322) | html | pdf |
    - 2.2.11.7. CP (Car–Parrinello) method (p. 322) | html | pdf |
    - 2.2.11.8. Order N schemes (pp. 322-323) | html | pdf |
  - 2.2.12. The linearized augmented plane wave method (pp. 323-324) | html | pdf |
  - 2.2.13. The local coordinate system (pp. 324-325) | html | pdf |
    - 2.2.13.1. Crystal harmonics (pp. 324-325) | html | pdf |
    - 2.2.13.2. Interpretation for bonding (p. 325) | html | pdf |
  - 2.2.14. Characterization of Bloch states (pp. 325-327) | html | pdf |
    - 2.2.14.1. Characterization by group theory (p. 325) | html | pdf |
    - 2.2.14.2. Energy regions (p. 325) | html | pdf |
    - 2.2.14.3. Decomposition according to wavefunctions (pp. 325-326) | html | pdf |
    - 2.2.14.4. Localized versus itinerant electrons (p. 326) | html | pdf |
    - 2.2.14.5. Spin polarization (p. 326) | html | pdf |
    - 2.2.14.6. The density of states (DOS) (pp. 326-327) | html | pdf |
  - 2.2.15. Electric field gradient tensor (pp. 327-330) | html | pdf |
    - 2.2.15.1. Introduction (p. 327) | html | pdf |
    - 2.2.15.2. EFG conversion formulas (pp. 327-328) | html | pdf |
    - 2.2.15.3. Theoretical approach (pp. 328-330) | html | pdf |
  - 2.2.16. Examples (pp. 330-332) | html | pdf |
    - 2.2.16.1. F.c.c. copper (pp. 330-331) | html | pdf |
    - 2.2.16.2. The rutile TiO₂ (p. 331) | html | pdf |
    - 2.2.16.3. Core electron spectra (p. 332) | html | pdf |
  - 2.2.17. Conclusion (p. 332) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.2.5.1. Plane waves (p. 317) | html | pdf |
    - Fig. 2.2.7.1. The Brillouin zone (BZ) and the irreducible wedge of the BZ for the f.c.c. direct lattice (p. 318) | html | pdf |
    - Fig. 2.2.12.1. Schematic partitioning of the unit cell into atomic spheres (I) and an interstitial region (II) (p. 323) | html | pdf |
    - Fig. 2.2.14.1. Relativistic radial wavefunctions (large component) of the uranium atom (p. 326) | html | pdf |
    - Fig. 2.2.15.1. Unit cell of the high-temperature superconductor YBa₂Cu₃O₇ with four non-equivalent oxygen sites (p. 329) | html | pdf |
    - Fig. 2.2.16.1. Character of energy bands of f.c.c. copper in the $[\Delta]$ direction (p. 330) | html | pdf |
    - Fig. 2.2.16.2. Decomposition of the Cu d bands into the $[e_{g}]$ and $[t_{2g}]$ manifold (p. 331) | html | pdf |
    - Fig. 2.2.16.3. The local coordinate system in rutile for titanium (small spheres) and oxygen (large spheres) (p. 331) | html | pdf |
    - Fig. 2.2.16.4. Schematic transitions in X-ray emission and absorption spectra (p. 331) | html | pdf |
  - Tables
    - Table 2.2.13.1. Picking rules for the local coordinate axes and the corresponding combinations ( $[\ell mp]$ ) of non-cubic groups taken from Kurki-Suonio (1977) (p. 324) | html | pdf |
    - Table 2.2.13.2. LM combinations of cubic groups as linear cominations of $[y_{\ell mp}]$ 's (given in parentheses) (p. 324) | html | pdf |
    - Table 2.2.15.1. Partial O 2p charges (in electrons) and electric field gradient tensor O EFG (in 10²¹ V m⁻²) for YBa₂Cu₃O₇ (p. 329) | html | pdf |
    - Table 2.2.16.1. $[W_{\ell\ell^{\prime}}]$ factors for X-ray emission spectra showing the $[\Delta\ell=\pm 1]$ selection rule (p. 332) | html | pdf |
- 2.3. Raman scattering (pp. 334-348) | html | pdf | chapter contents |
  I. Gregora
  - 2.3.1. Introduction (p. 334) | html | pdf |
  - 2.3.2. Inelastic light scattering in crystals – basic notions (pp. 334-335) | html | pdf |
    - 2.3.2.1. Kinematics (p. 334) | html | pdf |
    - 2.3.2.2. Cross section (pp. 334-335) | html | pdf |
    - 2.3.2.3. Experimental aspects (p. 335) | html | pdf |
  - 2.3.3. First-order scattering by phonons (pp. 335-342) | html | pdf |
    - 2.3.3.1. First-order scattering cross section and Raman spectral line shapes (p. 336) | html | pdf |
    - 2.3.3.2. Symmetry properties of the scattering cross section (pp. 336-337) | html | pdf |
    - 2.3.3.3. Raman tensor and selection rules at $[{\bf q}\approx 0]$ (pp. 337-339) | html | pdf |
    - 2.3.3.4. Centrosymmetric crystals (pp. 339-341) | html | pdf |
    - 2.3.3.5. Noncentrosymmetric crystals (pp. 341-342) | html | pdf |
    - 2.3.3.6. $[\bf q]$ -dependent terms (p. 342) | html | pdf |
  - 2.3.4. Morphic effects in Raman scattering (pp. 342-345) | html | pdf |
    - 2.3.4.1. General remarks (pp. 342-343) | html | pdf |
    - 2.3.4.2. Electric-field-induced scattering (pp. 343-344) | html | pdf |
    - 2.3.4.3. Raman scattering in a magnetic field (pp. 344-345) | html | pdf |
    - 2.3.4.4. Stress- (strain-) induced Raman scattering (p. 345) | html | pdf |
  - 2.3.5. Spatial-dispersion effects (pp. 345-346) | html | pdf |
  - 2.3.6. Higher-order scattering (pp. 346-347) | html | pdf |
  - 2.3.7. Conclusions (pp. 347-348) | html | pdf |
  - 2.3.8. Glossary (p. 348) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 2.3.3.1. Symmetry of Raman tensors in the 32 crystal classes (pp. 338-340) | html | pdf |
    - Table 2.3.3.2. Raman selection rules in crystals of the class (p. 341) | html | pdf |
    - Table 2.3.3.3. Raman selection rules in crystals of the 4mm class (p. 342) | html | pdf |
    - Table 2.3.4.1. Symmetrized (s) and antisymmetrized (a) sets of trilinear basis functions corresponding to symmetry species of the 4mm class (p. 343) | html | pdf |
    - Table 2.3.6.1. Thermal factors for second-order Raman scattering (p. 347) | html | pdf |
- 2.4. Brillouin scattering (pp. 349-355) | html | pdf | chapter contents |
  R. Vacher and E. Courtens
  - 2.4.1. Introduction (p. 349) | html | pdf |
  - 2.4.2. Elastic waves (pp. 349-350) | html | pdf |
    - 2.4.2.1. Non-piezoelectric media (p. 349) | html | pdf |
    - 2.4.2.2. Piezoelectric media (pp. 349-350) | html | pdf |
  - 2.4.3. Coupling of light with elastic waves (p. 350) | html | pdf |
    - 2.4.3.1. Direct coupling to displacements (p. 350) | html | pdf |
    - 2.4.3.2. Coupling via the electro-optic effect (p. 350) | html | pdf |
  - 2.4.4. Brillouin scattering in crystals (pp. 350-351) | html | pdf |
    - 2.4.4.1. Kinematics (p. 350) | html | pdf |
    - 2.4.4.2. Scattering cross section (pp. 350-351) | html | pdf |
  - 2.4.5. Use of the tables (p. 351) | html | pdf |
  - 2.4.6. Techniques of Brillouin spectroscopy (pp. 351-355) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 2.4.5.1. Definition of Laue classes (p. 351) | html | pdf |
    - Table 2.4.5.2. Cubic Laue classes $[C{_1}]$ and $[C{_2}]$ : longitudinal modes (p. 352) | html | pdf |
