International Tables for Crystallography (2010). Vol. B. ch. 1.5, pp. 175-192 | 1 | 2 |
https://doi.org/10.1107/97809553602060000762

Chapter 1.5. Crystallographic viewpoints in the classification of space-group representations

Contents

1.5. Crystallographic viewpoints in the classification of space-group representations (pp. 175-192) | html | pdf | chapter contents |
M. I. Aroyo and H. Wondratschek
- 1.5.1. List of abbreviations and symbols (p. 175) | html | pdf |
- 1.5.2. Introduction (pp. 175-176) | html | pdf |
- 1.5.3. Basic concepts (pp. 176-179) | html | pdf |
  - 1.5.3.1. Representations of finite groups (p. 176) | html | pdf |
  - 1.5.3.2. Space groups (pp. 176-177) | html | pdf |
  - 1.5.3.3. Representations of the translation group $[{\cal T}]$ and the reciprocal lattice (pp. 177-178) | html | pdf |
  - 1.5.3.4. Irreducible representations of space groups and the reciprocal-space group (pp. 178-179) | html | pdf |
- 1.5.4. Conventions in the classification of space-group irreps (pp. 179-181) | html | pdf |
  - 1.5.4.1. Fundamental regions (p. 179) | html | pdf |
  - 1.5.4.2. Minimal domains (pp. 179-180) | html | pdf |
  - 1.5.4.3. Wintgen positions (pp. 180-181) | html | pdf |
- 1.5.5. Examples and discussion (pp. 181-191) | html | pdf |
  - 1.5.5.1. Guide to the figures (pp. 182-184) | html | pdf |
  - 1.5.5.2. Guide to the k-vector tables (pp. 184-188) | html | pdf |
  - 1.5.5.3. Figures and tables (pp. 188-189) | html | pdf |
  - 1.5.5.4. Discussion (pp. 189-191) | html | pdf |
    - 1.5.5.4.1. Representation domains and asymmetric units (pp. 189-190) | html | pdf |
    - 1.5.5.4.2. Splitting of k-vector types (p. 190) | html | pdf |
    - 1.5.5.4.3. k-vector types for non-holosymmetric space groups (p. 190) | html | pdf |
    - 1.5.5.4.4. Ranges of independent parameters (pp. 190-191) | html | pdf |
- 1.5.6. Conclusions (p. 191) | html | pdf |
- Appendix 1.5.1. Reciprocal-space groups $[({\cal G})^{*}]$ (p. 192) | html | pdf |
- References | html | pdf |
- Figures
  - Fig. 1.5.5.1. Brillouin zone with asymmetric unit and representation domain of CDML for arithmetic crystal class $[m\overline{3}mI]$ (p. 183) | html | pdf |
  - Fig. 1.5.5.2. Brillouin zone with asymmetric unit and representation domain of CDML for arithmetic crystal class $[m\overline{3}I]$ (p. 184) | html | pdf |
  - Fig. 1.5.5.3. Brillouin zone with asymmetric unit and representation domain of CDML for arithmetic crystal class : $[c/a \,\lt \, 1]$ (p. 185) | html | pdf |
  - Fig. 1.5.5.4. Brillouin zone with asymmetric unit and representation domain of CDML for arithmetic crystal class : $[c/a\,\gt \, 1]$ (p. 186) | html | pdf |
  - Fig. 1.5.5.5. Brillouin zone with asymmetric unit and representation domain of CDML for arithmetic crystal class : $[a^{-2} \,\lt \, b^{-2}+c^{-2}]$ , $[b^{-2} \,\lt \, c^{-2}+a^{-2}]$ and $[c^{-2} \,\lt \, a^{-2}+b^{-2}]$ (p. 187) | html | pdf |
  - Fig. 1.5.5.6. Brillouin zone with asymmetric unit and representation domain of CDML for arithmetic crystal class : $[c^{-2}\,\gt \, a^{-2}+b^{-2}]$ (p. 188) | html | pdf |
  - Fig. 1.5.5.7. Brillouin zone with asymmetric unit and representation domain of CDML for arithmetic crystal class : $[a^{-2}\,\gt \, b^{-2}+c^{-2}]$ (p. 189) | html | pdf |
- Tables
  - Table 1.5.4.1. Conventional coefficients $[(k_{i})^{T}]$ of k expressed by the adjusted coefficients $[(k_{ai})]$ of IT A for the different Bravais types of lattices in direct space (p. 181) | html | pdf |
  - Table 1.5.4.2. Primitive coefficients $[(k_{pi})^{T}]$ of k from CDML expressed by the adjusted coefficients $[(k_{ai})]$ of IT A for the different Bravais types of lattices in direct space (p. 181) | html | pdf |
  - Table 1.5.5.1. List of k-vector types for arithmetic crystal class $[m\overline{3}mI]$ (p. 183) | html | pdf |
  - Table 1.5.5.2. List of k-vector types for arithmetic crystal class $[m\overline{3}I]$ (p. 184) | html | pdf |
  - Table 1.5.5.3. List of k-vector types for arithmetic crystal class : $[c/a \,\lt\, 1]$ (p. 185) | html | pdf |
  - Table 1.5.5.4. List of k-vector types for arithmetic crystal class : $[c/a \,\gt\, 1]$ (p. 186) | html | pdf |
  - Table 1.5.5.5. List of k-vector types for arithmetic crystal class : $[a^{-2} \,\lt\, b^{-2}+c^{-2}]$ , $[b^{-2} \,\lt\, c^{-2}+a^{-2}]$ and $[c^{-2} \,\lt\, a^{-2}+b^{-2}]$ (p. 187) | html | pdf |
  - Table 1.5.5.6. List of k-vector types for arithmetic crystal class : $[c^{-2}>a^{-2}+b^{-2}]$ (p. 188) | html | pdf |
  - Table 1.5.5.7. List of k-vector types for arithmetic crystal class : $[a^{-2}\,\gt \, b^{-2}+c^{-2}]$ (p. 189) | html | pdf |