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, pp. 781-782
Section 3.3.3.3. Non-symbolized symmetry elements^{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 |
Certain symmetry elements are not given explicitly in the full symbol because they can easily be derived. They are:
Example
The full symbol of space group Imma (74) is
The I-centring operation introduces additional rotation axes and glide planes for all three sets of lattice symmetry directions. The extended Hermann–Mauguin symbol is This symbol shows immediately the eight subgroups with a P lattice corresponding to point group mmm:
References
International Tables for X-ray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Revised editions: 1965, 1969 and 1977. Abbreviated as IT (1952).]Bertaut, E. F. (1976). Study of principal subgroups and their general positions in C and I groups of class mmm – D_{2h}. Acta Cryst. A32, 380–387.
Hermann, C. (1929). Zur systematischen Strukturtheorie IV. Untergruppen. Z. Kristallogr. 69, 533–555.
Zimmermann, H. (1976). Ableitung der Raumgruppen aus ihren klassengleichen Untergruppenbeziehungen. Z. Kristallogr. 143, 485–515.