DIELECTRIC-PROPERTIES OF PEROVSKITE CRYSTALS

The soft mode dynamical model has been used to study the dielectric properties of Perovskite-type crystals. The model Hamiltonian proposed by Pytte has been modified and designed in terms of creation and annihilation operators. The correlations appearing in the dynamical equation have been evaluated using double time thermal retarded Green's function and Dyson's equation. Without any decoupling the higher order correlations have been evaluated using the renormalized Hamiltonian and thus, all possible interactions among phonons have been taken into account. The expressions for phonon frequencies and widths have been calculated. Using appropriate parameters the softening of different modes at different transition temperatures give rise to a series of transitions from cubic to tetragonal, orthorhombic or trigonal phases. The significantly temperature-dependent modes are considered responsible for damping constant, dielectric constant, tangent loss and attenuation constant for these crystals. The dielectric properties arc directly related to the optical phonon frequencies and widths and acoustic attenuation to the acoustic and optical phonon widths. Using suitable approximations, the model explains the experimental results on dielectric properties and acoustic attenuation reported for LiNbO3, SrTiO3, BaTiO3 and LaAlO3.