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Mathematical Techniques in Crystallography and Materials book reviews Acta Crystallographica Section A Foundations of book reviews Crystallography Works intended for this column should be sent direct to the Book-Review Editor, whose address appears in this ISSN 0108-7673 issue. All reviews are also available from Crystallography Journals Online, supplemented where possible with direct links to the publisher's information. International tables for crystallography. The ®rst edition of ITA was reviewed by Nomenclature. Hence, unlike common texts Vol. A. 5th edition. Edited by Th. Hahn. Stadnicka et al.[Acta Cryst. (1987), A43, or tables, ITA is being continuously Pp. xx + 911. Dordrecht: Kluwer 156±159]. They concluded, after assessing all improved by a well organized and com- Academic Publishers, 2002. Price sections individually, that ITA is a clearly, petent community, whose recommendations, EUR 242, GBP 142, USD 225. ISBN thoroughly and coherently written book that after thorough discussion, are taken as input has been prepared carefully and is of good for subsequent editions. One example was 0-7923-6590-9. technical quality. an inconsistency in the concept of `symmetry The reader of ITA5 will ®rst notice a new element' [H. D. Flack et al. (2000). Acta Since its ®rst appearance in 1983, Volume A white (red)-green hard cover differing from Cryst. A56, 96±98], which has been removed of International Tables for Crystallography the blue (gold) predecessors, this time by de®ning the geometric element as a (hereafter ITA) has served `consumers' of without a book jacket. Although it looks labelled geometric item. Hence corrigenda symmetry-group data for about 20 years and more attractive at ®rst glance, the white part and addenda became necessary. Those of the has experienced, during a permanent dialog might lose its beauty more quickly. Then, third edition were summarized in Acta Cryst. with the readers, four more or less major looking at the layout of the interior, a (1995), A51, 592±595. revisions. ITA is the ®rst in a series of smaller font attracts the reader's attention Turning to changes of the crystallographic International Tables for Crystallography and which makes the arrangement of the text information supplied by ITA5 as compared treats one-, two- and three-dimensional more concise, because the number of lines to the previous edition, it should ®rst be crystallographic space groups. Extensions to per page is approximately maintained. mentioned that the incorporation of the `generalized symmetry' are beyond the Hence, more space between the subsections double-glide-plane symbol `e' into space- scope of this volume. A salient point of ITA along with an in-depth four-digit decimal group symbols has been completed is the adoption of an advanced level of classi®cation facilitates browsing ITA5 throughout the volume. This means that, in symmetry theory, which is strictly compat- considerably. The table of contents now addition to glide planes a, b, c, d, n used ible with the demands of computerization of covers 6 pages instead of 4 of the previous before 1995, a sixth symmetry element crystallographic problems. The Editor's goal edition. The plain rearrangement of the text appears in all parts (in centred cells only). to provide data that are useful for all aspects of the fourth edition is a noteworthy Secondly, subgroup and supergroup data of crystallography as well as text to satisfy achievement of ITA5 in itself. One compo- have been changed by adding space-group the needs of those interested in the theor- nent of that is bringing tables or ®gures numbers and rearranging the group symbols etical reasons behind these tables has led to closer to the place where they are quoted according to rising index and falling space- a fruitful combination of tables for practical ®rst. Moreover, instead of the creamy paper group number. This applies particularly to use in the ®rst part and a high-level textbook previously utilized, for the current edition Part 7 as the main part of ITA and facilitates in the second. ITA succeeded in proposing white paper has been used. Again this makes dealing with the various symbols. It is a compromise between competing view reading easier, apart from proper fractions recommended for future editions to obey points. I mention issues such as the hexag- which, due to the smaller font, appear a bit these rules in the examples of subgroups onal/trigonal versus rhombohedral sub- faint now. However, the general quality of given in Chapter 4.3 (by E. F. Bertaut), too. division and the so-called `monoclinic print is excellent. Thirdly, there are several improvements that monster', which, for the convenience of the Then a hidden change in ITA5 should be apply to individual groups only, such as reader, is a summary of all settings and cell mentioned, which will certainly become a changes in the sequence of the positions and choices of the