Chapter 3.1 Space-group determination and diffraction symbols
First Online Edition (2006)
Part 3. Determination of space groups
Published Online: 1 JAN 2006
© International Union of Crystallography 2006
International Tables for Crystallography
How to Cite
Looijenga-Vos, A. and Buerger, M. J. 2006. Space-group determination and diffraction symbols. International Tables for Crystallography. A:3:3.1:44–54.
- Published Online: 1 JAN 2006
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 due to anomalous dispersion are discussed, it is assumed that Friedel’s rule holds, i.e. that . This implies that the reciprocal lattice weighted by 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.
- space-group determination;
- diffraction symbols;
- Laue classes;
- reflection conditions;
- systematic absences