Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 1.6, p. 107

Section 1.6.1. Overview

U. Shmueli,a* H. D. Flackb and J. C. H. Spencec

aSchool of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel,bChimie minérale, analytique et appliquée, University of Geneva, Geneva, Switzerland, and cDepartment of Physics, Arizona State University, Rural Rd, Tempe, AZ 85287, USA
Correspondence e-mail:

1.6.1. Overview

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This chapter describes and discusses several methods of symmetry determination of single-domain crystals. A detailed presentation of symmetry determination from diffraction data is given in Section[link], followed by a brief discussion of intensity statistics, ideal as well as non-ideal, with an application of the latter to real intensity data from a [P\overline{1}] crystal structure in Section[link]. Several methods of retrieving symmetry information from a solved crystal structure are then discussed (Section[link]). This is followed by a discussion of chemical and physical restrictions on space-group symmetry (Section[link]), including some aids in symmetry determination, and by a brief section on pitfalls in space-group determination (Section[link]).

The following two sections deal with reflection conditions. Section 1.6.3[link] presents the theoretical background of conditions for possible general reflections and their corresponding derivation. A brief discussion of special reflection conditions is included. Section 1.6.4[link] presents an extensive tabulation of general reflection conditions and possible space groups.

Other methods of space-group determination are presented in Section 1.6.5[link]. Section[link] deals with an account of methods of space-group determination based on resonant (also termed `anomalous') scattering. Section[link] is a brief description of approaches to space-group determination in macromolecular crystallography. Section[link] deals with corresponding approaches in powder-diffraction methods.

The chapter concludes with a description and illustration of symmetry determination based on electron-diffraction methods (Section 1.6.6[link]), and principally focuses on convergent-beam electron diffraction.

This chapter deals only with single crystals. A supplement (Flack, 2015[link]) deals with twinned crystals and those displaying a specialized metric.


Flack, H. D. (2015). Methods of space-group determination – a supplement dealing with twinned crystals and metric specialization. Acta Cryst. C71, 916–920.

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