Coincidence-site lattices

Coincidence-site lattices are characterized mathematically, in the general case, by a method that can be applied to a pair of original lattices of any symmetry, either metrically identical or metrically different, does not involve inspection and is readily adaptable to computer calculations. The procedure is illustrated by several numerical examples. The proposed characterization of coincidence-site lattices is based on the theory of derivative lattices and makes extensive use of the concepts of superlattice and sublattice. Appended is a simple procedure for determining the transformation matrices needed to generate superlattices and sublattices of any multiplicity.