Coincidence sites for rational lattices

Abstract

The problem of identifying the coincidence site lattices produced by the disorientations of any rational lattice is investigated. A very simple new procedure for computing the CSLs is presented, based on Grimmer's reciprocity theorem and application of the reduction algorithm introduced by Buerger for finding reduced cells. The point symmetries of a lattice imply that any orientation relationship that produces a CSL can be alternatively expressed by a variety of different rotations. Two simple numerical methods (one based on integral matrix operations and one based on quaternions) are demonstrated for finding all the equivalent rotations that produce the same CSL and for obtaining a single “canonical” rotation as a representative of an equivalence class.