    - Table 2.4.5.3. Tetragonal $[T{_1}]$ and hexagonal $[H{_1}]$ Laue classes: longitudinal modes (p. 352) | html | pdf |
    - Table 2.4.5.4. Hexagonal Laue class $[H{_2}]$ : longitudinal modes (p. 352) | html | pdf |
    - Table 2.4.5.5. Tetragonal Laue class $[T{_2}]$ : longitudinal modes (p. 352) | html | pdf |
    - Table 2.4.5.6. Orthorhombic Laue class O: longitudinal modes (p. 352) | html | pdf |
    - Table 2.4.5.7. Trigonal Laue class $[R{_1}]$ : longitudinal modes (p. 352) | html | pdf |
    - Table 2.4.5.8. Trigonal Laue class $[R{_2}]$ : longitudinal modes (p. 352) | html | pdf |
    - Table 2.4.5.9. Cubic Laue classes $[C{_1}]$ and $[C{_2}]$ : transverse modes, backscattering (p. 353) | html | pdf |
    - Table 2.4.5.10. Tetragonal $[T{_1}]$ and hexagonal $[H{_1}]$ Laue classes: transverse modes, backscattering (p. 353) | html | pdf |
    - Table 2.4.5.11. Hexagonal Laue class $[H{_2}]$ : transverse modes, backscattering (p. 353) | html | pdf |
    - Table 2.4.5.12. Tetragonal Laue class $[T{_2}]$ : transverse modes, backscattering (p. 353) | html | pdf |
    - Table 2.4.5.13. Orthorhombic Laue class O: transverse modes, backscattering (p. 353) | html | pdf |
    - Table 2.4.5.14. Trigonal Laue class $[R{_1}]$ : transverse modes, backscattering (p. 353) | html | pdf |
    - Table 2.4.5.15. Trigonal Laue class $[R{_2}]$ : transverse modes, backscattering (p. 353) | html | pdf |
    - Table 2.4.5.16. Cubic Laue classes $[C{_1}]$ and $[C{_2}]$ : transverse modes, right-angle scattering (p. 354) | html | pdf |
    - Table 2.4.5.17. Tetragonal $[T{_1}]$ and hexagonal $[H{_1}]$ Laue classes: transverse modes, right-angle scattering (p. 354) | html | pdf |
    - Table 2.4.5.18. Hexagonal $[H{_2}]$ Laue class: transverse modes, right-angle scattering (p. 354) | html | pdf |
    - Table 2.4.5.19. Tetragonal $[T{_2}]$ Laue class: transverse modes, right-angle scattering (p. 354) | html | pdf |
    - Table 2.4.5.20. Orthorhombic Laue class O: transverse modes, right-angle scattering (p. 354) | html | pdf |
    - Table 2.4.5.21. Trigonal Laue class $[R{_1}]$ : transverse modes, right-angle scattering (p. 355) | html | pdf |
    - Table 2.4.5.22. Trigonal Laue class $[R{_2}]$ : transverse modes, right-angle scattering (p. 355) | html | pdf |
    - Table 2.4.5.23. Particular directions of incident light used in Tables 2.4.5.17 to 2.4.5.22 (p. 355) | html | pdf |

Symmetry aspects of phase transitions, twinning and domain structures
- 3.1. Structural phase transitions (pp. 358-396) | html | pdf | chapter contents |
  J.-C. Tolédano, V. Janovec, V. Kopský, J. F. Scott and P. Boček
  - 3.1.1. Introduction (pp. 358-360) | html | pdf |
    J.-C. Tolédano
  - 3.1.2. Thermodynamics of structural transitions (pp. 360-369) | html | pdf |
    J.-C. Tolédano
    - 3.1.2.1. Introduction (p. 360) | html | pdf |
    - 3.1.2.2. Basic ideas of Landau's theory of phase transitions (pp. 360-364) | html | pdf |
      - 3.1.2.2.1. Description of a prototype example (p. 360) | html | pdf |
      - 3.1.2.2.2. Basic assumptions and strategy (p. 361) | html | pdf |
      - 3.1.2.2.3. Symmetry constraints and form of the free energy (p. 361) | html | pdf |
      - 3.1.2.2.4. Reduction of the number of relevant degrees of freedom: order parameter (pp. 361-362) | html | pdf |
      - 3.1.2.2.5. Stable state below T_c and physical anomalies induced by the transition (pp. 362-363) | html | pdf |
      - 3.1.2.2.6. Symmetry considerations  (pp. 363-364) | html | pdf |
        3.1.2.2.6.1. Order-parameter symmetry  (p. 363) | html | pdf |
        3.1.2.2.6.2. Degeneracy of the low-symmetry phase  (pp. 363-364) | html | pdf |
    - 3.1.2.3. Free-energy models for discontinuous transitions (pp. 364-365) | html | pdf |
    - 3.1.2.4. Generalization of the approach (pp. 365-367) | html | pdf |
      - 3.1.2.4.1. Description of the phase transition (p. 366) | html | pdf |
      - 3.1.2.4.2. Order parameter (pp. 366-367) | html | pdf |
      - 3.1.2.4.3. Stable states and symmetry in the vicinity of (p. 367) | html | pdf |
    - 3.1.2.5. Application to the structural transformation in a real system (pp. 367-369) | html | pdf |
      - 3.1.2.5.1. Nature of the groups and of their irreducible representations (p. 367) | html | pdf |
      - 3.1.2.5.2. The example of gadolinium molybdate, Gd₂(MoO₄)₃  (pp. 367-369) | html | pdf |
        3.1.2.5.2.1. Experimental identification of the order-parameter symmetry  (pp. 367-368) | html | pdf |
        3.1.2.5.2.2. Construction of the free energy and stable states  (pp. 368-369) | html | pdf |
        3.1.2.5.2.3. Macroscopic behaviour of GMO  (p. 369) | html | pdf |
  - 3.1.3. Equitranslational phase transitions. Property tensors at ferroic phase transitions (pp. 370-381) | html | pdf |
    V. Janovec and V. Kopský
    - 3.1.3.1. Equitranslational phase transitions and their order parameters (p. 370) | html | pdf |
    - 3.1.3.2. Property tensors at ferroic phase transitions. Tensor parameters (pp. 370-375) | html | pdf |
    - 3.1.3.3. Tables of equitranslational phase transitions associated with irreducible representations (pp. 375-380) | html | pdf |
      - 3.1.3.3.1. Explanation of Table 3.1.3.1 (pp. 378-380) | html | pdf |
    - 3.1.3.4. Examples (pp. 380-381) | html | pdf |
  - 3.1.4. Example of a table for non-equitranslational phase transitions (p. 381) | html | pdf |
    J.-C. Tolédano
  - 3.1.5. Microscopic aspects of structural phase transitions and soft modes (pp. 381-392) | html | pdf |
    J. F. Scott
    - 3.1.5.1. Introduction (p. 381) | html | pdf |
    - 3.1.5.2. Displacive phase transitions (pp. 381-392) | html | pdf |
      - 3.1.5.2.1. Landau–Devonshire theory (pp. 381-382) | html | pdf |
      - 3.1.5.2.2. Soft modes (pp. 382-383) | html | pdf |
      - 3.1.5.2.3. Strontium titanate, SrTiO₃ (pp. 383-385) | html | pdf |
      - 3.1.5.2.4. Lanthanum aluminate, LaAlO₃ (p. 385) | html | pdf |
      - 3.1.5.2.5. Potassium nitrate, KNO₃ (p. 385) | html | pdf |
      - 3.1.5.2.6. Lanthanum pentaphosphate (pp. 385-386) | html | pdf |
      - 3.1.5.2.7. Barium manganese tetrafluoride (pp. 386-387) | html | pdf |
      - 3.1.5.2.8. Barium sodium niobate (p. 387) | html | pdf |
      - 3.1.5.2.9. Tris-sarcosine calcium chloride (TSCC) (pp. 387-388) | html | pdf |
      - 3.1.5.2.10. Potassium dihydrogen phosphate, KH₂PO₄ (pp. 388-389) | html | pdf |
      - 3.1.5.2.11. Sodium nitrite, NaNO₂ (pp. 389-390) | html | pdf |
