International Tables for Crystallography

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 ]


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 series consists of eight volumes and 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.