*Acta
Cryst.* (1995). A**51**,
234-235

**Pp. xxii +
480. Berlin: Springer-Verlag, 1994
Price DM 119. ISBN
3-540-56558-2**

This book, written by
one of the most respected crystallographers in Russia, is
the second edition of a work that first appeared in English translation
in
1981 (originally published in 1971 as *Sovremenaia
kristallografia*; *Simmetriia
kristallov*. *Metody
strukturnoi kristallografii* by Nauka Publishing House,
Moscow).
As the first of a four-volume set, it is a comprehensive overview of
crystallographic
symmetry, as well as of methods for data collection and structure
analysis. Chapter 1
is a general discussion of the crystalline state, showing how
crystalline habit follows
from the packing of a repetitive motif. (There is a small update on the
concept of
quasicrystals, a research topic that has emerged since publication of
the first edition,
with more information given in the final chapter of the book.) Chapter
2 is a
comprehensive treatment of symmetry, including cylindrical groups, which
are rarely
considered by other authors. Chapter 3 is an overview of crystal
geometry, viewed
in real and reciprocal space. Chapter 4 then treats the theory of
scattering from
crystals and discusses how the diffracted radiation is used for
structure analysis. This second
edition contains enlarged or new sections to this part; in the areas of
electron
diffraction, electron microscopy and surface probe microscopy. A new
Chapter 5
discusses topics that have advanced to the forefront of crystallographic
research
since publication of the original volume.

Little need be said here about the first three chapters, since they are essentially the same as those in the first edition. The material is covered very thoroughly by Professor Vainshtein and, indeed, much could be said for purchasing this book even if the symmetry and geometry components were its only contents. Obviously, there is much in these chapters that originates from Professor Vainshtein's personal experience, particularly in discussions of periodic objects that do not correspond to the usual concept of a three-dimensional crystal mounted on an X-ray diffractometer.

Similarly, the
discussions of structure analysis in Chapter 4 have a breadth not
seen in many other crystallographic textbooks. There is a nice overview
of scattering
theories for X-rays, neutrons and electrons by crystals, showing how
they are related
to one another, and how each radiation can be used to find different
kinds of
structural information. The deviation from the single-scattering
approximations is also
described in terms of dynamical theories. Apparatus for obtaining
diffraction
information from crystals is described for all radiation sources. It is
significant that
a discussion of electron microscopy and image analysis is presented
along with the
conventional diffraction analyses to emphasize that crystal structure
analysis is really
a branch of optics, conveniently
visualized in terms of
Fourier-transform pairs (a
concept also not touched on in many books on X-ray crystallography).
The use of electron
micrographs as a source of crystallographic phase information
independent of
conventional phasing techniques has become increasingly important in
recent years.
Optical principles are also important for understanding other aspects of
diffraction,
including the effect of finite crystallite size,
*via* the shape transform, as well as
the
overall effect of disorder, first as a Gaussian distribution of mass
centers around space
lattice sites, which Fourier transforms to another Gaussian function
that limits
diffraction resolution by the sifting operation. A discussion of
scattering from
noncrystalline objects is also presented. The need for a conservation
of scattering from
disordered crystalline specimens, expressed as a diffuse component added
to the
Bragg diffraction, is also stated.

It is appropriate that
electron diffraction techniques are discussed more
thoroughly in this volume as a technique for structure analysis, given
the significant
pioneering effort in this area by the author. (Sadly,
his 1964 book, *Structure Analysis by Electron
Diffraction*, remains out of print.)
Also, it is timely
to mention the scanning-probe microscopies such as scanning tunnelling
microscopy (STM) and atomic force microscopy (AFM) in a
crystallographic text, given the recent success in characterizing both
inorganic and
organic surfaces by these techniques.

Although Chapter 5 does not have the coherent organization of the preceding ones, it can be regarded as a current-topics section, treating new developments that eventually could be incorporated into the preceding chapters in later editions. The discussion of quasicrystalline symmetry is particularly interesting and is well presented. Newer concepts in the treatment of powder diffraction data by profile analysis are given in the presentation of the Rietveld method. Applied research areas that have been made available by the use of high-intensity synchrotron sources and improved detectors are also described, including the study of crystalline surfaces and the use of extended X-ray absorption fine-structure spectroscopy to study the local environment of a chemical element in a crystal.

As an overview of modern crystallographic research, this is an excellent resource to have at one's disposal. Generally speaking, it seems hard to find any area of crystallography that does not interest Professor Vainshtein, and his approach is encyclopedic. Inevitably, some will feel that certain areas are less thoroughly covered than others, but to do complete justice to all would require a book at least twice as large. Inevitably, one looks for more in one's own areas of interest. For myself, I found the discussion of direct phasing techniques to be somewhat perfunctory, given that this is now the major method for the solution of small-molecule structures, and, given the new discussion of high-resolution electron microscopy in this book, I would have expected some mention in that section of its relevance to the phase problem. It is valuable to have electron-diffraction structure analysis and high-resolution electron microscopy discussed in a crystallography book from a positive standpoint, and I heartily applaud Professor Vainshtein for doing this. However, I think that a realistic perspective of the difficulties could also have been presented. The Russian school of electron diffraction has often relied on the use of texture diffraction patterns for data collection from a large specimen area, sampling a relatively wide distribution of crystal orientations. Cowley has pointed out that this approach minimizes nonsystematic dynamical interactions, so that the two-beam dynamical theory is often adequate for such data sets. This is not necessarily the case for selected-area electron diffraction, where the sampled crystal area is generally much smaller and corrections must account for multiple-beam interactions. It is even less true for convergent-beam methods where a virtually flat specimen area is being used for the electron-diffraction experiment. More than a cursory mention of zone-axis convergent-beam diffraction patterns could have been made, particularly since they are quite useful for the determination of crystal point-group symmetries. While examples depicting a near correspondence to the weak phase object approximation in high-resolution electron micrographs of inorganics is valuable, this is a topic of considerable controversy nowadays. More than a passing mention of multislice calculations might have been given, with a frank discussion of where experimental images will cease to be useful for direct structure interpretation. At a different level of criticism, better copyediting would have corrected some minor deviations from standard spelling. In the newer sections, some references are out of sequence and some of the index citations are unreliable.

In general, I find this book to be a refreshing and comprehensive approach to crystallography in a style that could be imitated more often by other authors. While it will not, by itself, replace all other crystallography books on the shelf, each having its own strengths, it well deserves to be placed among them, especially in its newer version.

**Douglas L.
Dorset**

*
Electron Diffraction
Department
Hauptmann-Woodward
Medical Research Institute
73 High
Street
Buffalo
NY
14203
USA
*

**Copyright © 1997 International Union of Crystallography**