Symmetry analysis of the microstructure and phase transitions of a crystallographic space group: Applications

Two tables are presented which result from the symmetry analysis of the microstructure, i.e., atomic site locations, for a system with space-group symmetry R3¯c ($D_{3d}^6$). The first table contains information about transition order parameters. Representations, allowed subgroup symmetries, Landau and Lifshitz frequencies, changes in primitive-cell size, lattice relationships, etc., are listed. The second table gives the listing of the frequencies of subduction by the representation of the space group R3¯c for the representations of each site point group. After an explanation of the tables, examples are presented which show how the tables are used. Examples include the classification of lattice and magnetic modes, the testing of the tensor field criterion for phase transitions, and the determination of nuclear quadrupole resonance line splitting at phase transitions.