Abstract: A converse transformation matrix generation approach is used either i) to late a lattice structure of one crystalline material to the lattice structure(s) of one or more other crystalline materials for determining interlattice relationships which allow materials to be identified and classified relative to other materials; or ii) to relate a lattice structure of a material to itself for determining lattice symmetry. In particular, matrices which transform any primitive cell defining a lattice structure either into itself or into another cell defining a second lattice structure to within predetermined maximum tolerances of the cell parameters are generated.

Abstract: A converse transformation matrix generation approach is used either i) to late a lattice structure of one crystalline material to the lattice structure(s) of one or more other crystalline materials for determining interlattice relationships which allow materials to be identified and classified relative to other materials; or ii) to relate a lattice structure of a material to itself for determining lattice symmetry. In particular, matrices which transform any primitive cell defining a lattice structure either into itself or into another cell defining a second lattice structure to within predetermined maximum tolerances of the cell parameters are generated.