International Tables for Crystallography

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Space-group determination and diffraction symbols
A. Looijenga-Vos and M. J. Buerger. International Tables for Crystallography (2006). Vol. A, ch. 3.1, pp. 44-54  [ doi:10.1107/97809553602060000506 ]

Abstract

In this chapter, the determination of space groups from the Laue symmetry and the reflection conditions, as obtained from diffraction patterns, is discussed. Apart from a small section where differences between reflections hkl and [\bar{h}\bar{k}{\hbox to 1pt{}}\bar{l}] due to anomalous dispersion are discussed, it is assumed that Friedel's rule holds, i.e. that [|F(hkl)|^{2} = |F(\bar{h}\bar{k}{\hbox to 1pt{}}\bar{l})|^{2}]. This implies that the reciprocal lattice weighted by [|F(hkl)|^{2}] has an inversion centre, even if this is not the case for the crystal under consideration. Accordingly, the symmetry of the weighted reciprocal lattice belongs, as was discovered by Friedel, to one of the eleven Laue classes. Laue class plus reflection conditions in most cases do not uniquely specify the space group. A summary is given of methods that help to overcome these ambiguities, especially with respect to the presence or absence of an inversion centre in the crystal.


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.