Vibrational spectra and structure of silicates

506 Four topics are covered. “Far infrared spectra of four-membered ring compounds” (Blackwell and Lord) looks critically at the ring-puckering vibrations in these compounds and the potential functions governing these modes. A similar topic “Pseudorotation of five-membered rings” is dealt with by Jaan Laane. Many reviews on “High pressure vibrational spectroscopy” have appeared between I961 and 1969. Melveger, Brasch and Lippincolt update the coverage to mid-1970, and provide an excellent account of the newer techniques. Finally the editor in collaboration with S. M. Craven and W. C. Han-is deal with the topic of torsional barriers from far infrared spectra. This chapter comprises more than half the present volume and is excellently done. If the standard of future volumes is as high as this forerunner then the editor will clearly succeed in his stated aims. J. W. T. Vibrarional Spectra and Sfvucture of Silicates, by A. N. LAZAREV, Consultants Bureau, Plenum, New York, 1972, pp, ix and 302, price Q7.50 (paperback). The author’s aim was to present a systematic account of the methods currently available for the interpretation of the vibrational spectra of silicates and reiated compounds, and to illustrate certain of these methods by reference to specific problems associated with the study of the configurations of the complex anions, the mutual influences of the cation and anion (especially in the effects on individual bonds of the latter), the coordination of the atoms in the lattice, and the mechanisms of phase transformations in relation to the lattice dynamics. En this he can reasonably claim to have achieved a good measure of success. Chapter I, an introduction to the theory of the vibrational spectra of molecules and of complex ions in crystals, unfortunately suffers from overcondensation. This is particularly true of those sections concerned with the applications of space group theory to this problem; and some previous exposure to the basic ideas is necessary to appreciate this account. Chapters H and III are both concerned with the vibrational spectra and structure of complex anions in silicates; the former dealing with socalIed “island” structures, and the latter with highly condensed states. Chapter ZV deals with the use of spectroscopy in establishing the structures of complex anions, particularly in those cases in which either the impossibility of obtaining reasonably large single crystals, or the low symmetry of the system complicates the application of X-ray methods to the problem. Chapter V is an account of the applications of spectroscopic methods to “crystal-chemical investigations”, and Chapter VI, a discussion of the spectroscopic evidence for the flexibility in Si-O-Si and P-O-P bonds, for the mobilities of the oxygen bridges, and phase transformations in phosphates and silicates.

507 The book is generally well-written, and does not appear to have suffered greatly in translation from the original Russian - except for the omission of a few obvious conjunctions, and the reference, in the footnote to Table 1, to “. . . the sight (sic) group symbol. . .” Clearly, both its price and its highly specialised subject matter will restrict severely its sales potential: but it should certainly be a part of the library of any department in which the chemistry of silicates is a topic of investigation. T. H. Fourier Transforms and their Physical Applications, by D. C. CHAMPENEY, Academic Press, London and New York, 1973, pp. x-1-256, price k5.20. This book is the first to appear in a new “Techniques of Physics” series intended to present the basic principles underlying specialized techniques together with some of the more important applications in a compact, self-contained and readable form. In the case of a technique so ubiquitous in its applications as that of Fourier Transforms there is much to be said for a unified presentation providing an overall perspective together with much of the expertise in the way of useful “tricks of the trade” that can make ail the difference between a casual acquaintance with a subject and the capability to reach desired results by the most expeditious approaches. This the present book succeeds admirably in achieving without resorting to a level of mathematics beyond the scope of most experimentalists whether at the advanced undergraduate or research level. Theoreticians may also find it profitable reading but the more sophisticated quantum theorists are unlikely to find much to interest them. Inclusive of the appendices the mathematical foundations comprise one half of the book. The remaining half consists of applications to electric circuits, optical diffraction phenomena, optical coherence and holography, and X-ray, neutron and electron diffraction. Of the six chapters concerned with mathematical foundations the first summarizes the conventional properties of Fourier Series whilst the subject of the book proper commences with Chapter 2, a useful feature of which is the compilation of diagrammatic sketches of some of the more commonly encountered functions and their transforms. Convolution (faltung) properties are developed in subsequent chapters and in particular the importance of the Convolution Theorem in building up the Fourier Transforms of more complex functions from those of simpler ones is emphasized. Comparison is made with ‘he formally similar Correlation Function which in the time dependent form receives extensive discussion in the final chapter of the book. One minor criticism may be that whereas the parts of the applications section concerned with electric circuitry suffer from a certain proliferation of detail, later sections dealing with wave propagation, where the power of the technique can be more fully exploited, leave important questions unanswered. For example, al-