The Basics of Crystallography and Diffraction. Fourth Edition. By Christopher Hammond. IUCr Texts on Crystallography, No. 21. IUCr/Oxford Science Publications, 2015. Paperback, Pp. 544. Price GBP 34.99. ISBN 978-0-19-873868-8.

Abstract

The Basics of Crystallography and Diffraction is a textbook written for students at the beginning of their university education. It presupposes only elementary knowledge of mathematics. Crystallographic notions are introduced starting with everyday experience whenever possible. In this way the author attempts to arouse the interest of students in crystallography and to avoid frightening them off by mathematical formalism. Many notions are taken up again later when the notions of lattices and symmetry have been introduced, which allows for a treatment in more depth. The fact that the book now appears in its fourth edition shows that this approach meets the needs of many students. The book seems to have developed from lecture notes written by the author for his materials-science students at the University of Leeds. This becomes clear from the exercises, e.g. 1.10 ‘Make ball-and-stick models of the cubic-diamond and rhombohedralgraphite structures’. It is also reflected in the treatment of the symmetry of patterns in woven textiles in Section 2.8 and in a whole chapter devoted to the diffraction of visible light. The book consists of 14 chapters and seven appendices; the first chapter deals with crystal structures starting with sphere models, Chapters 2–5 are devoted to lattices and symmetry, Chapter 6 introduces the reciprocal lattice, which is used in Chapters 7–11 to discuss diffraction. The stereographic projection, which in many texts appears at the very beginning, is introduced in Chapter 12. Chapter 13 introduces Fourier analysis and Chapter 14 crystal physics. Among the seven appendices, let me point to the last one, new to the fourth edition, which introduces ‘Group theory in crystallography’. Let me now present the contents of the various chapters and appendices in more detail. Chapter 1 on ‘Crystals and crystal structures’ uses sphere models to discuss simple element structures and their packing densities. Interstitial sites and the corresponding radius ratios of spheres are considered in discussing binary ionic and covalent structures. The notions of stacking faults, twins, plastic deformation and dislocations are introduced. Different types of bonding are distinguished, coordination polyhedra are introduced and various types of inorganic structures discussed. Chapter 2 considers patterns, lattices and symmetry in two dimensions. Starting with periodic two-dimensional patterns, the notion of a (point) lattice is introduced. The five (Bravais types of) plane lattices and their symmetry elements are described. The symmetries of the 17 (types of) plane groups are discussed by means of corresponding patterns; symmorphic and non-symmorphic plane groups are distinguished. I appreciate that space-group symmetry is first introduced in two dimensions, where the distinctions between p3m1 and p31m and between symmorphic and non-symmorphic groups already appear and can easily be illustrated. Examples of the seven (types of) frieze patterns are given. In addition to the ten (monochromatic crystallographic) point groups the 11 black/ white ones are introduced. The 80 (types of) layer groups are mentioned and it is argued that only 52 of them can appear in woven textiles. Finally, Penrose tilings, Fibonacci series and the golden ratio are mentioned. In Fig. 2.12, which gives examples of black/white plane groups, the vertical periodicity is not well satisfied in parts (b) and (c). The letters K and L are misplaced in Fig. 2.20, which illustrates continued similarity. ISSN 2053-2733