monoclinic space groups. great advantage for future application symmetry operations for the `rhombohedral Because symmetry is the basis of crystal- compared to editions 1±4. It is the computer- axes' descriptions of certain R groups. While lography, previous editions of ITA had to be based production of ITA5, accomplished by changes of Parts 1, 3±6, 11±13 (by Th. Hahn, reissued several times: 1st edition 1983, M. I. Aroyo and P. B. Konstantinov. All A. Looijenga-Vos, M. J. Buerger, E. F. reprinted with corrections 1984, 2nd revised space-group tables were reprogrammed, Bertaut, H. Arnold, W. Fischer, E. Koch, edition 1987, 2nd revised edition reprinted whereas the space-group diagrams were H. Burzlaff, H. Zimmermann, Y. Billiet) with corrections 1989, 3rd revised edition scanned from the existing presentations, are mainly of formal character, substantial 1992, 4th revised edition 1995, 4th revised which in turn had been improved several revisions and reorganizations of the text edition reprinted with corrections 1996, 4th times over the years. One promising future have been carried out in the remaining parts. edition reprinted 1998, 5th revised edition option of this computerization is the linking They can in most cases be considered 2002. The volume has increased from xv + of ITA5 to other volumes of this series. successful in expressing the fundamentals 854 pages in 1983 to xx + 911 pages in 2002. Because ITA is published for the Inter- more clearly, apparently stimulated by the This 5th edition (ITA5) is more extensively national Union of Crystallography (IUCr), feedback from students, and in taking new revised than any of the preceding editions. its content has been the subject of perma- developments into account. While the number of parts (15) is main- nent attention by Commissions of the IUCr, Examples are the presentation of general tained in ITA5, the number of authors has in particular by the Commission on Inter- and special re¯ection conditions (Section increased. national Tables and the Commission on 2.2.13) and the way monoclinic space groups Acta Cryst. (2004). A60, 641±642 641 book reviews are treated (Section 2.2.16), both by Th. relevant symbols, ITA delivers not only the Crystal structure determination. By Hahn & A. Looijenga-Vos. The text of Part 8 complete listings but also a comprehensive Werner Massa. Second completely (by H. Wondratschek) has been updated to explanation of the theory behind them and updated edition. Pp. XI + 210. Berlin, bridge the gap to topics that are not the detailed instructions for use. Hence, it is Heidelberg, New York: Springer-Verlag, subject of ITA but are of current interest to indispensable for people dealing with the 2004. Price EUR 48.10. ISBN 3 540 crystallographers, like symmetry in spaces of symmetry of crystals. The present revised 20644 2. dimension >3 and incommensurate struc- edition, ITA5, is another step towards tures, as well as to topics which have now minimization of inaccuracies and improve- been dealt with comprehensively in subse- ment of readability. Chapters of different A review of the ®rst edition of this book was quent volumes of the International Tables authors of ITA5 have become more homo- published in the May 2001 issue of Acta series, like subperiodic groups. The concept geneous by cross references and due to the Cryst. A57, page 368. The second edition has of a `lattice system of space groups' and its rearrangement of topics between them. I been considerably updated, especially the relationship to Bravais ¯ocks and the have been strikingly unsuccessful in the chapter on experimental methods, which is concept of `normalizers of space groups' has search for errors. Minor ¯aws (some now mainly concerned with modern data been worked out in a much clearer manner mentioned above) may readily be corrected. collection using area detectors. Many tips in the revised formulation. With regard to Being published in the 21st century, historic and insights help readers to recognise and normalizers, `special topics' have been remarks like `something is known since the avoid possible errors and traps, and to judge removed in view of the extended Part 15. last century' (e.g. on p. 738) should now the quality of results. Part 9 on crystal lattices has been better read ` ... since the 19th century' to enlarged by a new chapter on the Delaunay avoid further corrections in 2102. I feel reduction (by H. Burzlaff & H. Zimmer- personal indebtedness to the Editor and to mann) and by a chapter on `further proper- the other authors of this useful volume and ties of lattices', where B. Gruber deals with the huge work that has been done. Buerger cells, lattice characters and sublat- Mathematical techniques in crystallog- Peter Paufler tices of n-dimensional lattices. The former raphy and materials science. By Edward authors contribute also a list of the 24 Chair of Crystallography Prince. 3rd ed. Pp.
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