International Tables for Crystallography (2006). Vol. C, ch. 9.8, pp. 907-955
doi: 10.1107/97809553602060000624

Chapter 9.8. Incommensurate and commensurate modulated structures

Contents

  • 9.8. Incommensurate and commensurate modulated structures  (pp. 907-955) | html | pdf | chapter contents |
    • 9.8.1. Introduction  (pp. 907-913) | html | pdf |
      • 9.8.1.1. Modulated crystal structures  (pp. 907-908) | html | pdf |
      • 9.8.1.2. The basic ideas of higher-dimensional crystallography  (pp. 908-909) | html | pdf |
      • 9.8.1.3. The simple case of a displacively modulated crystal  (pp. 909-910) | html | pdf |
        • 9.8.1.3.1. The diffraction pattern  (p. 909) | html | pdf |
        • 9.8.1.3.2. The symmetry  (pp. 909-910) | html | pdf |
      • 9.8.1.4. Basic symmetry considerations  (pp. 910-913) | html | pdf |
        • 9.8.1.4.1. Bravais classes of vector modules  (pp. 910-911) | html | pdf |
        • 9.8.1.4.2. Description in four dimensions  (p. 911) | html | pdf |
        • 9.8.1.4.3. Four-dimensional crystallography  (pp. 911-912) | html | pdf |
        • 9.8.1.4.4. Generalized nomenclature  (p. 912) | html | pdf |
        • 9.8.1.4.5. Four-dimensional space groups  (pp. 912-913) | html | pdf |
      • 9.8.1.5. Occupation modulation  (p. 913) | html | pdf |
    • 9.8.2. Outline for a superspace-group determination  (pp. 913-915) | html | pdf |
    • 9.8.3. Introduction to the tables  (pp. 915-937) | html | pdf |
      • 9.8.3.1. Tables of Bravais lattices  (pp. 915-916) | html | pdf |
      • 9.8.3.2. Table for geometric and arithmetic crystal classes  (p. 916) | html | pdf |
      • 9.8.3.3. Tables of superspace groups  (pp. 916-935) | html | pdf |
        • 9.8.3.3.1. Symmetry elements  (pp. 916-921) | html | pdf |
        • 9.8.3.3.2. Reflection conditions  (pp. 921-935) | html | pdf |
      • 9.8.3.4. Guide to the use of the tables  (pp. 935-936) | html | pdf |
      • 9.8.3.5. Examples  (p. 936) | html | pdf |
      • 9.8.3.6. Ambiguities in the notation  (pp. 936-937) | html | pdf |
    • 9.8.4. Theoretical foundation  (pp. 937-945) | html | pdf |
      • 9.8.4.1. Lattices and metric  (pp. 937-938) | html | pdf |
      • 9.8.4.2. Point groups  (pp. 938-939) | html | pdf |
        • 9.8.4.2.1. Laue class  (pp. 938-939) | html | pdf |
        • 9.8.4.2.2. Geometric and arithmetic crystal classes  (p. 939) | html | pdf |
      • 9.8.4.3. Systems and Bravais classes  (pp. 939-940) | html | pdf |
        • 9.8.4.3.1. Holohedry  (pp. 939-940) | html | pdf |
        • 9.8.4.3.2. Crystallographic systems  (p. 940) | html | pdf |
        • 9.8.4.3.3. Bravais classes  (p. 940) | html | pdf |
      • 9.8.4.4. Superspace groups  (pp. 940-941) | html | pdf |
        • 9.8.4.4.1. Symmetry elements  (p. 940) | html | pdf |
        • 9.8.4.4.2. Equivalent positions and modulation relations  (pp. 940-941) | html | pdf |
        • 9.8.4.4.3. Structure factor  (p. 941) | html | pdf |
    • 9.8.5. Generalizations  (pp. 941-943) | html | pdf |
      • 9.8.5.1. Incommensurate composite crystal structures  (pp. 941-942) | html | pdf |
      • 9.8.5.2. The incommensurate versus the commensurate case  (pp. 942-943) | html | pdf |
    • Appendix 9.8.1. Glossary of symbols  (pp. 943-944) | html | pdf |
    • Appendix 9.8.2. Basic definitions  (pp. 944-945) | html | pdf |
    • References | html | pdf |
    • Tables
      • Table 9.8.3.1. (2 + 1)- and (2 + 2)-Dimensional Bravais classes for incommensurate structures  (pp. 915-916) | html | pdf |
      • Table 9.8.3.2. (3 + 1)-Dimensional Bravais classes for incommensurate and commensurate structures  (pp. 917-918) | html | pdf |
      • Table 9.8.3.3. (3 + 1)-Dimensional point groups and arithmetic crystal classes  (pp. 919-920) | html | pdf |
      • Table 9.8.3.4. (2 + 1)- and (2 + 2)-Dimensional superspace groups  (pp. 920-921) | html | pdf |
      • Table 9.8.3.5. (3 + 1)-Dimensional superspace groups superspace group finder   (pp. 922-934) | html | pdf |
      • Table 9.8.3.6. Centring reflection conditions for (3 + 1)-dimensional Bravais classes  (p. 935) | html | pdf |