International
Tables for Crystallography Volume A Space-group symmetry Edited by Th. Hahn © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. A, ch. 14.2, pp. 849-870
Section 14.2.3.1. Introduction^{a}Institut für Mineralogie, Petrologie und Kristallographie, Philipps-Universität, D-35032 Marburg, Germany |
For the study of relations between crystal structures, lattice-complex symbols are desirable that show as many relations between point configurations as possible. To this end, Hermann (1960) derived descriptive lattice-complex symbols that were further developed by Donnay et al. (1966) and completed by Fischer et al. (1973). These symbols describe the arrangements of the points in the point configurations and refer directly to the coordinate descriptions of the Wyckoff positions. Since a lattice complex, in general, contains Wyckoff positions with different coordinate descriptions, it may be represented by several different descriptive symbols. The symbols are further affected by the settings of the space group. The present section is restricted to the fundamental features of the descriptive symbols. Details have been described by Fischer et al. (1973). Tables 14.2.3.1 and 14.2.3.2 give for each Wyckoff position of a plane group or a space group, respectively, the multiplicity, the Wyckoff letter, the oriented site symmetry, the reference symbol of the corresponding lattice complex and the descriptive symbol.^{1} The comparatively short descriptive symbols condense complicated verbal descriptions of the point configurations of lattice complexes.
References
Donnay, J. D. H., Hellner, E. & Niggli, A. (1966). Symbolism for lattice complexes, revised by a Kiel symposium. Z. Kristallogr. 123, 255–262.Fischer, W., Burzlaff, H., Hellner, E. & Donnay, J. D. H. (1973). Space groups and lattice complexes. NBS Monograph No. 134. Washington: National Bureau of Standards.
Hermann, C. (1960). Zur Nomenklatur der Gitterkomplexe. Z. Kristallogr. 113, 142–154.