International Tables for Crystallography

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Incommensurate and commensurate modulated structures
T. Janssen, A. Janner, A. Looijenga-Vos and P. M. de Wolff. International Tables for Crystallography (2006). Vol. C, ch. 9.8, pp. 907-955  [ doi:10.1107/97809553602060000624 ]

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.


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.