The soft mode dynamics and related properties of perovskite, ABO₃-type crystals have been studied using the operator form of the model Hamiltonian proposed by Pytte. The correlations have been evaluated using the double time thermal Green’s function technique and Dyson’s equation. Without any decoupling, the higher order correlations, appearing in the dynamical equation, have been evaluated using the renormalized Hamiltonian. The dielectric properties are directly related to the optical soft mode. The phonon width and shift have been calculated for different structural phases. The analysis of the temperature dependence of microwave loss tangent and dielectric constant explains the experimental results.

The dielectric constant and loss tangent of barium titanate and barium titanate doped with 0.4% (mole) La ceramics have been studied in the frequency range 22 KHz-70 MHz at room temperature and in the temperature range 20°C–170°C at 22 KHz using aQ-meter. It is observed that the dielectric constant at room temperature of the samples increases nearly a hundred fold on doping. The maximum of the dielectric constant broadens and shifts to a lower temperature in the La doped samples. The loss tangent is also relatively high in the doped sample. The dielectric constant and loss tangent of the doped samples decrease faster with frequency than that of the undoped samples.