      - 3.1.5.2.12. Fast ion conductors (p. 390) | html | pdf |
      - 3.1.5.2.13. High-temperature superconductors (pp. 390-392) | html | pdf |
    - 3.1.5.3. Low-temperature ferroelectric transitions (p. 392) | html | pdf |
  - 3.1.6. Group informatics and tensor calculus (pp. 392-394) | html | pdf |
    V. Kopský and P. Boček
  - 3.1.7. Glossary (p. 394) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 3.1.2.1. Model of a structural transition (p. 360) | html | pdf |
    - Fig. 3.1.2.2. (a) Variation of the free energy as function of the amplitude of the displacement of the central ion in Fig. 3.1.2.1 (p. 360) | html | pdf |
    - Fig. 3.1.2.3. Plots representative of the equations $[\alpha_1(p, T)=0]$ and $[\alpha_2(p, T)=0]$ (p. 362) | html | pdf |
    - Fig. 3.1.2.4. Plots of the Landau free energy as a function of the order parameter, for values of the temperature above or below or coincident with (p. 362) | html | pdf |
    - Fig. 3.1.2.5. (a) Qualitative temperature dependence of the specific heat at a continuous transition (p. 363) | html | pdf |
    - Fig. 3.1.2.6. (a) Plots of the free energy as a function of the order parameter for various temperature values in the framework of the model of a discontinuous transition associated with equation (3.1.2.13) (p. 365) | html | pdf |
    - Fig. 3.1.2.7. Plots of the free energy as a function of the order parameter for various temperatures in the framework of the model of a discontinuous transition associated with equation (3.1.2.16) (p. 365) | html | pdf |
    - Fig. 3.1.2.8. Schematic representation of the displacement associated with the order parameter in a crystal having trigonal (rhombohedral) symmetry (p. 365) | html | pdf |
    - Fig. 3.1.2.9. Rotations/reflections belonging to the point group of gadolinium molybdate (p. 368) | html | pdf |
    - Fig. 3.1.2.10. Temperature dependence of the macroscopic susceptibility (or elastic compliance, $[s_{ij}]$ ) in gadolinium molybdate (p. 369) | html | pdf |
    - Fig. 3.1.3.1. Lattice of subgroups of the group $[m\bar3m]$ (p. 379) | html | pdf |
    - Fig. 3.1.3.2. Lattice of subgroups of the group (p. 379) | html | pdf |
    - Fig. 3.1.5.1. Free energy and order parameter from the Landau–Devonshire theory [equation (3.1.5.1a)] for a continuous second-order ferroelectric phase transition (p. 383) | html | pdf |
    - Fig. 3.1.5.2. Free energy and order parameter from the Landau–Devonshire theory [equation (3.1.5.1a)] for a discontinuous first-order ferroelectric phase transition (p. 383) | html | pdf |
    - Fig. 3.1.5.3. Three-dimensional graph of phase boundaries as functions of temperature T, pressure p and applied electric field E, showing a tricritical point where three continuous phase boundaries intersect (p. 383) | html | pdf |
    - Fig. 3.1.5.4. Structure of strontium titanate above (undisplaced ions) and below (arrows) its anti-ferrodistortive phase transition at ca. 105 K (p. 384) | html | pdf |
    - Fig. 3.1.5.5. Rotation angle versus temperature for the oxygen octahedron distortion below 105 K in strontium titanate described in Fig. 3.1.5.4 (p. 384) | html | pdf |
    - Fig. 3.1.5.6. Raman spectra of strontium titanate below its cubic–tetragonal phase transition temperature (p. 384) | html | pdf |
    - Fig. 3.1.5.7. Temperature dependence of phonon branches observed in the Raman spectra of tetragonal strontium titanate (p. 384) | html | pdf |
    - Fig. 3.1.5.8. (a) Structure of lanthanum aluminate above (undistorted) and below (arrows) its cubic–rhombohedral phase transition near 840 K (p. 385) | html | pdf |
    - Fig. 3.1.5.9. Phase diagram of potassium nitrate, KNO₃ (p. 385) | html | pdf |
    - Fig. 3.1.5.10. (a) `Soft' optical phonon frequency versus temperature in LaP₅O₁₄, showing displacive character of the phase transition (p. 386) | html | pdf |
    - Fig. 3.1.5.11. (a) Structure of barium metal fluoride BaMF₄ (M = Co, Mn, Mg, Zn, Ni) at ambient temperature (300 K) (p. 386) | html | pdf |
    - Fig. 3.1.5.12. Structure of the tungsten bronze barium sodium niobate Ba₂NaNb₅O₁₅ in its highest-temperature phase above 853 K (p. 387) | html | pdf |
    - Fig. 3.1.5.13. Sequence of phases encountered with raising or lowering the temperature in barium sodium niobate (p. 387) | html | pdf |
    - Fig. 3.1.5.14. Structure of tris-sarcosine calcium chloride, (CH₃NHCH₂COOH)₃CaCl₂ (p. 388) | html | pdf |
    - Fig. 3.1.5.15. `Soft' optical phonon frequencies versus temperature in both ferroelectric and paraelectric phases of tris-sarcosine calcium chloride (p. 388) | html | pdf |
    - Fig. 3.1.5.16. The structure of potassium dihydrogen phosphate, KH₂PO₄, showing the O⋯H⋯O hydrogen bonds (p. 388) | html | pdf |
    - Fig. 3.1.5.17. Double-well models (p. 389) | html | pdf |
    - Fig. 3.1.5.18. Pressure dependence of the `soft' optical phonon branch Raman spectra in potassium dihydrogen phosphate (p. 389) | html | pdf |
    - Fig. 3.1.5.19. Structure of sodium nitrite, NaNO₂ (p. 389) | html | pdf |
    - Fig. 3.1.5.20. Raman spectra of sodium nitrite, showing diffusive Debye-like response due to large-amplitude flopping over of nitrite ions (p. 390) | html | pdf |
    - Fig. 3.1.5.21. Phase diagram for sodium nitrite for `conjugate' electric fields applied along the polar b axis, showing triple point, tricritical point and critical end point (p. 390) | html | pdf |
    - Fig. 3.1.5.22. Phase diagram for sodium nitrite for electric fields applied perpendicular to the polar b axis (p. 390) | html | pdf |
    - Fig. 3.1.5.23. (a) Crystal structure of silver iodide tungstate (Ag₁₃I₉W₂O₈); (b) showing conduction paths for Ag ions (p. 391) | html | pdf |
    - Fig. 3.1.5.24. Evidence for three phase transitions in silver iodide tungstate: (a) dielectric and conductivity data; (b) specific heat data; (c) Raman data (p. 391) | html | pdf |
    - Fig. 3.1.5.25. Raman spectra of YBa₂Cu₃O_7−x below an apparent phase transition at ca. 235 K (p. 392) | html | pdf |
  - Tables
    - Table 3.1.1.1. Ferroic classification of structural parameters (p. 359) | html | pdf |
    - Table 3.1.2.1. Transformation of the components of $[\bf d]$ under the symmetry operations of group (p. 363) | html | pdf |
    - Table 3.1.2.2. Matrices defining the irreducible representations of for $[{\bf k}={\bf a}_1^*+{\bf a}_2^*]$ (p. 368) | html | pdf |
    - Table 3.1.2.3. Action of the generators of on the order parameter and on the polarization and strain components (p. 369) | html | pdf |
