International Tables for Crystallography

Topics on space groups treated in Volumes A1 and E of International Tables for Crystallography
H. Wondratschek, U. Müller, D. B. Litvin and V. Kopský. International Tables for Crystallography (2016). Vol. A, ch. 1.7, pp. 132-139  [ doi:10.1107/97809553602060000925 ]


The subgroups and supergroups of the space groups were listed as part of the space-group tables in the first to fifth editions of Volume A (from 1983 to 2005), but the listing was incomplete and lacked additional information. Therefore, they are no longer included in this sixth edition. Instead they now form the separate Volume A1. There, a complete listing is given of all maximal subgroups of all space groups, including information on any basis transformations and origin shifts that may be involved. The listing in Volume A1 also includes the infinitely many isomorphic subgroups, specified in a parametrized form. In addition, for every Wyckoff position of every space group there is a listing of the Wyckoff positions that result therefrom in all maximal subgroups. This chapter gives a short outline of the content of Volume A1 with illustrative examples of the uses of the data listed in it, and also of the content of Volume E, in which two- and three-dimensional subperiodic groups are treated. Volume E also offers a comprehensive study of the relationship between the space group of a crystal and the subperiodic-group symmetry of planes that transect the crystal. Illustrative examples of the application of this relationship in determining the layer-group symmetry of such planes in crystals and of domain walls are discussed.

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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The series consists of eight volumes and 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.