Electric field dependent sound velocity change in Ba_1−xCa_xTiO₃ ferroelectric perovskites

Abstract

By using double time temperature dependent Green’s function technique, an expression for the sound velocity change in the mixed crystal perovskites (Ba_1−xCa_xTiO₃) has been obtained with the help of the modified Silverman-Joseph Hamiltonian. Third- and fourth-order anharmonic and electric moment terms in the modified Hamiltonian for Ba_1−xCa_xTiO₃ crystal perovskites have been considered. The effect of defect, electric field and anharmonic contributions on velocity change in Ba_1−xCa_xTiO₃ for paraelectric phase has been studied. The presence of higher order anharmonicity and electric moment terms decreases the sound velocity. In the vicinity of the phase transition, it decreases as the consequence of the soft mode. It also varies with electric field and defect concentration in Ba_1−xCa_xTiO₃.