    - Table 3.1.3.1. Point-group symmetry descents associated with irreducible representations (pp. 372-377) | html | pdf |
    - Table 3.1.3.2. Symmetry descents $[G\Downarrow F_1]$ associated with two irreducible representations (p. 378) | html | pdf |
    - Table 3.1.3.3. Important property tensors (p. 380) | html | pdf |
    - Table 3.1.4.1. Possible symmetry changes across transitions from a parent phase with space group , , , , or (p. 382) | html | pdf |
    - Table 3.1.5.1. Low-temperature ferroelectrics (p. 392) | html | pdf |
- 3.2. Twinning and domain structures (pp. 397-412) | html | pdf | chapter contents |
  V. Janovec, Th. Hahn and H. Klapper
  - 3.2.1. Introduction and history (pp. 397-398) | html | pdf |
  - 3.2.2. A brief survey of bicrystallography (pp. 398-399) | html | pdf |
  - 3.2.3. Mathematical tools (pp. 399-410) | html | pdf |
    - 3.2.3.1. Sets, pairs, mappings and equivalence classes (pp. 400-401) | html | pdf |
      - 3.2.3.1.1. Sets (p. 400) | html | pdf |
      - 3.2.3.1.2. Pairs (p. 400) | html | pdf |
      - 3.2.3.1.3. Mappings (pp. 400-401) | html | pdf |
      - 3.2.3.1.4. Equivalence relation on a set, partition of a set (p. 401) | html | pdf |
    - 3.2.3.2. Groups and subgroups (pp. 401-405) | html | pdf |
      - 3.2.3.2.1. Groups (pp. 401-402) | html | pdf |
      - 3.2.3.2.2. Subgroups (p. 402) | html | pdf |
      - 3.2.3.2.3. Left and right cosets (pp. 402-403) | html | pdf |
      - 3.2.3.2.4. Conjugate subgroups (p. 403) | html | pdf |
      - 3.2.3.2.5. Normalizers (p. 403) | html | pdf |
      - 3.2.3.2.6. Normal subgroups (p. 403) | html | pdf |
      - 3.2.3.2.7. Halving subgroups and dichromatic (black-and-white) groups (p. 404) | html | pdf |
      - 3.2.3.2.8. Double cosets (pp. 404-405) | html | pdf |
    - 3.2.3.3. Action of a group on a set (pp. 405-410) | html | pdf |
      - 3.2.3.3.1. Group action (pp. 405-406) | html | pdf |
      - 3.2.3.3.2. Stabilizers (isotropy groups) (pp. 406-407) | html | pdf |
      - 3.2.3.3.3. Orbits (pp. 407-408) | html | pdf |
      - 3.2.3.3.4. Orbits and left cosets (p. 408) | html | pdf |
      - 3.2.3.3.5. Intermediate subgroups and partitions of an orbit into suborbits (pp. 408-410) | html | pdf |
      - 3.2.3.3.6. Orbits of ordered pairs and double cosets (p. 410) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 3.2.3.1. Four types of double cosets (p. 404) | html | pdf |
- 3.3. Twinning of crystals (pp. 413-487) | html | pdf | chapter contents |
  Th. Hahn and H. Klapper
  - 3.3.1. Crystal aggregates and intergrowths (pp. 413-414) | html | pdf |
  - 3.3.2. Basic concepts and definitions of twinning (pp. 414-418) | html | pdf |
    - 3.3.2.1. Definition of a twin (p. 415) | html | pdf |
    - 3.3.2.2. Essential addenda to the definition (p. 415) | html | pdf |
    - 3.3.2.3. Specifications and extensions of the orientation relations (p. 417) | html | pdf |
      - 3.3.2.3.1. Binary twin operations (twin elements) (pp. 415-417) | html | pdf |
      - 3.3.2.3.2. Pseudo n-fold twin rotations (twin axes) with $[n\ge 3]$ (pp. 416-417) | html | pdf |
    - 3.3.2.4. Notes on the definition of twinning (pp. 417-418) | html | pdf |
  - 3.3.3. Morphological classification, simple and multiple twinning (pp. 418-419) | html | pdf |
    - 3.3.3.1. Morphological classification (p. 419) | html | pdf |
  - 3.3.4. Composite symmetry and the twin law (pp. 419-423) | html | pdf |
    - 3.3.4.1. Composite symmetry (pp. 419-420) | html | pdf |
    - 3.3.4.2. Equivalent twin laws (p. 421) | html | pdf |
    - 3.3.4.3. Classification of composite symmetries (pp. 421-422) | html | pdf |
    - 3.3.4.4. Categories of composite symmetries (pp. 422-423) | html | pdf |
  - 3.3.5. Description of the twin law by black–white symmetry (p. 423) | html | pdf |
  - 3.3.6. Examples of twinned crystals (pp. 423-436) | html | pdf |
    - 3.3.6.1. Macroscopic identification of twins and of twin laws (p. 423) | html | pdf |
    - 3.3.6.2. Inversion twins in orthorhombic crystals (pp. 425-426) | html | pdf |
    - 3.3.6.3. Twinning of gypsum, CaSO₄·2H₂O (pp. 426-427) | html | pdf |
    - 3.3.6.4. Twinning of low-temperature quartz (α-quartz, SiO₂) (pp. 427-428) | html | pdf |
      - 3.3.6.4.1. Dauphiné twins (p. 427) | html | pdf |
      - 3.3.6.4.2. Brazil twins (pp. 427-428) | html | pdf |
      - 3.3.6.4.3. Combined Dauphiné–Brazil (Leydolt, Liebisch) twins (p. 428) | html | pdf |
      - 3.3.6.4.4. Japanese twins (or La Gardette twins) (p. 428) | html | pdf |
    - 3.3.6.5. Twinning of high-temperature quartz (β-quartz) (pp. 428-429) | html | pdf |
    - 3.3.6.6. Twinning of rhombohedral crystals (p. 429) | html | pdf |
    - 3.3.6.7. Spinel twins (pp. 429-431) | html | pdf |
    - 3.3.6.8. Growth and transformation twins of K₂SO₄ (p. 431) | html | pdf |
    - 3.3.6.9. Pentagonal–decagonal twins (pp. 431-432) | html | pdf |
    - 3.3.6.10. Multiple twins of rutile, TiO₂ (pp. 432-433) | html | pdf |
    - 3.3.6.11. Variety of twinning in gibbsite, Al(OH)₃ (p. 433) | html | pdf |
    - 3.3.6.12. Plagioclase twins (pp. 433-434) | html | pdf |
    - 3.3.6.13. Staurolite (pp. 434-435) | html | pdf |
    - 3.3.6.14. BaTiO₃ transformation twins (p. 435) | html | pdf |
    - 3.3.6.15. Merohedral growth twinning of pentaerythrite (p. 435) | html | pdf |
    - 3.3.6.16. Twins of twins (pp. 435-436) | html | pdf |
  - 3.3.7. Genetic classification of twins (pp. 436-440) | html | pdf |
    - 3.3.7.1. Growth twinning (pp. 436-438) | html | pdf |
      - 3.3.7.1.1. Twinning by nucleation (pp. 436-437) | html | pdf |
      - 3.3.7.1.2. Twinning during crystal growth (pp. 437-438) | html | pdf |
    - 3.3.7.2. Transformation twinning (pp. 438-439) | html | pdf |
    - 3.3.7.3. Mechanical twinning (pp. 439-440) | html | pdf |
  - 3.3.8. Lattice aspects of twinning (pp. 440-446) | html | pdf |
    - 3.3.8.1. Basic concepts of Friedel's lattice theory (p. 441) | html | pdf |
    - 3.3.8.2. Lattice coincidences, twin lattice, twin lattice index (pp. 441-442) | html | pdf |
    - 3.3.8.3. Twins with three-dimensional twin lattices (`triperiodic' twins) (pp. 442-443) | html | pdf |
    - 3.3.8.4. Approximate (pseudo-)coincidences of two or more lattices (p. 444) | html | pdf |
    - 3.3.8.5. Twin obliquity and lattice pseudosymmetry (pp. 444-446) | html | pdf |
    - 3.3.8.6. Twinning of isostructural crystals (p. 446) | html | pdf |
    - 3.3.8.7. Conclusions (p. 446) | html | pdf |
