International
Tables for Crystallography Volume A Space-group symmetry Edited by M. I. Aroyo © International Union of Crystallography 2016 |
International Tables for Crystallography (2016). Vol. A, ch. 1.6, p. 107
Section 1.6.1. Overview^{a}School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel,^{b}Chimie minérale, analytique et appliquée, University of Geneva, Geneva, Switzerland, and ^{c}Department of Physics, Arizona State University, Rural Rd, Tempe, AZ 85287, USA |
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 1.6.2.1, 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 crystal structure in Section 1.6.2.2. Several methods of retrieving symmetry information from a solved crystal structure are then discussed (Section 1.6.2.3). This is followed by a discussion of chemical and physical restrictions on space-group symmetry (Section 1.6.2.4), including some aids in symmetry determination, and by a brief section on pitfalls in space-group determination (Section 1.6.2.5).
The following two sections deal with reflection conditions. Section 1.6.3 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 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. Section 1.6.5.1 deals with an account of methods of space-group determination based on resonant (also termed `anomalous') scattering. Section 1.6.5.2 is a brief description of approaches to space-group determination in macromolecular crystallography. Section 1.6.5.3 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), and principally focuses on convergent-beam electron diffraction.
This chapter deals only with single crystals. A supplement (Flack, 2015) deals with twinned crystals and those displaying a specialized metric.
References
Flack, H. D. (2015). Methods of space-group determination – a supplement dealing with twinned crystals and metric specialization. Acta Cryst. C71, 916–920.