ABSTRACT

We discuss coincidence site lattices (CSLs) for 3-dimensional cubic lattices and 4-dimensional hypercubic lattices. In these cases coincidence rotations can be parameterized by integer quaternions, which makes a detailed analysis of the CSLs possible, which does not only allow to determine the coincidence rotations and their corresponding coincidence index Σ, but also the number of CSLs, the equivalence classes of CSLs the number of inequivalent CSLs, their symmetry groups and in case of 3 dimensions their Bravais classes.