Maximal symmetry transition paths for reconstructive phase transitions

An essential part of the description of a reconstructive phase transition consists in the determination of the so-called transition path, which defines the possible atomic displacements and lattice strains that occur during the transformation. We present a systematic procedure for the determination of possible transition paths in phase transitions with no group-subgroup relation between their phases. It is assumed that the transformation involves, at least locally, an intermediate state described by a common subgroup of the symmetry groups of the two end phases. The possible mappings between the end structures are restricted by symmetry constraints following from the occupied atomic orbits, and tolerances for lattice strains and atomic displacements. The concept of maximal symmetry transition paths is used for the classification of the different symmetry allowed transition paths. The application of the procedure is illustrated by the determination of maximal symmetry transition paths for the transformations from wurtzite to rocksalt, zincblende to rocksalt and rocksalt to caesium chloride structure types.