Temperature-Dependent Polarizabilities in Paraelectric BaTiO3and SrTiO3

A generalized internal-field theory of the pressure, temperature, and composition dependence of the dielectric constant is presented which allows the independent determination of two polarizabilities from experimental data. The model is shown to involve the total polarizabilities of $A$ and $B$ and the electronic polarizability of O for the perovskite lattice, $\mathrm{AB}{\mathrm{O}}_3$, so that certain comparisons with optical data can be made via the oxygen polarizability. The three polarizabilities are determined parametrically using experimental data for BaTi${\mathrm{O}}_3$ (120 to 350°C) and SrTi${\mathrm{O}}_3$ (-150 to 0°C), and it is found that acceptable polarizability solutions are limited to a surprisingly narrow "band" for each polarizability. These solutions are then used to determine the explicit temperature and volume dependences of the polarizabilities in both crystals. For BaTi${\mathrm{O}}_3$ it is concluded that the explicit temperature dependence of the oxygen polarizability is very weak, and that the major contribution to ${\left(\frac{\partial \epsilon }{\partial T}\right)}_p$ is the explicit dependence of the Ti polarizability (ionic) on temperature (i.e., the Slater model). For SrTi${\mathrm{O}}_3$, the data are interpreted as requiring an explicit temperature dependence of the oxygen polarizability, in contrast to the BaTi${\mathrm{O}}_3$ case, and all contributions to ${\left(\frac{\partial \epsilon }{\partial T}\right)}_p$ for SrTi${\mathrm{O}}_3$ are found to be of equal importance, also in contrast to BaTi${\mathrm{O}}_3$