International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 2.1, p. 157

Section 2.1.3.6.6. Trigonal R (rhombohedral) space groups

Th. Hahna and A. Looijenga-Vosb

2.1.3.6.6. Trigonal R (rhombohedral) space groups

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The seven rhombohedral space groups are treated in two versions, the first based on `hexagonal axes' (obverse setting), the second on `rhombohedral axes' (cf. Sections 2.1.1.2[link] and 2.1.3.2[link]). The pairs of diagrams are similar to those in IT (1952)[link] and IT A (2002)[link]; the left or top one displays the symmetry elements, the right or bottom one the general position. This is illustrated in Fig. 2.1.3.9[link], which gives the axes a and b of the triple hexagonal cell and the projections of the axes of the primitive rhombohedral cell, labelled arh, brh and crh. For convenience, all `heights' in the space-group diagrams are fractions of the hexagonal c axis. For `hexagonal axes', the projection direction is [001], for `rhombohedral axes' it is [111]. In the general-position diagrams, the circles drawn in heavier lines represent atoms that lie within the primitive rhombohedral cell (provided the symbol `−' is read as [1 - z] rather than as [- z]).

[Figure 2.1.3.9]

Figure 2.1.3.9 | top | pdf |

Rhombohedral space groups. Obverse triple hexagonal cell with `hexagonal axes' a, b and primitive rhombohedral cell with projections of `rhombohedral axes' arh, brh, crh. Note: In the actual space-group diagrams the edges of the primitive rhombohedral cell (dashed lines) are only indicated in the general-position diagram of the rhombohedral-axes description ([\hbox{\sf G}] = general-position diagram).

The symmetry-element diagrams for the hexagonal and the rhombohedral descriptions of a space group are the same. The edges of the primitive rhombohedral cell (cf. Fig. 2.1.3.9[link]) are only indicated in the general-position diagram of the rhombohedral description.

References

International Tables for Crystallography (2002). Vol. A, 5th ed., edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers. [Abbreviated as IT A (2002).]
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).]








































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