Site symmetry approach to phase transitions in perovskite-related ferroelectric compounds

The phonon symmetry of a series of Aurivillius compounds ${[{\mathrm{Bi}}_{2}{\mathrm{O}}_{2}]}^{2+}$${[{A}_{n\ensuremath{-}1}{B}_{n}{\mathrm{O}}_{3n+1}]}^{2\ensuremath{-}}$ is studied by a site symmetry analysis of bulk crystals followed by the consecutive analysis of their common structural subunits, i.e., the metal-oxygen octahedra $B{\mathrm{O}}_{6}$ and individual layers. The division of the bulk crystals into rigid units $(B{\mathrm{O}}_{6})$ allowed to distinguish in the bulk phonon spectra the rigid unit modes involving the rotations of $B{\mathrm{O}}_{6}$ octahedra, which may be responsible for phase transitions from the tetragonal to intermediate phases. The symmetries of the rigid unit modes were found to vary in different Aurivillius compounds leading to different transition schemes within the Aurivillius family. The division of crystals into separate layers revealed the existence of Davydov doublets and quartets in the bulk spectra originating from the the same layer modes that considerably facilitates their symmetry assignment in Raman and infrared spectra. The group-theory predictions are in a good agreement with the ab initio calculations and experimental data that supports the validity of the single layer approach.