Equivalence of superspace groups

Titelangaben

van Smaalen, Sander ; Campbell, Branton J. ; Stokes, Harold T.:
Equivalence of superspace groups.
In: Acta Crystallographica Section A. Bd. 69 (2013) Heft 1 . - S. 75-90.
ISSN 1600-5724
DOI: https://doi.org/10.1107/S0108767312041657

Volltext

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Abstract

An algorithm is presented which determines the equivalence of two settings of a (3 + \it d)-dimensional superspace group (\it d = 1, 2, 3). The algorithm has been implemented as a web tool \tt findssg on \tt SSG(3+d)D, providing the transformation of any user-given superspace group to the standard setting of this superspace group in \tt SSG(3+d)D. 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.