International
Tables for Crystallography Volume A Space-group symmetry Edited by M. I. Aroyo © International Union of Crystallography 2016 |
International Tables for Crystallography (2016). Vol. A, ch. 3.3, p. 780
Section 3.3.2.5. International short symbols^{a}Universität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and ^{b}Institut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany |
The international symbol of a space group consists of two parts, just like the Shubnikov symbol. The first part is a capital letter that describes the type of centring of the conventional cell. It is followed by a modified point-group symbol that refers to the lattice symmetry directions. Centring type and point-group symbol determine the Bravais type of the translation group (cf. Section 3.1.1 ) and thus the point group of the lattice and the appropriate lattice symmetry directions. To derive the short international symbol of a given space group, the short symbol of the related point group must be modified in such a way that not only the rotation parts of the generating operations but also their translation parts can be constructed. This can be done by the following procedure:
Example
Again consider space group . The space group contains glide planes c and b perpendicular to the primary set, c and a normal to the secondary set of symmetry directions and m and n perpendicular to the tertiary set. To determine the short symbol, one generator must be chosen from each pair. The standardization rules (see the following section) lead to the symbol Ibam.
References
Buerger, M. J. (1967). Some desirable modifications of the international symmetry symbols. Proc. Natl Acad. Sci. USA, 58, 1768–1773.Donnay, J. D. H. (1969). Symbolism of rhombohedral space groups in Miller axes. Acta Cryst. A25, 715–716.
Donnay, J. D. H. (1977). The structural classification of crystal point symmetries. Acta Cryst. A33, 979–984.