Crystal structure determination. Second edition. By Werner Massa. Pp. xi + 210. Translated into English by Robert O. Gould. Berlin: Springer, 2004. Price EUR 44.95, USD 49.95. ISBN 3-540-20644-2.

This textbook, Crystal structure determination, is a translation by Robert O. Gould based on the third German edition of Kristallstrukturbestimmung by Werner Massa of the University of Marburg, Germany, published in 2002. This new edition in English has been updated from previous editions, particularly in the chapter on experimental methods. It is an excellent teaching text, highly recommended, particularly for those interested in the general principles of this experimental technique and its application to small-molecule crystallography (although the general principles described here are similar for all sizes of molecules). The chapters are short and to the point (179 pages, plus a worked example). The translation is excellent and I understand that the translator worked with the author in order to clarify certain portions of the text. Different students have different needs for the amounts of mathematics used in a textbook of this kind. I recommend they try this text as it contains a medium amount of mathematics.

Initially, we are introduced to crystals and crystal lattices. It seems that not enough emphasis is given to examining the symmetry of the crystal when determining which crystal system it belongs to, although the problem of β near 90° in a monoclinic crystal (which could be mistaken for orthorhombic) is discussed. The descriptions of centered, hexagonal, trigonal, rhombohedral and reduced unit cells, however, are excellent. Then the geometry of X-ray diffraction is described. The reason the characteristic spectral lines are obtained plus a background of white radiation is explained, as is how to select and collimate one component only (usually Kα). Diffraction is then described, starting with a one-dimensional lattice and proceeding to the Laue equations and the indexing of lattice planes, and finally presenting the Bragg equation and how to calculate scattering angles of diffracted beams if the unit-cell dimensions are known. Then follows a description of the reciprocal lattice that the student should find very helpful. I found this chapter particularly clear. In the chapter on structure factors, I particularly liked the description of what happens to the diffraction pattern as more and more atoms are added to the unit cell.

In the chapter on symmetry, the essentials are described clearly with some fine figures to illustrate each topic. Interestingly (and successfully), the author starts with space groups and then proceeds to Bravais lattices and crystal classes (although the two latter were also mentioned earlier in Chapter 2). I thought the section on space-group determination was very helpful, but the section on group–subgroup relationships was somewhat hard to follow and could have been expanded, for example, by a more comprehensive figure.

The newly expanded chapter on experimental methods will be of great use to students. Some useful recipes for crystallizing small molecules are given. Advice on crystal size, choice of radiation and what to do if the crystal is unstable is given for small molecules only. The various useful film methods are described – again I would have liked more information in the figure captions. There is a good section on reflection profiles and scan types (as seen with the four-circle diffractometer). This involves a discussion of mosaic structure and which portion of reciprocal space needs to be measured (thereby teaching again about symmetry). While nothing is written about the crystallization of macromolecules, the section on area detectors (used now also for small molecules) is highly recommended for all crystallographers. Charge-coupled-device (CCD) systems and image plates are nicely described. The photographs of diffraction and equipment are good. Neutron diffraction is also touched on. There is an excellent treatment of accuracy and estimated standard deviations and absorption coefficients.

The chapter on structure determination begins with the Patterson function. The extension to macromolecules is briefly mentioned, including the multiple isomorphous replacement (MIR) and multiwavelength anomalous dispersion (MAD) methods. Again the diagrams need more explanation. It is nice to see Harker–Kasper inequalities (Section 8.3.1) and the Sayre equation (Section 8.3.3) given prominence. Then follows the work of Karle and Hauptman for which the 1985 Nobel Prize was awarded. I am not sure that the left side of Fig. 8.4b is correct. There is a good description of strategies of phase determination. The author gives information on the programs available and also describes what all the terms derived in these programs are. So there is a good mixture of theory and practice in this chapter, which should help students.

In the chapter on structure refinement, it is stressed that there are errors in both the model and the data and this is an excellent fact to stress. It is pointed out how important the advances in computing power have been for X-ray crystallographic research, especially structure refinement. Problems with hydrogen atoms (bond lengths, isotropic refinement only) are also touched on. The refinement of rigid groups is described, as is Rietveld refinement of powder diffraction data.

In a chapter entitled Additional topics, the author tackles disorder in crystals. This was most interesting to me. He describes how to refine such a model with disorder, e.g. orientational disorder, and also the problem of dynamic and static disorder. He also mentions the crystal defects that occur on increasing the temperature, together with one- and two-dimensional disorder, modulated structures and quasicrystals. There is also a description of anomalous dispersion and chiral and polar space groups. An excellent example of the structure of a compound with possible inversion twinning is given. Extinction is well described, and the Renninger and λ/2 effects and thermal diffuse scattering are mentioned.

There is also an excellent chapter on Errors and pitfalls that all crystallographers should read. The author provides an interesting example from the literature of a structure with some incorrect atom types and shows how this problem was identified and rectified. There is a nice section with a clear example on the various possible types of twinning and how to analyze them. This subject is becoming more important especially for precious proteins where twinned crystals may be all one can obtain. There is also a table (11.1) showing a possible cause of incorrect space-group choices giving the cause of the problem (space groups that differ only in the presence or absence of a center of symmetry so that the condition for reflections is the same). There are also some hints on what may be wrong if anisotropic displacement parameters are poor.

The chapter on Interpretation and presentation of results covers the meaning of x, y, z and the use of drawing programs and stereo. Deformation density with X–X and X–N maps is also mentioned. Crystallographic databases describes how to use these and, importantly, how to put your structures in them or ensure that they are there. The ICSD (Inorganic Crystal Structure Database), CSD (Cambridge Structural Database), CRYST-MET (Metals Crystallographic Data File) and Structure Reports are described. The use of crystallographic information files (CIFs) and how to use the Internet to find crystal structures is also described.

The ending of the book is superb for the crystallographic experimentalist. In the outline of a crystal structure determination, the author tells the reader where to find information on each step within the book. There is also a nice list of questions at the end to ensure that the data collection and analysis were done properly. Finally, there is a worked example of a structure determination. This is a nice example of a small-molecule structure. It goes into experimental details as well as structure determination and refinement. Both Patterson and direct methods are used for structure determination.

My criticisms are minor. The main one is that the author has not paid sufficient attention to the captions for figures. This is something most of us are guilty of. It would be helpful to have a more complete description of what the figure shows and all the symbols used should be described in the caption. There is probably not enough written on structure solution but the example at the end may help clarify that. Also some terms in the text are not adequately described – maybe a glossary would help. For example, in Fig. 3.5, what is 2π?

This book is an excellent blend of theor­etical and experimental information and will help students and teachers alike. The student can browse through several such texts and find the one that best satisfies his or her needs with respect to explanation and the use of mathematical and physical concepts. I suspect this book, with its outstanding blend of theory and experiment, will be ideal for many such students.