Orientation relationships between two crystal lattices: matrix description

Orientation relationships between two crystal lattices are frequently specified in terms of parallel directions and planes in each lattice. The corresponding matrix, relating the vector bases of the lattices, can be obtained by a general method involving the metric matrices of the two lattices and the crystallographic indices of parallel planes and directions. Equivalent matrices can be defined by changing the lattice bases: different selections of the invariants of such matrices are indicated. Finally, criteria for choosing the 'best' matrix relating the two lattices are discussed in the context of phase transformations and of interfacial structure.