(International Tables) Physical properties of crystals

International Tables for Crystallography
Volume D: Physical properties of crystals

First online edition (2006) ISBN: 978-1-4020-0714-9 eISBN: 978-1-4020-5409-9 doi: 10.1107/97809553602060000104

Edited by A. Authier

Preface (p. xi) | html | pdf |
A. Authier

Part 1. Tensorial aspects of physical properties
- 1.1. Introduction to the properties of tensors (pp. 3-33) | 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 (p. 11) | 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 (p. 12) | 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  (p. 13) | 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 (pp. 14-15) | 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 $[{\bar 3}]$ , ; , $[{\bar 4}]$ , ; , $[{\bar 6}]$ , ; $[(A_{\infty}/M)C]$ , $[A_{\infty}]$   (p. 16) | 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 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. 72-98) | 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 homog

International Tables for CrystallographyVolume D: Physical properties of crystals

Edited by A. Authier

Contents

International Tables for Crystallography
Volume D: Physical properties of crystals