Symmetry-mode analysis of displacive phase transitions using International Tables for Crystallography

The symmetry-mode analysis of a structural phase transition involves the use of methods of the representation theory of space groups. The aim of the paper is to present an alternative approach for the determination of the primary and secondary symmetry modes that contribute to the structural distortion of the low-symmetry phase. It only requires the systematic use of the data from International Tables for Crystallography, Vol. A, and is based on a fact, well known to crystallographers: the fully symmetrical displacements of any orbit of atoms (i.e. the modes compatible with the symmetry of the structure) follow in a straightforward way from the coordinate triplets of the corresponding Wyckoff positions. This property, systematically used for all intermediate subgroups between the space groups of the two phases, allows the determination 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 distortion of potassium selenate are divided.