Tables for
Volume G
Definition and exchange of crystallographic data
Edited by S. R. Hall and B. McMahon

International Tables for Crystallography (2006). Vol. G. ch. 3.4, pp. 137-138

Section Description of symmetry

G. Madariagaa*

aDepartamento de Física de la Materia Condensada, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
Correspondence e-mail: Description of symmetry

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The symmetry of a modulated or composite structure is described by a superspace group which leaves the (3 + d)-dimensional embedding of the structure invariant. Superspace is built of two orthogonal subspaces and both of them are kept invariant separately by the superspace symmetry operations. (In reciprocal space this means that, for these structures, main reflections and satellite reflections are never transformed into one another by superspace symmetry operations.) Consequently, superspace groups are not general (3 + d)-dimensional space groups. The standard notation for superspace groups only covers the one-dimensional superspace groups, which are listed in Janssen et al. (2004[link]). As a consequence, msCIFs must include a list of all the symmetry operations in an (x, y, z) format (using as symbols [x_{1}\ldots x_{3+d}]) similar to that used in the core CIF dictionary. Superspace-group names for one-dimensional structures can be expressed either according to Janssen et al. (2004[link]) or according to the original notation of de Wolff et al. (1981[link]). Alternative names or higher-dimensional superspace groups can also be included, but not parsed.

In the particular case of K2SeO4, the superspace group is [P^{Pnma}_{\;\overline{1}ss}] (de Wolff et al., 1981[link]) or [Pnma(\alpha00)0ss] (Janssen et al., 2004[link]). This information would appear in a CIF as shown in Example[link].

Example Symmetry description of a superspace group.

[Scheme scheme41]


First citationJanssen, T., Janner, A., Looijenga-Vos, A. & de Wolff, P. M. (2004). Incommensurate and commensurate modulated structures. International Tables for Crystallography, Volume C, Mathematical, chemical and physical tables, 3rd ed., edited by E. Prince, ch. 9.8. Dordrecht: Kluwer Academic Publishers.Google Scholar
First citationWolff, P. M. de, Janssen, T. & Janner, A. (1981). The superspace groups for incommensurate crystal structures with a one-dimensional modulation. Acta Cryst. A37, 625–636.Google Scholar

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