Structural phase transitions in crystals with P63/mmc symmetry

A study of the possible phase symmetries derived from a prototype phase with space group P6 3 /mmc (D 6h 4 ) has been performed. Only those phases that can be explained as the result of the onset of an order parameter transforming according to one irreducible representation of the prototype space group are considered. The different space groups for the possible distorted phases have been investigated. All the irreducible representations which belong to symmetry points in the hexagonal Brillouin zone are analysed. The Landau and Lifshitz criteria have been considered to determine those transitions which should necessarily be first order. For every representation the authors have calculated the subspace in the representation space along which the displacement of the order parameter must take place to describe the different permitted symmetries for the distorted phase. Every considered irreducible representation D(k, j) and every relevant subgroup G of P6 3 /mmc, of the number of times that the identity representation is contained in the representation subduced in G by D(k,j). This information together with the chain subduction criterion permits a complete investigation of the symmetry in the representation space.