Phenomenological analysis of tetragonal tungsten bronze ferroelectrics

Abstract

A simple Devonshire form has been derived for the phenomenological elastic Gibbs function to describe the elasto-dielectric parameters of simple proper ferroelectrics in the tungsten bronze structure family which has 4/mmm prototypic point symmetry. For the assumption that all temperature dependence is carried by the Curie-Weiss behaviour implicit in the quadratic term and that the expansion may be terminated at the first sixth-order term, reasonable agreement between calculated and derived P _s against T curves in the ferroelectric phase can be obtained for a wide range of bronze compositions. From the fitting it is clear that second and sixth rank terms are remarkably constant over a very wide range of bronze compositions. Variation in the negative fourth rank term is larger, but this is to be expected since it contains large contributions from electrostrictive and elastic terms which will depend on boundary conditions. These initial studies suggest that the phenomenological method may be used to derive expectation values for tensor parameters across the whole family of ferroelectric bronzes. The study also points up the need for more careful detailed studies of lattice strain, birefringence and permittivity as a function of temperature in model bronze compounds to provide more detailed checks of the method.