The generating function for coincidence site lattices in the cubic system

The derivation of the generating function given by Bleris & Delavignette [Acta Cryst. (1981), A37, 779- 786] is simplified and made rigorous. It is shown that their main result can also be deduced directly from Grimmer [Acta Cryst. (1974), A30, 685-688]. The following applications of the generating function are described: determining all rotations that generate coincidence site lattices (CSLs) by giving their axis and angle or their matrix, determining the equivalence classes of rotations with respect to cubic symmetry and the 180° and minimum-angle rotations that they contain, determining the number of rotations in each equivalence class and the total number of rotations that generate a CSL with given unit-cell volume Σ. We also discuss how a basis for the CSL can be computed and how a bicrystal with a plane grain boundary can be characterized.