# Book Review Crystalline Symmetries. An Informal Mathematical Introduction. By M. Senechal

код для вставкиСкачатьarise from giving the results of calculations with too high a precision. One should not refer to “activated alkenes” without indicating whether they are activated in the direction of electron deficiency (unsaturated esters, nitriles or ketones) or electron excess (vinyl ethers, enamines). In this light many reactions are quickly seen to be plausible. Sodium sulfate is a water-binding agent, not a dehydrating agent (p. 876). On page 947 the precursor of quinuclidine has a carbon atom missing. What is meant by the statement on page 879 that sodium chlorite (NaClO,) is oxidized to chlorine? On page 258 the formula of 0-sulfohydroxylamine is shown without the crucially important oxygen atom between N and S. In two preparative methods on pages 444 and 468 one of the reagents has been omitted in each case. The fact that in over 1500 pages only about twenty printing errors could be found is an indication of the high quality of the typesetting. However, one of these is an incorrect spelling of the name Birkofer; this is again repeatedly shown with an extra “h”, despite this error having been pointed out by Richard Kuhn in a reviewr*’ of the 4th Edition. A tribute must be paid to the hard work by the authors. Since a chemist’s range of interests is not nowadays defined in terms of compound classes, a specialist dealing with a particular class of compounds is now a rarity. Despite all the aids that are now available, collecting together the required information is still an arduous task; the essential job of evaluating facts costs time and effort. Ernst Schrnitz [NB 1171 IE] Zentralinstitut fur Organische Chemie Bereich Organische Synthese Berlin-Adlershof (FRG) Crystalline Symmetries. An Informal Mathematical Introduction. By M . Senechal. Adam Hilger, Bristol 1990. xi, 137 pp., hardcover E 79.50.-ISBN 0-7503-0041-8 Chemists are generally comfortable with the geometry of structure, the algebra of stoichiometry, and the calculus of kinetics. Most of them have learned to live with the eigenvalue problems of quantum mechanics. As to the less familiar mathematics of group theory graph theory or topology, many chemists have only a vague concept of the mathematical fundamentals and employ terminology in a manner that is at best intuitive and idiosyncratic. Discussing the application of mathematics to chemistry with a real mathematician can be an uncomfortable, confusing, and humbling experience. In this small, aptly-titled book Professor Senechal, a professional mathematician, provides a friendly introduction to the mathematical fundamentals of crystallography that will entertain and reward casual readers as well as chemists and materials scientists who work with crystallography. Almost two-thirds of the text involves familiar concepts of symmetry, lattices and space groups, but the treatment is novel: it is written by a mathematician for experimental scientists. Familiar and less familiar concepts, such as orbits, cosets, the Voronoi‘ cell, isometries, and symmorphic space groups, are clearly defined and illustrated. Simple theorems are proven while others are invoked or outlined with reference to an extensive bibliography for more detailed treatment. After reading this book one can feel more comfortable with the assertion that there are 4901 four-dimensional space groups, or with the impossibility of having space groups with [‘I AngeM,. Chem. 72 (1960) 502 Angew. Chem. Int. Ed. Engl. 30 (1991) No. 11 0 VCH fivefold rotation axes. Most of the discussion is clear and satisfying, with only the occasional difficulty, such as on page 56 where an unnatural definition of density in a two-dimensional lattice leads to difficulty in relating the reciprocal lattice to crystal form. There are appetizing but less complete chapters that introduce the modern topics of color symmetry and N-dimensional crystallography, including mention of Penrose tiling and local fivefold symmetry, and a fifteen-page chapter which discusses crystal classification and how to interpret space group information in the International Tables for X-Ray Crystallography. The bibliography includes twenty books and journal articles published since 1980. Throughout the book, particularly in the first chapter, special attention is given to the historical development of crystallography as an experimental, mathematical, and artistic science. This emphasis is effective both for holding the reader’s interest and for illuminating the logic of the subject. A four-page appendix provides concise information about the contributions to crystallography by 34 natural philosophers and mathematicians from Pluto to Roger Penrose. Professor Senechal notes that although the French mathematician Jordan had combined the proper motions (rotations, translations, and screw rotations) with Bravais’ lattices by 1868, it took another 23 years before Fedorov and Schoenflies completed the 232 space groups by adding the reflections, glides and rotary reflections that interconvert enantiomers. This seems curious because by 1850 Pasteur had already demonstrated the need for such improper symmetry elements by revealing the relation between molecular and morphological chirality. Senechal wonders, “Was [this delay] due to differences in scientific fields, or differences in language? Are there similar gaps today of which we are unaware?”. By providing a simple introduction to the mathematics of crystallography this small book should help to bridge one of the gaps between scientific fields that persists today. J Michael McBride [NB 1196 IE] Department of Chemistry, Yale University New Haven, CT (USA) Microbial Polyesters. By I: Doi. VCH Verlagsgesellschaft, Weinheim/VCH Publishers, New York 1990. ix, 156 pp., DM 74.00.-ISBN 3-527-27860-510-89573-746-9 In the future biopolymers are likely to play an ever increasing role. Such compounds are interesting for several reasons: for one thing they are biodegradable and therefore do not contribute to environmental problems; for another they are produced from renewable resources. Commercial utilization of such materials has already begun : shampoo containers manufactured from polyesters which have been made by biotechnological methods have appeared on the market. A comprehensive review of polyesters that are produced by microbial synthesis is therefore welcome, even if the present author has chosen to give pride of place to his own contributions. The monograph, which has a convenient A5 format (8; x 5; inches), presents in eight chapters a discussion and comparison of the properties of poly-(R)-3-hydroxybutyrate (PHB) and of two copolymers, poly(3-hydroxybufyrate-co3-hydroxyvalerate) (P(3-HB/3-HV)) and poly(3-hydroxybutyrate-co-4-hydroxybutyrate)(P(3-HB/4-HB)), the latter discovered and investigated by the present author. Verlagsgesellschaji mbH, W-6940 Weinheim, 1991 0570-0833/9f/1ill-1525S 3.50f .25/0 1525

1/--страниц