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Equivalence of superspace groups.
- Source :
-
Acta Crystallographica: Section A (Wiley-Blackwell) . Jan2013, Vol. 69 Issue 1, p75-90. 16p. 4 Diagrams, 6 Charts. - Publication Year :
- 2013
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01087673
- Volume :
- 69
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Acta Crystallographica: Section A (Wiley-Blackwell)
- Publication Type :
- Academic Journal
- Accession number :
- 84483098
- Full Text :
- https://doi.org/10.1107/S0108767312041657