  - 3.3.9. Twinning by merohedry and pseudo-merohedry (pp. 446-450) | html | pdf |
    - 3.3.9.1. Definitions of merohedry (p. 447) | html | pdf |
    - 3.3.9.2. Types of twins by merohedry and pseudo-merohedry (pp. 447-450) | html | pdf |
      - 3.3.9.2.1. Merohedral twins of lattice index (p. 447) | html | pdf |
      - 3.3.9.2.2. Pseudo-merohedral twins of lattice index (pp. 447-448) | html | pdf |
      - 3.3.9.2.3. Twinning with partial lattice coincidence (lattice index ) (p. 448) | html | pdf |
      - 3.3.9.2.4. Twinning with partial lattice pseudo-coincidence (lattice index ) (pp. 448-450) | html | pdf |
    - 3.3.9.3. Pseudo-merohedry and ferroelasticity (p. 450) | html | pdf |
  - 3.3.10. Twin boundaries (pp. 450-469) | html | pdf |
    - 3.3.10.1. Contact relations in twinning (pp. 450-451) | html | pdf |
    - 3.3.10.2. Strain compatibility of interfaces (pp. 451-455) | html | pdf |
      - 3.3.10.2.1. Sapriel approach to permissible (compatible) boundaries in ferroelastic (non-merohedral) transformation twins (p. 452) | html | pdf |
      - 3.3.10.2.2. Extension to non-merohedral growth and mechanical twins (pp. 452-454) | html | pdf |
      - 3.3.10.2.3. Permissible boundaries in merohedral twins (lattice index [j] = 1) (p. 454) | html | pdf |
      - 3.3.10.2.4. Permissible twin boundaries in twins with lattice index $[[j]\, \gt\, 1]$ (pp. 454-455) | html | pdf |
    - 3.3.10.3. Electrical constraints of twin interfaces (pp. 455-456) | html | pdf |
      - 3.3.10.3.1. Merohedral twins (pp. 455-456) | html | pdf |
      - 3.3.10.3.2. Non-merohedral twins (p. 456) | html | pdf |
      - 3.3.10.3.3. Non-pyroelectric noncentrosymmetric crystals (p. 456) | html | pdf |
    - 3.3.10.4. Displacement and fault vectors of twin boundaries (pp. 456-459) | html | pdf |
      - 3.3.10.4.1. Twin displacement vector $[{\bf t}]$ (pp. 457-458) | html | pdf |
      - 3.3.10.4.2. Fault vectors of twin boundaries in merohedral twins (p. 458) | html | pdf |
      - 3.3.10.4.3. Examples of fault-vector determinations (pp. 458-459) | html | pdf |
    - 3.3.10.5. Examples of structural models of twin boundaries (pp. 459-461) | html | pdf |
      - 3.3.10.5.1. Aragonite, CaCO₃ (p. 459) | html | pdf |
      - 3.3.10.5.2. Dauphiné twins of $[\alpha]$ -quartz (pp. 459-460) | html | pdf |
      - 3.3.10.5.3. Potassium lithium sulfate, KLiSO₄ (pp. 460-461) | html | pdf |
      - 3.3.10.5.4. Twin models of molecular crystals (p. 461) | html | pdf |
    - 3.3.10.6. Observations of twin boundaries by transmission electron microscopy (pp. 461-464) | html | pdf |
      - 3.3.10.6.1. Anatase, TiO₂ (Penn & Banfield, 1998, 1999) (pp. 461-462) | html | pdf |
      - 3.3.10.6.2. Rutile, TiO₂ (p. 462) | html | pdf |
      - 3.3.10.6.3. Cassiterite, SnO₂ (rutile structure) (p. 462) | html | pdf |
      - 3.3.10.6.4. Σ3 (111) twin interface in BaTiO₃ [cf. Section 3.3.8.3(iii)] (pp. 462-463) | html | pdf |
      - 3.3.10.6.5. Σ = 3 bicrystal boundaries in Cu and Ag (p. 463) | html | pdf |
      - 3.3.10.6.6. Fivefold cyclic twins in nanocrystalline materials (pp. 463-464) | html | pdf |
    - 3.3.10.7. Twin textures (pp. 464-467) | html | pdf |
      - 3.3.10.7.1. Merohedral (non-ferroelastic) twins (see Sections 3.3.9 and 3.3.10.2.3) (p. 464) | html | pdf |
      - 3.3.10.7.2. Non-merohedral (ferroelastic) twins (p. 464) | html | pdf |
      - 3.3.10.7.3. Fitting problems of ferroelastic twins (pp. 464-466) | html | pdf |
      - 3.3.10.7.4. Tweed microstructures (pp. 466-467) | html | pdf |
      - 3.3.10.7.5. Twin textures in polycrystalline aggregates (p. 467) | html | pdf |
    - 3.3.10.8. Twinning dislocations (pp. 467-468) | html | pdf |
    - 3.3.10.9. Coherent and incoherent twin interfaces (pp. 468-469) | html | pdf |
  - 3.3.11. Effect of twinning in reciprocal space (pp. 469-477) | html | pdf |
    - 3.3.11.1. Basic features of twin diffraction records (pp. 469-470) | html | pdf |
    - 3.3.11.2. General (non-merohedral, inclined-lattice) twins (p. 470) | html | pdf |
    - 3.3.11.3. Twinning by (strict) merohedry (parallel-lattice twins, Σ1 merohedral twins) (pp. 470-471) | html | pdf |
    - 3.3.11.4. Twinning by reticular merohedry (partially-parallel-lattice twins, Σ > 1 merohedral twins) (pp. 471-474) | html | pdf |
      - 3.3.11.4.1. General survey (pp. 471-472) | html | pdf |
      - 3.3.11.4.2. The four Σm merohedral twin families (pp. 472-474) | html | pdf |
    - 3.3.11.5. Pseudo-merohedral twins (pp. 474-477) | html | pdf |
      - 3.3.11.5.1. General remarks (pp. 474-475) | html | pdf |
      - 3.3.11.5.2. Example: pseudohexagonal (cyclic) twins of orthorhombic crystals (pseudo-coincident Σ3 twins) (pp. 475-477) | html | pdf |
    - 3.3.11.6. Programs for structure determinations with twinned crystals (p. 477) | html | pdf |
  - 3.3.12. Domain structures (by V. Janovec) (p. 477) | html | pdf |
  - 3.3.13. Glossary (pp. 477-478) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 3.3.1.1. Parallel intergrowth (a) of spinel octahedra and (b) of hexagonal quartz prisms (p. 413) | html | pdf |
    - Fig. 3.3.1.2. (a) Optical anomaly of a cubic mixed (K,NH₄)-alum crystal grown from aqueous solution, as revealed by polarized light between crossed polarizers (p. 413) | html | pdf |
    - Fig. 3.3.2.1. Schematic illustration of the orientation relations of noncentrosymmetric triclinic twin partners, see Section 3.3.2.3.1 (p. 416) | html | pdf |
    - Fig. 3.3.2.2. As Fig. 3.3.2.1, (a) for twin element (iii) `rational twofold twin axis' and (b) for twin element (iv) `irrational twin mirror plane' (see text); common lattice row [uvw] for both cases (p. 416) | html | pdf |
    - Fig. 3.3.2.3. Illustration of the Kantennormalengesetz (complex twin) for twin elements (v) and (vi) (see text); common lattice row [uvw] for both cases (p. 416) | html | pdf |
    - Fig. 3.3.2.4. (a) Triple growth twin of orthorhombic aragonite, CaCO₃, with pseudo-threefold twin axis (p. 417) | html | pdf |
    - Fig. 3.3.3.1. Schematic illustration of simple (polysynthetic) and multiple (cyclic) twins (p. 418) | html | pdf |
    - Fig. 3.3.4.1. Gypsum dovetail twin: schematic illustration of the coset of alternative twin operations (p. 420) | html | pdf |
    - Fig. 3.3.4.2. Twinning of an orthorhombic crystal (eigensymmetry 2/m 2/m 2/m) with equivalent twin mirror planes (110) and $[({\bar 1}10)]$ (p. 421) | html | pdf |
