Modes vs. modulations: Symmetry-mode analysis of commensurate modulated structures compared with the superspace method

Abstract

We know from Landau theory that the natural language to deal with distorted structures is the one of symmetry-adapted modes. A symmetry-mode decomposition is both useful for investigating the mechanisms responsible of these phases and for pure crystallographic purposes. Some symmetry-mode components are usually dominant, introducing a parameter hierarchy or reducing in practice the crystallographic degrees of freedom. Several computer tools are now freely available allowing structure refinements directly using symmetry-mode collective coordinates. Alternatively, the superspace formalism is a very efficient method for similar purposes. By means of several examples we compare the two approaches.