International
Tables for Crystallography Volume A Space-group symmetry Edited by M. I. Aroyo © International Union of Crystallography 2016 |
International Tables for Crystallography (2016). Vol. A, ch. 3.3, p. 779
Section 3.3.2.1. Introduction^{a}Universität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and ^{b}Institut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany |
Each space group is related to a crystallographic point group. Space-group symbols, therefore, can be obtained by a modification of point-group symbols. The simplest modification which merely gives an enumeration of the space-group types (cf. Section 1.3.4.1 ) has been used by Schoenflies. The Shubnikov and Hermann–Mauguin symbols, however, reveal the glide or screw components of the symmetry operations and are designed in such a way that the nature of the symmetry elements and their relative locations can be deduced from the symbol. [A detailed discussion and listings of computer-adapted space-group symbols implemented in crystallographic software, such as the so-called Hall symbols (Hall, 1981a,b) or explicit symbols (Shmueli, 1984), can be found in Chapter 1.4 of International Tables for Crystallography, Volume B (2008).]
References
International Tables for Crystallography (2008). Vol. B, Reciprocal Space. Edited by U. Shmueli, 3rd ed. Heidelberg: Springer.Hall, S. R. (1981a). Space-group notation with an explicit origin. Acta Cryst. A37, 517–525.
Hall, S. R. (1981b). Space-group notation with an explicit origin; erratum. Acta Cryst. A37, 921.
Shmueli, U. (1984). Space-group algorithms. I. The space group and its symmetry elements. Acta Cryst. A40, 559–567.