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

International Tables for Crystallography (2006). Vol. A, ch. 3.1, p. 44

Section 3.1.1. Introduction

A. Looijenga-Vosa and M. J. Buergerb§

aLaboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands, and bDepartment of Earth and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

3.1.1. Introduction

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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 Section 3.1.6.5[link], 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 (1913)[link], to one of the eleven Laue classes of Table 3.1.2.1[link]. As described in Section 3.1.5[link], Laue class plus reflection conditions in most cases do not uniquely specify the space group. Methods that help to overcome these ambiguities, especially with respect to the presence or absence of an inversion centre in the crystal, are summarized in Section 3.1.6[link].

References

Friedel, M. G. (1913). Sur les symétries cristallines que peut révéler la diffraction des rayons Röntgen. C. R. Acad. Sci. Paris, 157, 1533–1536.








































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