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. 1.2, p. 4
https://doi.org/10.1107/97809553602060000501 Chapter 1.2. Printed symbols for conventional centring types^{a}Institut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany This chapter lists the printed symbols used for the centring types of lattices and cells throughout this volume. The list is accompanied by notes and cross-references to recent IUCr nomenclature reports. |
1.2.1. Printed symbols for the conventional centring types of one-, two- and three-dimensional cells
For `reflection conditions', see Tables 2.2.13.1 and 2.2.13.3 . For the new centring symbol S, see Note (iii) below.
^{†}The two-dimensional triple hexagonal cell h is an alternative description of the hexagonal plane net, as illustrated in Fig. 5.1.3.8
. It is not used for systematic plane-group description in this volume; it is introduced, however, in the sub- and supergroup entries of the plane-group tables (Part 6
). Plane-group symbols for the h cell are listed in Chapter 4.2
. Transformation matrices are contained in Table 5.1.3.1
.
^{‡}In the space-group tables (Part 7 ), as well as in IT (1935) and IT (1952), the seven rhombohedral R space groups are presented with two descriptions, one based on hexagonal axes (triple cell), one on rhombohedral axes (primitive cell). In the present volume, as well as in IT (1952), the obverse setting of the triple hexagonal cell R is used. Note that in IT (1935) the reverse setting was employed. The two settings are related by a rotation of the hexagonal cell with respect to the rhombohedral lattice around a threefold axis, involving a rotation angle of 60°, 180° or 300° (cf. Fig. 5.1.3.6 ). Further details may be found in Chapter 2.1 , Section 4.3.5 and Chapter 9.1 . Transformation matrices are contained in Table 5.1.3.1 . ^{§}The triple hexagonal cell H is an alternative description of the hexagonal Bravais lattice, as illustrated in Fig. 5.1.3.8 . It was used for systematic space-group description in IT (1935), but replaced by P in IT (1952). In the space-group tables of this volume (Part 7 ), it is only used in the sub- and supergroup entries (cf. Section 2.2.15 ). Space-group symbols for the H cell are listed in Section 4.3.5 . Transformation matrices are contained in Table 5.1.3.1 . |
References
Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). I. Band, edited by C. Hermann. Berlin: Borntraeger. [Reprint with corrections: Ann Arbor: Edwards (1944). Abbreviated as IT (1935).]International Tables for X-ray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Abbreviated as IT (1952).]
Wolff, P. M. de, Belov, N. V., Bertaut, E. F., Buerger, M. J., Donnay, J. D. H., Fischer, W., Hahn, Th., Koptsik, V. A., Mackay, A. L., Wondratschek, H., Wilson, A. J. C. & Abrahams, S. C. (1985). Nomenclature for crystal families, Bravais-lattice types and arithmetic classes. Report of the International Union of Crystallography Ad-hoc Committee on the Nomenclature of Symmetry. Acta Cryst. A41, 278–280.