An expression is obtained for the sound attenuation constant in a doped displacive ferroelectrics in the presence of an external electric field, using double-time temperature-dependent Green’s function technique. The mass and force constant changes due to impurity atoms, are taken into account along with higher order anharmonic and electric dipole moment terms, in the Silverman-Joseph Hamiltonian. The attenuation constant increases with an external electric field. The soft mode is responsible for the anomalously increasing behaviour of the attenuation constant in the vicinity of the Curie temperature. The results agree with those attained by Tani and Tsuda and Heuter and Neuhaus.

An expression is obtained for the sound velocity change in doped displacive ferroelectrics, in the presence of an electric field by considering higher order anharmonic terms in the modified Silverman-Joseph Hamiltonian. The mass and force constant changes due to impurity may give cancellation effects. The presence of higher order anharmonicity decreases the sound velocity which in turn varies with the applied electric field. The sound velocity decreases anomalously near the Curie temperature.

The electric field dependence of the complex dielectric constant in an anharmonic defect ferroelectric crystal is calculated in its paraelectric phase from the Silverman-Joseph-Hamiltonian augmented with fourth-order phonon coordinates using double-time Green’s functions. The field and impurity dependence of the shift in the Curie temperature is discussed. An expression is obtained for the electric field dependence of dielectric loss at microwave frequencies in defect ferroelectrics.

Expressions for the complex dielectric constant, microwave absorption and the Curie temperature in doped displacive ferroelectrics, subjected to an external electric field are discussed, using the approach made in our previous study. A cross-term of defect parameters with electric field and anharmonic parameters is obtained. The intrinsic parametersB andC are modified by impurity terms. The qualitativeE² dependence of tan δ is discussed.

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 anomalous ultrasonic attenuationα_c of longitudinal waves propagating along (100) direction in KTaO₃ has been analyzed above the phase transition temperature in the frequency range 150–300 MHz in the paraelectric phase. The attenuation of longitudinal ultrasonic waves in KTaO₃ is primarily due to a strong interaction with thermally-excited phonons in the soft mode. Frequency and temperature variations of attenuation are discussed.

Using Green’s function method, microwave lossess were theoretically calculated for BaTiO₃, SrTiO₃ and KTaO₃ ferroelectric perovskites. In microwave range, an increase in frequency is followed by an increase in the dielectric loss. In the paraelectric phase, the dielectric loss decreases with increasing temperature showing the Curie-Weiss behaviour of the tangent loss.

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.