Historical note and arrangement of the tables

Bertaut, E. F.

doi:10.1107/97809553602060000509

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

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International Tables for Crystallography (2006). Vol. A. ch. 4.3, pp. 68-70

Section 4.3.3.1. Historical note and arrangement of the tables

E. F. Bertaut^a ^‡

^a Laboratoire de Cristallographie, CNRS, Grenoble, France

4.3.3.1. Historical note and arrangement of the tables

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The synoptic table of IT (1935) contained space-group symbols for the six orthorhombic `settings ', corresponding to the six permutations of the basis vectors a, b, c. In IT (1952), left-handed systems like $[\bar{\bf c}\bf{ba}]$ were changed to right-handed systems by reversing the orientation of the c axis, as in $[{\bf cba}]$ . Note that reversal of two axes does not change the handedness of a coordinate system, so that the settings $[{\bar{\bf c}}{\bf ba}]$ , $[{\bf c}{\bar{\bf b}}{\bf a}]$ , $[{\bf cb}{\bar{\bf a}}]$ and $[{\bar{\bf c}}{\bar{\bf b}}{\bar{\bf a}}]$ are equivalent in this respect. The tabulation thus deals with the $[6 \times 4 = 24]$ possible right-handed settings. For further details see Section 2.2.6.4.

An important innovation of IT (1952) was the introduction of extended symbols for the centred groups A, B, C, I, F. These symbols are systematically developed in Table 4.3.2.1. Settings which permute the two axes a and b are listed side by side so that the two C settings appear together, followed by the two A and the two B settings.

In crystal classes mm2 and 222, the last symmetry element is the product of the first two and thus is not independent. It was omitted in the short Hermann–Mauguin symbols of IT (1935) for all space groups of class mm2, but was restored in IT (1952). In space groups of class 222, the last symmetry element cannot be omitted (see examples below).

For the new `double' glide plane symbol `e', see the Foreword to the Fourth Edition (IT 1995) and Section 1.3.2, Note (x) .

References

Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). 1. Band, edited by C. Hermann. Berlin: Borntraeger. [Revised edition: Ann Arbor: Edwards (1944). Abbreviated as IT (1935).]Google Scholar

International Tables for Crystallography (1995). Vol. A, fourth, revised ed., edited by Th. Hahn. Dordrecht: Kluwer Academic Publishers. [Abbreviated as IT (1995).]Google Scholar

International Tables for X-ray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Abbreviated as IT (1952).]Google Scholar

International Tables for Crystallography (2006). Vol. A. ch. 4.3, pp. 68-70