Electric Field Dependence of Soft Mode Frequency in Ba_1-Xca_xtio₃ Ferroelectric Perovskites

An expression has been obtained for the soft mode frequency in Ba_1-xCa_xTiO₃ ferroelectric perovskites in the presence of external electric field by using double time temperature dependent Green's function technique. The mass and force constants change due to the impurity atoms which are taken into account in the presence of higher order anharmonic and electric moment terms in the Silverman Joseph Hamiltonian. The soft mode frequency is obtained in the presence of both the electric field and defect concentrations of Ca in pure BaTiO₃. The soft mode frequency increases with increase in electric field and defect concentration.