    - Fig. 3.3.6.1. X-ray topographs (Mo Kα radiation) of a $[(11 \bar 2 0)]$ plate (about 12 × 12 mm, about 1 mm thick) cut from a hexagonal KLiSO₄ (phase III) crystal (point group 6; cf (p. 426) | html | pdf |
    - Fig. 3.3.6.2. X-ray transmission topograph of a (110) crystal plate (2.4 mm thick, width about 15 mm) cut from a very perfect crystal of polar lithium formate monohydrate, HCOOLi·H₂O, point group mm2, grown from aqueous solution (reflection 111, Mo Kα radiation) (p. 426) | html | pdf |
    - Fig. 3.3.6.3. Dovetail twin (a) and Montmartre twin (b) of gypsum (p. 427) | html | pdf |
    - Fig. 3.3.6.4. Distinction of the four different domain states generated by the three merohedral twin laws of low-quartz and of quartz homeotypes (p. 428) | html | pdf |
    - Fig. 3.3.6.5. The four variants of Japanese twins of quartz (p. 429) | html | pdf |
    - Fig. 3.3.6.6. Twin intergrowth of `obverse' and `reverse' rhombohedra of rhombohedral FeBO₃ (p. 430) | html | pdf |
    - Fig. 3.3.6.7. Contact growth twin of calcite with the same twin law as FeBO₃ in Fig. 3.3.6.6 (p. 430) | html | pdf |
    - Fig. 3.3.6.8. Spinel (111) twins of cubic crystals (two orientation states) (p. 430) | html | pdf |
    - Fig. 3.3.6.9. Pseudo-hexagonal growth twin of K₂SO₄ showing six sector domains in three orientation states (p. 431) | html | pdf |
    - Fig. 3.3.6.10. Pentagonal–decagonal twins (p. 431) | html | pdf |
    - Fig. 3.3.6.11. Various forms of rutile (TiO₂) twins with one or several equivalent twin reflection planes {011} (p. 432) | html | pdf |
    - Fig. 3.3.6.12. Sixfold reflection twin of gibbsite, Al(OH)₃, with equivalent (110) and $[({\bar 1}10]$ ), both as twin mirror and composition planes (p. 433) | html | pdf |
    - Fig. 3.3.6.13. Polysynthetic albite twin aggregate of triclinic feldspar, twin reflection and composition plane (010) (p. 434) | html | pdf |
    - Fig. 3.3.6.14. Pericline twin of triclinic feldspar (p. 434) | html | pdf |
    - Fig. 3.3.6.15. Twinning of staurolite (p. 435) | html | pdf |
    - Fig. 3.3.6.16. The various steps (idealized) of phillipsite growth twins: (a) monoclinic untwinned, (b) orthorhombic, (c) tetragonal, (d) cubic, and (e) `filled-in' pseudo rhomb-dodecahedron (after Ramdohr & Strunz, 1967, p (p. 436) | html | pdf |
    - Fig. 3.3.7.1. Orthoclase (monoclinic K-feldspar) (p. 437) | html | pdf |
    - Fig. 3.3.7.2. Photographs of (001) plates ( $[\approx]$ 20 mm diameter, $[\approx]$ 1 mm thick) of NH₄LiSO₄ between crossed polarizers (p. 437) | html | pdf |
    - Fig. 3.3.7.3. Mechanical twins of calcite, CaCO₃ (p. 439) | html | pdf |
    - Fig. 3.3.8.1. Lattice relations of $[\Sigma 5]$ twins of tetragonal crystals with primitive lattice (p. 443) | html | pdf |
    - Fig. 3.3.8.2. (a) A (110) silicon slice (10 cm diameter, 0.3 mm thick), cut from a Czochralski-grown tricrystal for solar-cell applications (p. 443) | html | pdf |
    - Fig. 3.3.10.1. (a) Classical description of mechanical twinning by homogeneous shear deformation (p. 451) | html | pdf |
    - Fig. 3.3.10.2. Boundaries B–B between 180° domains (merohedral twins) of pyroelectric crystals (p. 456) | html | pdf |
    - Fig. 3.3.10.3. Charged and uncharged boundaries B–B of non-merohedral twins of pseudo-hexagonal NH₄LiSO₄ (p. 456) | html | pdf |
    - Fig. 3.3.10.4. Lattice representation of twin displacement vectors (p. 457) | html | pdf |
    - Fig. 3.3.10.5. HRTEM micrograph of anatase, TiO₂, with a (112) reflection twin boundary (arrows), viewed edge-on along $[[1{\bar 3}1]]$ (p. 458) | html | pdf |
    - Fig. 3.3.10.6. Structural model of the (110) twin boundary of aragonite (after Bragg, 1924), projected along the pseudo-hexagonal c axis (p. 460) | html | pdf |
    - Fig. 3.3.10.7. Simplified structural model of a $[\{10{\bar 1}0\}]$ Dauphiné twin boundary in quartz (p. 460) | html | pdf |
    - Fig. 3.3.10.8. KLiSO₄: Bulk tetrahedral framework structures and models of (0001) twin boundary structures of phases III and IV (p. 461) | html | pdf |
    - Fig. 3.3.10.9. (a) HRTEM micrograph of a coherent (111) twin boundary in BaTiO₃, projected along $[[1{\bar 1}0]]$ (p. 462) | html | pdf |
    - Fig. 3.3.10.10. (a) Schematic block diagram of a $[\Sigma = 3]$ bicrystal (spinel twin) for $[\varphi[{\bar 1}10] = 0^\circ]$ (p. 463) | html | pdf |
    - Fig. 3.3.10.11. HRTEM micrograph of a fivefold-twinned Ge nanocrystal (right) in an amorphous Ge film formed by vapour deposition on an NaCl cleavage plane (p. 464) | html | pdf |
    - Fig. 3.3.10.12. Illustration of space-filling problems of domains for a (ferroelastic) orthorhombic $[\longrightarrow]$ monoclinic phase transition with an angle $[\varepsilon]$ (exaggerated) of spontaneous shear (p. 465) | html | pdf |
    - Fig. 3.3.10.13. Thin section of tetragonal leucite, K(AlSi₂O₆), between crossed polarizers (p. 465) | html | pdf |
    - Fig. 3.3.10.14. Twin textures generated by the two different hexagonal-to-orthorhombic phase transitions of KLiSO₄ (p. 466) | html | pdf |
    - Fig. 3.3.10.15. Definition of the Burgers vector b of a twinning dislocation TD (p. 467) | html | pdf |
    - Fig. 3.3.11.1. Rhombohedral Σ3 (reverse/obverse) twins in direct space, described with hexagonal axes, viewed down the common c axis (p. 472) | html | pdf |
    - Fig. 3.3.11.2. Reciprocal lattice of the rhombohedral Σ3 twins for the layers l = 3n (a), l = 3n + 1 (b), l = 3n + 2 (c), described with hexagonal axes (p. 473) | html | pdf |
    - Fig. 3.3.11.3. Tetragonal lattices (a–b planes, common c axis pointing upwards) of twin domain I (start domain, lattice points small circles, right-handed green unit cell a₁, b₁, c₁), of the Σ5 twin-related domain II (small crosses, left-handed blue unit cell a₂, b₂, c₂) and the Σ5 coincidence lattice (large black points, right-handed red unit cell a_T, b_T, c_T) (p. 473) | html | pdf |
    - Fig. 3.3.11.4. Reciprocal tetragonal lattices (hk0 lattice planes) of twin domain I (start domain, lattice points small circles) and of the Σ5 twin-related domain II (small crosses) (p. 473) | html | pdf |
    - Fig. 3.3.11.5. Hexagonal lattices (a–b planes, common c axis pointing upwards) of twin domain I (start domain, lattice points small circles, right-handed green unit cell a₁, b₁, c₁), of the Σ7 twin-related domain II (small crosses, left-handed blue unit cell a₂, b₂, c₂) and of the Σ7 coincidence lattice (large black points, right-handed red unit cell a_T, b_T, c_T) (p. 474) | html | pdf |
