Symmetry relationships between crystal structures

Ulrich Müller 
Oxford University Press 
2013 | 360pp | £49.95
ISBN 9780199669950
Reviewed by William Clegg
This book brings together material from a number of sources, as explained in the preface, particularly texts from Hans Wondratschek and Hartmut Bärnighausen and drawing extensively on the contents of the most relevant volumes of the International tables for crystallography concerning symmetry. 
The book has two major parts, together with some short appendices, a glossary and index. Most of the chapters conclude with exercises, for which a full set of answers is provided, so the reader can check progress and understanding.
In part one, Crystallographic foundations, the author wisely and skilfully interleaves chapters on Basics of crystallography (lattices, geometry, crystallographic symmetry, notation and descriptions of International tables information), which will be reasonably familiar material for many readers, with rigorous mathematical treatment of group theory concepts and related topics such as mappings and transformations. Here, ideas, terminology and notation for subgroup and supergroup relationships are also explained in detail.
With this theoretical basis, part two, Symmetry relations between space groups as a tool to disclose connections between crystal structures, explores a range of applications and examples. These include structures based on sphere packings, phase transitions and other solid-state reactions, structure prediction, and some of the problems related to symmetry that can arise during a crystal structure determination. After the depth and concentration of part one, this half of the book makes for rather easier reading.
The book should appeal to crystallographers and materials chemists with inorganic interests; there is just one brief chapter on molecular compounds. It is a very useful tool for understanding and applying symmetry concepts and demonstrates the relationships among structures. It is particularly valuable as a guide to the dense symmetry volumes of the International tables, including some of their internal inconsistencies and incomplete treatment.
In a fairly rapid reading, I detected very few and only minor typographical errors. The quality of writing is thorough and excellent, with just an occasional odd expression that can be seen as German thinking in not quite the right English words, but this does not detract from a book that can be strongly recommended to researchers and advanced students in this area.

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