International Tables for Crystallography

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Methods of space-group determination
U. Shmueli, H. D. Flack and J. C. H. Spence. International Tables for Crystallography (2016). Vol. A, ch. 1.6, pp. 107-131  [ doi:10.1107/97809553602060000924 ]

Abstract

This chapter describes several methods of symmetry determination of single-domain crystals. A detailed presentation of symmetry determination from diffraction data is 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. Several methods of retrieving symmetry information from a solved crystal structure are then described. This is followed by a discussion of chemical and physical restrictions on space-group symmetry, including some aids in symmetry determination, and by a brief section on pitfalls in space-group determination. The theoretical background of conditions for possible general reflections and their corresponding derivation are given along with a brief discussion of special reflection conditions. An extensive tabulation of general reflection conditions and possible space groups is presented. Other methods of space-group determination, including methods based on resonant scattering, are described, including approaches to space-group determination in macromolecular crystallography and in powder diffraction. The chapter concludes with a description and illustration of symmetry determination based on electron-diffraction methods, principally using convergent-beam electron diffraction.


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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.