International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

International Tables for Crystallography (2006). Vol. A, ch. 1.4, p. 8

Section 1.4.4. Notes on graphical symbols of symmetry planes

Th. Hahna*

aInstitut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany
Correspondence e-mail: hahn@xtal.rwth-aachen.de

1.4.4. Notes on graphical symbols of symmetry planes

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  • (i) The graphical symbols and their explanations (columns 2 and 3) are independent of the projection direction and the labelling of the basis vectors. They are, therefore, applicable to any projection diagram of a space group. The printed symbols of glide planes (column 4), however, may change with a change of the basis vectors, as shown by the following example.

    In the rhombohedral space groups [R3c] (161) and [R\bar{3}c] (167), the dotted line refers to a c glide when described with `hexagonal axes' and projected along [001]; for a description with `rhombohedral axes' and projection along [111], the same dotted glide plane would be called n. The dash-dotted n glide in the hexagonal description becomes an a, b or c glide in the rhombohedral description; cf. the first footnote[link] in Section 1.3.1.

  • (ii) The graphical symbols for glide planes in column 2 are not only used for the glide planes defined in Chapter 1.3[link] , but also for the further glide planes g which are mentioned in Section 1.3.2[link] (Note x[link] ) and listed in Table 4.3.2.1[link] ; they are explained in Sections 2.2.9[link] and 11.1.2[link] .

  • (iii) In monoclinic space groups, the `parallel' glide vector of a glide plane may be along a lattice translation vector which is inclined to the projection plane.

  • (iv) In 1992, the International Union of Crystallography introduced the `double' glide plane e and the graphical symbol ..--..-- for e glide planes oriented `normal' and `inclined' to the plane of projection (de Wolff et al., 1992[link]); for details of e glide planes see Chapter 1.3[link] . Note that the graphical symbol [\downarrow\hskip -6pt\raise5pt\hbox{$\rightarrow$}] for e glide planes oriented `parallel' to the projection plane has already been used in IT (1935)[link] and IT (1952)[link].

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, Billiet, Y., Donnay, J. D. H., Fischer, W., Galiulin, R. B., Glazer, A. M., Hahn, Th., Senechal, M., Shoemaker, D. P., Wondratschek, H., Wilson, A. J. C. & Abrahams, S. C. (1992). Symbols for symmetry elements and symmetry operations. Final Report of the International Union of Crystallography Ad-hoc Committee on the Nomenclature of Symmetry. Acta Cryst. A48, 727–732.








































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