International Tables for Crystallography (2006). Vol. B, ch. 1.5, pp. 162-188
doi: 10.1107/97809553602060000553

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. 162-188) | html | pdf | chapter contents |
    M. I. Aroyo and H. Wondratschek
    • 1.5.1. List of symbols  (p. 162) | html | pdf |
    • 1.5.2. Introduction  (p. 162) | html | pdf |
    • 1.5.3. Basic concepts  (pp. 162-165) | html | pdf |
      • 1.5.3.1. Representations of finite groups  (pp. 162-163) | html | pdf |
      • 1.5.3.2. Space groups  (pp. 163-164) | html | pdf |
      • 1.5.3.3. Representations of the translation group [{\cal T}] and the reciprocal lattice  (pp. 164-165) | html | pdf |
      • 1.5.3.4. Irreducible representations of space groups and the reciprocal-space group  (p. 165) | html | pdf |
    • 1.5.4. Conventions in the classification of space-group irreps  (pp. 165-168) | html | pdf |
      • 1.5.4.1. Fundamental regions  (pp. 165-166) | html | pdf |
      • 1.5.4.2. Minimal domains  (pp. 166-167) | html | pdf |
      • 1.5.4.3. Wintgen positions  (pp. 167-168) | html | pdf |
    • 1.5.5. Examples and conclusions  (pp. 168-176) | html | pdf |
      • 1.5.5.1. Examples  (p. 168) | html | pdf |
      • 1.5.5.2. Results  (pp. 169-171) | html | pdf |
      • 1.5.5.3. Parameter ranges  (pp. 171-172) | html | pdf |
      • 1.5.5.4. Conclusions  (pp. 172-176) | html | pdf |
    • Appendix 1.5.1. Reciprocal-space groups [{\cal G}^{*}]  (p. 176) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 1.5.5.1. Symmorphic space group [Fm\bar{3}m]  (p. 169) | html | pdf |
      • Fig. 1.5.5.2. Symmorphic space group [F\bar{3}m]  (p. 171) | html | pdf |
      • Fig. 1.5.5.3. ( a ), ( b ) Symmorphic space group [I4/mmm]  (p. 173) | html | pdf |
      • Fig. 1.5.5.4. Symmorphic space group Imm 2  (p. 177) | 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. 167) | 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. 167) | html | pdf |
      • Table 1.5.5.1. The k -vector types for the space groups [Im\bar{3} m] and [Ia\bar{3} d]   (p. 168) | html | pdf |
      • Table 1.5.5.2. The k -vector types for the space groups [Im\bar{3}] and [Ia\bar{3}]   (p. 170) | html | pdf |
      • Table 1.5.5.3. The k -vector types for the space groups [I4/mmm], [I4/mcm], [I4_{1}/amd] and [I4_{1}/acd]   (p. 172) | html | pdf |
      • Table 1.5.5.4. The k -vector types for the space groups Fmm 2 and Fdd 2  (pp. 174-175) | html | pdf |