    - Fig. 3.3.11.6. Reciprocal hexagonal lattices (hk0 lattice planes) of twin domain I (start domain, lattice points small circles) and of the Σ7 twin-related domain II (small crosses) (p. 474) | html | pdf |
    - Fig. 3.3.11.7. (a) Morphologically idealized pseudo-hexagonal threefold sector twin of an orthorhombic crystal with b/a = tan 58.5°, generated by the two symmetry-equivalent twin mirror planes (110) and $[(1 \bar 1 0)]$ (p. 475) | html | pdf |
    - Fig. 3.3.11.8. (a) (001) plate of ammonium lithium sulfate, NH₄LiSO₄, (about 11 mm diameter, 0.8 mm thick) between crossed polarizers, exhibiting sectorial pseudo-hexagonal growth twinning (p. 476) | html | pdf |
  - Tables
    - Table 3.3.4.1. Gypsum, dovetail twins: coset of alternative twin operations (twin law), given in orthorhombic axes of the composite symmetry $[{\cal K}_D]$ (p. 420) | html | pdf |
    - Table 3.3.4.2. Reduced composite symmetries $[{\cal K}^*(1,2)={\cal H}^*\cup k_2\times{\cal H}^*]$ and $[{\cal K}^*(1,3)={\cal H}^*\cup k_3 \times {\cal H}^*]$ for the orthorhombic example in Fig. 3.3.4.2 (p. 422) | html | pdf |
    - Table 3.3.6.1. Types of X-ray reflections generating (`yes') or not generating (`no') X-ray topographic domain contrast (yes/no) for the $[6\rightarrow 6mm]$ growth twins of KLiSO₄ (p. 425) | html | pdf |
    - Table 3.3.6.2. Orthorhombic inversion twins: coset of alternative twin operations (twin law) (p. 426) | html | pdf |
    - Table 3.3.6.3. Gypsum: cosets of alternative twin operations of the dovetail and the Montmartre twins, referred to their specific orthorhombic axes (subscripts D and M) (p. 427) | html | pdf |
    - Table 3.3.6.4. Dauphiné twins of α-quartz: coset of alternative twin operations (twin law) (p. 428) | html | pdf |
    - Table 3.3.6.5. The four different variants of Japanese twins according to Frondel (1962) (p. 429) | html | pdf |
    - Table 3.3.6.6. Plagioclase: albite and pericline twins (p. 434) | html | pdf |
    - Table 3.3.8.1. Lattice planes (hkl) and lattice rows [uvw] that are mutually perpendicular (after Koch, 2004) (p. 441) | html | pdf |
    - Table 3.3.8.2. Examples of calculated obliquities $[\omega]$ and lattice indices [j] for selected (hkl)[uvw] combinations and their relation to twinning (p. 445) | html | pdf |
    - Table 3.3.9.1. Staurolite, 60° and 90° twins (p. 449) | html | pdf |
    - Table 3.3.10.1. Examples of permissible twin boundaries for higher-order merohedral twins ([j]> 1) (p. 455) | html | pdf |
    - Table 3.3.11.1. Relative frequencies of the four coincidence cases (i)–(iv) for the general Σm twins and the specific twins Σ3, Σ5 and Σ7 treated in this chapter. (p. 472) | html | pdf |
- 3.4. Domain structures (pp. 484-559) | html | pdf | chapter contents |
  V. Janovec and J. Přívratská
  - 3.4.1. Introduction (pp. 484-486) | html | pdf |
    - 3.4.1.1. Basic concepts (pp. 484-485) | html | pdf |
    - 3.4.1.2. Scope of this chapter (pp. 485-486) | html | pdf |
  - 3.4.2. Domain states (pp. 486-505) | html | pdf |
    - 3.4.2.1. Principal and basic domain states (pp. 486-490) | html | pdf |
    - 3.4.2.2. Degenerate (secondary) domain states, partition of principal domain states (pp. 490-493) | html | pdf |
      - 3.4.2.2.1. Ferroelastic domain state (pp. 491-492) | html | pdf |
      - 3.4.2.2.2. Ferroelectric domain states (p. 492) | html | pdf |
      - 3.4.2.2.3. Domain states with the same stabilizer (pp. 492-493) | html | pdf |
    - 3.4.2.3. Property tensors associated with ferroic domain states (pp. 493-495) | html | pdf |
    - 3.4.2.4. Synoptic table of ferroic transitions and domain states (pp. 495-497) | html | pdf |
      - 3.4.2.4.1. Explanation of Table 3.4.2.7 (pp. 496-497) | html | pdf |
    - 3.4.2.5. Basic (microscopic) domain states and their partition into translation subsets (pp. 497-505) | html | pdf |
  - 3.4.3. Domain pairs: domain twin laws, distinction of domain states and switching (pp. 505-528) | html | pdf |
    - 3.4.3.1. Domain pairs and their symmetry, twin law (pp. 506-508) | html | pdf |
    - 3.4.3.2. Twinning group, distinction of two domain states (pp. 508-510) | html | pdf |
    - 3.4.3.3. Switching of ferroic domain states (pp. 510-511) | html | pdf |
    - 3.4.3.4. Classes of equivalent domain pairs and their classifications (pp. 511-512) | html | pdf |
    - 3.4.3.5. Non-ferroelastic domain pairs: twin laws, domain distinction and switching fields, synoptic table (pp. 512-515) | html | pdf |
      - 3.4.3.5.1. Explanation of Table 3.4.3.4 (pp. 512-515) | html | pdf |
    - 3.4.3.6. Ferroelastic domain pairs (pp. 515-528) | html | pdf |
      - 3.4.3.6.1. Spontaneous strain (pp. 516-517) | html | pdf |
      - 3.4.3.6.2. Equally deformed planes of a ferroelastic domain pair (pp. 517-518) | html | pdf |
      - 3.4.3.6.3. Disoriented domain states, ferroelastic domain twins and their twin laws (pp. 518-521) | html | pdf |
      - 3.4.3.6.4. Ferroelastic domain pairs with compatible domain walls, synoptic table (pp. 521-527) | html | pdf |
        3.4.3.6.4.1. Explanation of Table 3.4.3.6 (pp. 526-527) | html | pdf |
      - 3.4.3.6.5. Ferroelastic domain pairs with no compatible domain walls, synoptic table (pp. 527-528) | html | pdf |
    - 3.4.3.7. Domain pairs in the microscopic description (p. 528) | html | pdf |
  - 3.4.4. Domain twins and domain walls (pp. 528-539) | html | pdf |
    - 3.4.4.1. Formal description of simple domain twins and planar domain walls of zero thickness (pp. 528-529) | html | pdf |
    - 3.4.4.2. Layer groups (pp. 529-530) | html | pdf |
    - 3.4.4.3. Symmetry of simple twins and planar domain walls of zero thickness (pp. 530-533) | html | pdf |
    - 3.4.4.4. Non-ferroelastic domain twins and domain walls (pp. 533-535) | html | pdf |
    - 3.4.4.5. Ferroelastic domain twins and walls. Ferroelastic twin laws (p. 535) | html | pdf |
    - 3.4.4.6. Domain walls of finite thickness – continuous description (pp. 535-538) | html | pdf |
    - 3.4.4.7. Microscopic structure and symmetry of domain walls (p. 538) | html | pdf |
  - 3.4.5. Glossary (p. 539) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 3.4.1.1. Domain structure of tetragonal barium titanate (BaTiO₃) (p. 484) | html | pdf |
    - Fig. 3.4.1.2. Domain structure of a BaGa₂O₄ crystal seen by high-resolution transmission electron microscopy (p. 484) | html | pdf |
    - Fig. 3.4.1.3. Elastic hysteresis of ferroelastic lead phosphate Pb₃(PO₄)₂ (Salje, 1990) (p. 485) | html | pdf |
