SYMMETRY-MODE ANALYSIS OF DISPLACIVE PHASE-TRANSITIONS USING INTERNATIONAL TABLES FOR CRYSTALLOGRAPHY

The symmetry-mode analysis of a structural phase transition involves t he use of methods of the representation theory of space groups. The ai m of the paper is to present an alternative approach for the determina tion of the primary and secondary symmetry modes that contribute to th e structural distortion of the low-symmetry phase. It only requires th e systematic use of the data from International Tables for Crystallogr aphy, Vol. A, and is based on a fact, well known to crystallographers: the fully symmetrical displacements of any orbit of atoms (i.e. the m odes compatible with the symmetry of the structure) follow in a straig htforward way from the coordinate triplets of the corresponding Wyckof f positions. This property, systematically used for all intermediate s ubgroups between the space groups of the two phases, allows the determ ination of the relevant symmetry modes. Their distinction into primary and secondary modes comes out directly in the process of calculation. As an example, primary and secondary modes in the ferroelectric disto rtion of potassium selenate are divided.