Chapter

Chapter 9.8 Incommensurate and commensurate modulated structures

Mathematical, physical and chemical tables

First Online Edition (2006)

Part 9. Basic structural features

  1. T. Janssen1,
  2. A. Janner1,
  3. A. Looijenga-Vos2,
  4. P. M. de Wolff3

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000624

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Janssen, T., Janner, A., Looijenga-Vos, A. and de Wolff, P. M. 2006. Incommensurate and commensurate modulated structures. International Tables for Crystallography. C:9:9.8:907–955.

Author Information

  1. 1

    Institute for Theoretical Physics, University of Nijmegen, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands

  2. 2

    Roland Holstlaan 908, NL-2624 JK Delft, The Netherlands

  3. 3

    Meermanstraat 126, 2614 AM, Delft, The Netherlands

Publication History

  1. Published Online: 1 JAN 2006

Abstract

This chapter discusses incommensurate and commensurate modulated structures. After an introduction to the concepts used to describe modulated structures, including the basic ideas of higher-dimensional crystallography, four-dimensional space groups and displacive and occupational modulation, superspace-group determination is outlined. Tables of Bravais lattices, geometric and arithmetic crystal classes, and superspace groups (with reflection conditions) are presented and their use is illustrated with different examples.

Keywords:

  • arithmetic crystal classes;
  • basic structural features;
  • Bravais classes;
  • centring reflection conditions;
  • composite crystal structures;
  • crystallographic systems;
  • higher-dimensional crystallography;
  • holohedry;
  • incommensurate modulated structures;
  • lattices;
  • Laue classes;
  • modulated crystal structures;
  • modulations;
  • occupation modulations;
  • point groups;
  • structure factors;
  • superspace groups