    - Fig. 3.4.1.4. Transmission electron microscopy image of the ferroelastic domain structure in a YBa₂Cu₃O_7−y crystal (p. 485) | html | pdf |
    - Fig. 3.4.1.5. Non-ferroelastic ferroelectric domains in triglycine sulfate (TGS) revealed by a liquid-crystal method (p. 485) | html | pdf |
    - Fig. 3.4.2.1. Hierarchy in domain-structure analysis (p. 487) | html | pdf |
    - Fig. 3.4.2.2. Exploded view of single-domain states $[{\bf S}_1]$ , $[{\bf S}_2]$ , $[{\bf S}_3]$ and $[{\bf S}_4 ]$ (solid rectangles with arrows of spontaneous polarization) formed at a phase transition from a parent phase with symmetry $[G=4_z/m_zm_xm_{xy} ]$ to a ferroic phase with symmetry (p. 487) | html | pdf |
    - Fig. 3.4.2.3. Oriented symmetry operations of the cubic group $[m\bar3m]$ and of its subgroups (p. 495) | html | pdf |
    - Fig. 3.4.2.4. Oriented symmetry operations of the hexagonal group and of its hexagonal and trigonal subgroups (p. 496) | html | pdf |
    - Fig. 3.4.2.5. Four basic single-domain states $[{{\sf S}_1}= 1_1]$ , $[{{\sf S}_2}= 1_2]$ , $[{{\sf S}_3}= 2_1]$ , $[{{\sf S}_4}= 2_2 ]$ of the ferroic phase of a calomel (Hg₂Cl₂) crystal (p. 505) | html | pdf |
    - Fig. 3.4.3.1. Transposable domain pairs (p. 507) | html | pdf |
    - Fig. 3.4.3.2. Non-transposable domain pairs (p. 507) | html | pdf |
    - Fig. 3.4.3.3. Domain structure in lead germanate observed using a polarized-light microscope (p. 515) | html | pdf |
    - Fig. 3.4.3.4. Temperature dependence of lattice parameters in leucite (p. 516) | html | pdf |
    - Fig. 3.4.3.5. Two ways of constructing a ferroelastic domain twin (p. 517) | html | pdf |
    - Fig. 3.4.3.6. High-resolution electron microscopy image of a ferroelastic twin in the orthorhombic phase of WO₃ (p. 519) | html | pdf |
    - Fig. 3.4.3.7. Ferroelastic twins in a very thin YBa₂Cu₃O_7−δ crystal observed in a polarized-light microscope (p. 519) | html | pdf |
    - Fig. 3.4.3.8. Exploded view of four ferroelastic twins with disoriented ferroelastic domain states $[{\bf R}_1^+, {\bf R}_2^-]$ and $[{\bf R}_1^-, {\bf R}_2^+ ]$ formed from a single-domain pair $[({\bf S}_1,{\bf S}_2)]$ (p. 520) | html | pdf |
    - Fig. 3.4.3.9. Splitting of diffraction spots at a tetragonal-to-orthorhombic transition (p. 520) | html | pdf |
    - Fig. 3.4.3.10. Domain pairs in calomel (p. 528) | html | pdf |
    - Fig. 3.4.4.1. Symbols of a simple twin (p. 529) | html | pdf |
    - Fig. 3.4.4.2. A simple twin under the action of four types of operation that do not change the orientation of the wall plane p (p. 531) | html | pdf |
    - Fig. 3.4.4.3. Engineered periodic non-ferroelastic ferroelectric stripe domain structure within a lithium tantalate crystal with symmetry descent $[\bar 6\supset 3 ]$ (p. 534) | html | pdf |
    - Fig. 3.4.4.4. Microscopic structure of two domain states and two parallel mutually reversed domain walls in the $[\alpha]$ phase of quartz (p. 534) | html | pdf |
    - Fig. 3.4.4.5. Transmission electron microscopy (TEM) image of the incommensurate triangular ( modulated) phase of quartz (p. 535) | html | pdf |
    - Fig. 3.4.4.6. Profile of the one-component order parameter $[\eta(\xi)]$ in a symmetric wall (S) (p. 536) | html | pdf |
    - Fig. 3.4.4.7. Profiles of the one-component order parameter $[\eta(\xi)]$ in a symmetric wall (solid curve) and in the reversed wall (dotted curve) (p. 537) | html | pdf |
    - Fig. 3.4.4.8. Profiles of the one-component order parameter $[\eta(\xi)]$ in an asymmetric wall (solid curve) and in the reversed asymmetric wall (dotted curve) (p. 537) | html | pdf |
    - Fig. 3.4.4.9. Profiles of the one-component order parameter $[\eta(\xi)]$ in an asymmetric wall (solid curve) and in the reversed asymmetric wall (dotted curve) (p. 537) | html | pdf |
    - Fig. 3.4.4.10. A profile of the second order parameter component in a degenerate domain wall (p. 538) | html | pdf |
    - Fig. 3.4.4.11. Microscopic structure of a ferroelastic domain wall in calomel (p. 539) | html | pdf |
  - Tables
    - Table 3.4.2.1. Left and double cosets, principal and secondary domain states and their tensor parameters for the phase transition with $[G=4_z/m_zm_xm_{xy} ]$ and (p. 489) | html | pdf |
    - Table 3.4.2.2. Crystal systems, holohedries, crystal families and number of spontaneous strain components (p. 491) | html | pdf |
    - Table 3.4.2.3. Classification of ferroic phases according to ferroelastic and ferroelectric domain states (p. 492) | html | pdf |
    - Table 3.4.2.4. Morphic properties, tensor parameters, order parameters and domain states (p. 494) | html | pdf |
    - Table 3.4.2.5. Symbols of symmetry operations of the point group $[m\bar 3m ]$ (p. 495) | html | pdf |
    - Table 3.4.2.6. Symbols of symmetry operations of the point group (p. 496) | html | pdf |
    - Table 3.4.2.7. Group–subgroup symmetry descents $[G \supset F_1]$ (pp. 498-502) | html | pdf |
    - Table 3.4.3.1. Classification of domain pairs, ferroic phases and of switching (state shifts) (p. 510) | html | pdf |
    - Table 3.4.3.2. Four types of domain pairs (p. 511) | html | pdf |
    - Table 3.4.3.3. Decomposition of into left cosets of (p. 512) | html | pdf |
    - Table 3.4.3.4. Non-ferroelastic domain pairs, domain twin laws and distinction of non-ferroelastic domains (pp. 513-514) | html | pdf |
    - Table 3.4.3.5. Property tensors and switching fields (p. 514) | html | pdf |
    - Table 3.4.3.6. Ferroelastic domain pairs and twins with compatible domain walls (pp. 521-526) | html | pdf |
    - Table 3.4.3.7. Ferroelastic domain pairs with no compatible domain walls (p. 527) | html | pdf |
    - Table 3.4.4.1. Crystallographic layer groups with continuous translations (p. 530) | html | pdf |
    - Table 3.4.4.2. Action of four types of operations g on a twin $[({\bf S}_1 |{\bf n}| {\bf S}_j) ]$ (p. 531) | html | pdf |
    - Table 3.4.4.3. Classification of domain walls and simple twins (p. 532) | html | pdf |
    - Table 3.4.4.4. Symmetries of non-ferroelastic domain twins and walls (p. 533) | html | pdf |
    - Table 3.4.4.5. Symmetry properties of domain walls in α quartz (p. 534) | html | pdf |
    - Table 3.4.4.6. Symmetry properties of ferroelastic domain twins and compatible domain walls (p. 536) | html | pdf |
    - Table 3.4.4.7. Sectional layer groups and twin (wall) symmetries of the twin $[({\sf S}_1|[100];s{\bf d}|{\sf S}_3)]$ in a calomel crystal (p. 539) | html | pdf |