Group actions as applied to symmetry breaking in hexagonal crystals with space group P63/m

Abstract

A procedure is outlined that allows one to predict the possible low-symmetry space groups for a commensurate phase transition associated with a broken symmetry. By considering each irreducible representation of the high-symmetry space group and using a subduction procedure involving the theory of group actions, one may determine a complete set of representative order parameters and their little groups. Each little group can be identified as a possible space group for the low-symmetry phase. The method is used to deduce all possible broken symmetries of space group P63/m that can result from a phase transition associated with one of the symmetry points in the Brillouin zone. As a specific application of the resulting tables of possible order parameters and associated low-symmetry space groups, changes in the X nuclear quadrupole resonance spectrum due to structural phase transitions in hexagonal AX3 crystals with the high-symmetry space group P63/m are considered.