Section 3.4.4.2. Description of symmetry

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). As a consequence, msCIFs must include a list of all the symmetry operations in an (x, y, z) format (using as symbols ) 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) or according to the original notation of de Wolff et al. (1981). Alternative names or higher-dimensional superspace groups can also be included, but not parsed.

In the particular case of K₂SeO₄, the superspace group is (de Wolff et al., 1981) or (Janssen et al., 2004). This information would appear in a CIF as shown in Example 3.4.4.3.