Chapter 3.1 Space‐group determination and diffraction symbols

Space‐group symmetry

First Online Edition (2006)

Part 3. Determination of space groups

  1. A. Looijenga‐Vos1,
  2. M. J. Buerger2

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000506

International Tables for Crystallography

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.

Author Information

  1. 1

    Laboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands

  2. 2

    Department of Earth and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

Publication History

  1. 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 equation image due to anomalous dispersion are discussed, it is assumed that Friedel’s rule holds, i.e. that equation image. This implies that the reciprocal lattice weighted by equation image 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