Crystallography Matters!

Resources for crystallographic education

Matrices, mappings, and crystallographic symmetry

Hans Wondratschek

Institut für Kristallographie, Universität Karlsruhe, Germany

This pamphlet is based on the manuscript for a summer school in Suez, Egypt, in April 1997. Part I describes some elementary mathematics, similar to the manuscript that was distributed to the school participants in advance of the school. It is intended to remind the readers of selected mathematical concepts. Part II contains the material that was covered in my six lectures and three exercise sessions at the school. A carefully prepared Index is included for quick references.

In the analytical description of crystallographic symmetry, group theory is an instrument of utmost importance. Regrettably, there was no time to introduce group theory during the school. The group-theoretical aspects of crystallography could only be mentioned occasionally but not treated systematically. Therefore, also in this pamphlet emphasis was put onto matrix methods. These are considered to be more basic from the point of view of applications. The group-theoretical methods can lead to a deeper insight into the crystallographic concepts and their relationships later.