Materials crystal chemistry. By Relva C. Buchanan and Taeun Park. Pp. vii + 462. New York: Marcel Dekker, Inc., 1998. Price US $175. ISBN 0-8247-9798-1

This book is `intended primarily for engineers, advanced undergraduates and graduate students in materials engineering, materials science and allied scientific disciplines'. It contains four chapters, entitled: Fundamentals of Atoms, Molecules and Solids (130 pp.); Fundamentals of Crystallography (94 pp.); Crystal Structures (84 pp.) and Structure Changes in Crystals (112 pp.). Two appendices, special functions in quantum mechanics and quantum mechanical background for the simple expression of the lattice energy of ionic crystals, a bibliography and an index make up the rest of the work.

When I began to leaf through the first two chapters, with their large numbers of detailed subtopics, I had high hopes that I was looking at a new genre of texts for teaching this subject. Usually, texts on crystal chemistry treat atomic theory and bonding at the level of freshman chemistry and crystallography receives only a cursory overview. The primary emphasis in most texts is on crystal structures and the crystallography section needs to be supplemented with a second text. It seemed that this text covered these topics in sufficient depth to be used alone. Alas, my hopes were quickly dashed, and I was forced to conclude that this book fails on two levels, both at the level of scientific detail and at the level of basic communication.

My disappointment began on p. 9 of chapter 1, where the authors define potential energy `as the work done by the electron in moving from infinity (zero energy) to r'. The equation appears, however, as

instead of with a lower limit of and, with the absolute signs removed in the next lines, there are inconsistencies in the signs of the resultant work and force terms. Misprints or misconceptions? It is difficult to say, as both abound throughout the text. Bad editing and poor proofreading are evident in the misplacement or omission of definite and indefinite articles, mispellings and different spellings for the same word in the same line (`micelle' and `miscelle', etc.) and downright confusion of language. What, for example, is one to make of this sentence on p. 104? `The metallic radii are defined in the same way as ionic crystals except for no difference between atoms as cation and anion.', or the particularly egregious error on p. 132 where, in a section headed `3. Block (sic) Equation', a paragraph begins `The base of band theory in solid state physics is Block theory which descibes (sic) the wave function of an electron in a periodic potential. In crystal, the position…'. After these experiences, I admit that I did not go carefully through the remaining mathematical equations, either in the chapter or in the appendices.

I had higher hopes for chapter 2, Fundamentals of Crystallography, but here too problems quickly emerged. The first page of the chapter discusses stacking directions of points to form a lattice and introduces the concept of the unit cell, but then a statement appears that when the `atomic arrangement is taken into account, the stacking direction is no longer arbitrary' as if one could not always select a triclinic unit cell as long as it contains the asymmetric unit. Confusion between the metric of a unit cell and the dimensional requirements imposed by symmetry is present throughout the chapter. Thus the circular `lattice provides the basis for crystal symmetry' where later the authors state that the geometry of the unit cell is determined by the symmetry. They also state that `Any solid exists in one of three states: single-crystal, polycrystal and non-crystalline (amorphous). All have periodicity ranging from perfect for a single-crystal to essentially nonexistential (sic) for the amorphous state.' Why a polycrystalline material is a separate state is not clarified. `Parallelipiped' is used in a discussion of what the authors refer to as `planar lattices' that is so involved as to obscure their significance, though it is eventually defined correctly. There is a good discussion of Miller indices, with many examples, but there is recurring confusion between lattice points and atom site occupancy, e.g. `The motif placed on (sic) each lattice point…'; a `symmorphic space group exists when only a single atom or ion exists at the Bravais lattice points…'. Finally, to gladden the heart of every crystallographer, `The actual atomic positions are obtainable from the analysis of the lattice of a crystal.' and `Knowing the space group and equipoints … one can readily determine the crystal structure and arrangement of the atoms or ions in the unit cell or crystal.'. X-ray diffraction intensities and structure factors are never mentioned and although International Tables for Crystallography are mentioned once in a parenthesis in the text, there is no reference to them in the Reference section or in the index.

Ch. 3 deals with crystal structures and contains sections on space filling by atoms, simple binary ionic crystals, more complex structures with closest packing such as perovskites and spinels, and covalent crystals. It is a standard treatment of topics found in all books dealing with solid-state chemistry.

The concluding chapter deals extensively with polymorphism, thermodynamic discussion of phase changes, and various types of transformation with illustrative examples such as in quartz. There are also discussions of defects, substitution and silicate structures. But even here the very first equation of the chapter has `The free energy change with temperature and pressure is given by:

…', correct only when temperature and pressure are constant.

In summary, I cannot recommend this book in its present state. The large number of errors and misstatements disqualify it as a textbook and its price puts it totally out of reach of most students. The choice of topics for a course in materials engineering is a good one, however, and I hope that the authors will eventually revise their work so that it meets the goals they set themselves.