Crystal structure analysis. Principles and practice. Edited by William Clegg. IUCr Texts on Crystallography, 6. New York: Oxford University Press/International Union of Crystallography, 2002. Pp. xiv + 265. Price US$ 90.00, GBP 49.50. ISBN 0-19-850618-X.

According to the preface, this textbook was developed from the contents of a biennial Intensive Course in X-ray Structure Analysis, sponsored by the British Crystallographic Association between 1987 and 1999. The editor and the other three contributors (A. J. Blake, R. O. Gould and P. Main) were the principal lecturers in the 1999 course, and the book reflects its origin in extensive course notes, refined over years of use.

The book is very well written, has an excellent organization of material and is filled with many illustrative examples of the subject matter. The subject matter spans all of the basics of small molecule crystallography, from crystal growth and intensity data collection to structure solution, refinement, and derivation and interpretation of results. Only four-circle serial diffractometers and instruments with area detectors are discussed, no photographic methods are covered, and it should be noted that there is essentially no coverage of macromolecular crystallography. An outstanding feature is the inclusion of numerous pertinent problems at the end of most chapters, with answers provided in Appendix 3. Another good aspect is the strong emphasis on structure refinement and the assessment of quality and accuracy of results.

A summary of the book's contents, with brief discussion, follows. An overview of the entire crystallographic structure determination process is presented in Chapter 1. It includes discussions of scattering from electrons, atoms and crystal lattices; structure factor and electron density equations, Bragg's Law, resolution and the phase problem.

The established standard crystal growing and mounting techniques are surveyed in Chapter 2, as well as how to evaluate crystal quality by both microscopic and diffraction examination.

Symmetry operations, point groups, crystal systems, crystal morphology and space groups and their symbols are discussed in Chapter 3, together with space-group determination from systematic absences, E(hkl) values and the statistical distribution of diffraction data. A useful table of the 23 most frequently encountered space groups is provided.

Chapter 4 provides the background for the diffraction process. It includes a derivation of Bragg's Law, the development of the reciprocal lattice, the use and determination of orientation matrices in diffractometry, and the derivation of symmetry from the diffraction pattern. Kappa geometry is briefly discussed, but without diagrams. Data collection using four-circle diffractometers is discussed in Chapter 5. Topics in the first half include choosing the appropriate radiation, the advantages of crystal cooling in data collection, searching for and indexing initial diffractometer reflections, and obtaining a good orientation matrix and accurate cell parameters. The rest of the chapter is devoted to how to collect accurate data, set scan type, width and speed; detector aperture, weak reflections, and checking and reorientation of intensity standards. Two final sections deal with systematic errors in data and possible means for correction. Of course, one feels the need to comment that the methodology in this chapter has been largely supplanted by area detector technology, which is discussed in Chapter 6. That chapter opens with an interesting brief history of area detectors and a comparison of photographic methods with area detector technology. There is a valuable table comparing the advantages and disadvantages of area detectors versus conventional serial diffractometers. All the typical area detectors are included: multi-wire proportional chambers, phosphors coupled to a TV camera, image plates and charge-coupled devices (CCDs). Characteristics and associated data-correction needs of area detectors in general are outlined, including spatial distortion, non-uniform density response, bad pixels and dark current corrections. A typical area-detector experiment is outlined in the last section.

Fourier syntheses are introduced in Chapter 7, beginning with one- and two- dimensional examples and proceeding to three-dimensional syntheses in Patterson and real space. The basic mathematics of Patterson functions are discussed in Chapter 8, followed by a description, with examples, of the heavy-atom method. The use of Patterson search methods is introduced.

The various constraints on electron density are presented in Chapter 9 as a basis of direct phasing methods. The calculation and statistics of normalized structure factors are discussed. The use of the largest E(hkl) in phase estimation and initial electron density map production is presented. Chapter 10 is a brief but well illustrated presentation of the basic ideas of maximum entropy.

Least-squares fitting of parameters is discussed in Chapter 11, which covers the mathematics and principles involved in refinement of a derived structure: weighted mean, linear regression, variance–covariance, restraints, constraints and the application of non-linear least squares. Practical aspects of structure refinement are covered in Chapter 12. Factors to be considered in finding the best fit of structure model to measured data are presented: (i) use of |F| versus F², (ii) least-squares weighting schemes, (iii) atomic parameters and scale factors, (iv) treatment of H atoms, (v) constraints–restraints and (vi) thermal displacement parameters. Lastly, disorder, twinning and absolute structure are discussed.

The derivation of results is treated in Chapter 13. The statistical background for structure determination is thoroughly discussed, including distributions, sampling, estimated standard deviations, correlation and covariance, agreement between observed and calculated data, thermal motion. Chapter 14 treats the interpretation of results. The use of statistics is presented: comparison and averaging of geometrical parameters, planarity of groups of atoms, and comparison of different structures. Systematic data errors are considered: absorption, extinction, thermal diffuse scattering, instrument calibration errors. Possible errors in the model are discussed: scattering factors, constraints–restraints, incorrect symmetry, high thermal motion and wrong structures.

Chapter 15 is an extensive discussion of graphical and tabular presentation of structural results. It's last section discusses archiving of final results. Chapter 16 gives an excellent introduction to the preparation and use of the CIF and Chapter 17 lists the various crystallographic databases with primary emphasis on the Cambridge Structural Database. Chapter 18 deals with twinning, anomalous dispersion and X-ray sources.

Three appendices present mathematics and formulae, a crystallographic dictionary, and answers to exercises.

This textbook should definitely be considered for use in introductory courses in X-ray structure determination as it provides a good framework for course organization. The concise treatment of the material (all of small-molecule X-ray crystallography in 265 pages) will work well when supplemented with lectures and additional class discussions.