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

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arise 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
AngeM,. Chem. 72 (1960) 502
Angew. Chem. Int. Ed. Engl. 30 (1991) No. 11
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
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
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introduction, crystalline, book, mathematica, sénéchal, symmetries, review, informat
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