Acta Cryst. (2013). A69, 75-90 [ doi:10.1107/S0108767312041657 ]
Abstract: An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool on , providing the transformation of any user-given superspace group to the standard setting of this superspace group in . It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic structure unit cell) and a transformation of the internal-space lattice vectors (new modulation wavevectors are linear combinations of old modulation wavevectors plus a three-dimensional reciprocal-lattice vector). The need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases are illustrated by an analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them. A compilation is provided of standard settings of compounds with two- and three-dimensional modulations. The problem of settings of superspace groups is discussed for incommensurate composite crystals and for chiral superspace groups.
Keywords: symmetry; superspace groups; two-dimensionally modulated crystals; three-dimensionally modulated crystals.
Zip compressed file (1080.0 kbytes)
Portable Document Format (PDF) file
To open or display or play some files, you may need to set your browser up to use the appropriate software. See the full list of file types for an explanation of the different file types and their related mime types and, where available links to sites from where the appropriate software may be obtained.
The download button will force most browsers to prompt for a file name to store the data on your hard disk.
Where possible, images are represented by thumbnails.
Copyright © International Union of Crystallography