CONCEPTS OF CRYSTALLOGRAPHY FOR UNDERGRADUATES

Dieter Schwarzenbach

Institute of Crystallography, University of Lausanne, CH-1015 Lausanne, Switzerland.
Dieter.Schwarzenbach@ic.unil.ch

Keywords: teaching crystallography, symmetry, diffraction

Crystallography is fundamentally important to all disciplines of the exact sciences. Its concepts are fundamental to such a degree that many Universities do not offer any courses in crystallography, or they offer only advanced courses. Physics teachers claim that they do not need crystallographers to teach Bragg's law and to conduct laboratory courses including powder and Laue diagrams. For chemists, crystallography is an analytical technique; they are interested more in the results and less in the process of structure determination. Introductory chapters of textbooks in solid state physics, materials science, chemistry and mineralogy often include notions of crystallography. Thus, introductory crystallography seems to be in good hands. Is there any need to teach it in a dedicated course?

This question calls for the next: What is basic crystallography? It is different things for different disciplines. But whatever it is, I do not believe that it is restricted to structure determination, i.e. a demonstration of an easy solution of a crystal structure terminated by the appearance of an ellipsoid plot on the screen. I believe that it is a science based on classical mathematical and physical principles which are hardly touched upon in high-schools and are thus very unfamiliar to the students: geometrical symmetries and the diffraction grating. Corresponding catchwords are "Bravais lattice" and "Bragg's law". Both are too often marginally presented by a few figures.

Why should students have a deeper understanding? For practical applications, solid state scientists need to understand the meaning of space group symbols and atomic coordinates; they should be able to obtain drawings of structures from this information (typically alloys and ceramics). They should understand the production and various uses of powder diffraction diagrams, of pole figures, and of Laue diagrams for the study and orientation of single crystals. The existence of aperiodic structures may be mentioned to them. Chemists need to interpret critically the structural information contained in many publications and data bases. They ought to be told that the solution of the crystallographic phase problem is achieved on the basis of the independent-rigid-atom-model. They should understand the origin and significance of atomic population factors in disordered structures. They may be informed qualitatively on Hirshfeld's rigid-bond criterion. All these practical topics demand a deeper understanding of space symmetries, the implications of oblique coordinate systems (reciprocal coordinates), the meaning of coordinates listed in International Tables (cosets with respect to the translation subgroup), basic diffraction theory, the determination of the lattice, intensities and extinction rules. Physicists may realize that diffraction is just a manifestation of the general behaviour of waves in periodic media.

A dedicated course on crystallography? Not necessarily, crystallography may be taught as a chapter in a more general course. But this chapter should correctly present the fundamental principles. For the students, these are not trivial, but they may be taught at a descriptive level according to the audience concerned. Crystallography belongs to the foundations of solid state science, and modern chemistry would not have developed without it.