International
Tables for Crystallography Volume E Subperiodic groups Edited by V. Kopský and D. B. Litvin © International Union of Crystallography 2010 |
International Tables for Crystallography (2010). Vol. E, ch. 1.2, p. 16
Section 1.2.11. Positions^{a}Freelance research scientist, Bajkalská 1170/28, 100 00 Prague 10, Czech Republic, and ^{b}Department of Physics, The Eberly College of Science, Penn State – Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA |
The entries under Positions (more explicitly called Wyckoff positions) consist of the General position (upper block) and the Special positions (blocks below). The columns in each block, from left to right, contain the following information for each Wyckoff position.
The two types of positions, general and special, are characterized as follows:
Example: Layer group (L18)
The general position 8f of this layer group contains eight equivalent points per cell each with site symmetry 1. The coordinate triplets of four points (1) to (4) are given explicitly, the coordinate triplets of the other four points are obtained by adding the components (1/2, 1/2, 0) of the c-centring translation to the coordinate triplets (1) to (4).
This layer group has five special positions with the Wyckoff letters a to e. The product of the multiplicity and the order of the site-symmetry group is the multiplicity of the general position. For position 4d, for example, the four equivalent points have the coordinates , , and . Since each point of position 4d is mapped onto itself by a twofold rotation, the multiplicity of the position is reduced from eight to four, whereas the order of the site symmetry is increased from one to two.