Phasing methods for powder data

Powder diffractometry plays (and will probably continue to play in the near future) a central role in research and technology, because it allows us to investigate materials which are not available as a single crystal of adequate size and quality. Therefore, recently, much effort has been devoted to the development of powder diffraction. Improvements include the design of better instruments (e.g. optimized synchrotron radiation lines, time-of-flight technology at pulsed neutron sources, optics, generators, detectors), as well as more sophisticated methods for data analysis. As a result, in favourable cases, high quality powder patterns of proteins may be collected which contain sufficient information to allow identification of the unit cell and of the space group, a result unthinkable 30 years ago. This has opened the way for qualitative analysis and study of the polymorphism of macromolecules (Margiolaki et al., 2005; Collings et al., 2010). Advances in the experimental and the theoretical aspects of powder crystallography have been able to reduce losses of information from a powder pattern with respect to single crystal data, and have made ab initio crystal structure solution from powder experiments possible. The reader may deduce the increasing popularity of powder techniques from: (i) Table 1.11, where, among the CSD (Cambridge Structural Database), entries on 1 January 2012, 2354 powder diffraction studies were counted; (ii) Figure 12.1, where the cumulative statistics (up to the year 2006) on the number of structures solved via powder diffraction data is shown (SDPD database); (iii) Figure 12.2, where the statistics on the number of studies in the ICDD (Inorganic Crystal Structure Database) (to the year 2005) for different types of data is given. For the powder case, 21 472 cases are counted for which powder data have been used, mostly for refinement purposes. In this chapter, we will neglect experimental aspects, unless unrelated to the phasing problem. We will describe in Sections 12.2 to 12.5, the basic features of powder pattern diagrams, and in Sections 12.6 and 12.7, the procedures for full pattern indexing and space group determination. Ab initio phasing will be treated in Section 12.8 and non-ab initio methods in Section 12.9. The combination of anomalous dispersion techniques with powder methods is postponed to Section 15.9.