Model of the Ferroelectric Phase Transition in the Tetragonal Tungsten-Bronze-Structure Ferroelectrics

A microscopic model is presented for the ferroelectric phase transition in the tetragonal tungsten-bronze-structure ferroelectrics (e.g., ${\mathrm{Sr}}_{1-x}{\mathrm{Ba}}_x{\mathrm{Nb}}_2{\mathrm{O}}_6$) which, for the first time, provides a description of its essential features, including the fact that it is a displacive transition but has no "soft"-phonon mode. The model employs an interaction between the ferroelectric phonon displacement and local structural changes, which are important in these materials; and it describes well important features of the Raman spectra, dielectric constant, and refractive index.