International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.3, p. 780

Section 3.3.2.5. International short symbols

H. Burzlaffa and H. Zimmermannb*

aUniversität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and bInstitut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany
Correspondence e-mail:  helmuth.zimmermann@krist.uni-erlangen.de

3.3.2.5. International short symbols

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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[link] ) 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:

  • (i) The glide/screw parts of generators and indicators are symbolized by applying the symbols for glide planes in Table 3.3.2.1[link] and the appropriate rules for screw rotations.

  • (ii) The generators are chosen in such a way that the related symmetry elements do intersect as far as possible. Exceptions may occur for space groups related to the pure rotation point groups 222, 422, 622, 23 and 432. In these cases, the axes of the generators may or may not intersect.

  • (iii) Subgroups of lattice point groups may have lattice symmetry directions with which no symmetry elements are associated. Such symmetry directions are symbolized by `1'. This symbol can only be omitted if no ambiguity arises, e.g. [P4/m11] is reduced to [P4/m]. P31m and P3m1, however, cannot be reduced. The use of the symbol `1' is discussed by Buerger (1967[link]) and Donnay (1969[link], 1977[link]).

Example

Again consider space group [D_{2h}^{26}\ (72)]. 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[link]) 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.








































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