Sound attenuation in Ba_xSr_1-x TiO₃ perovskites

Abstract

An expression is obtained for the sound attenuation constant in anharmonic Ba_xSr_1-x TiO₃ ferroelectric crystal, using double-time temperature dependent Green's function technique. The mass and force constant changes due to impurity atoms, are taken into account in the Silverman-Joseph Hamiltonian augmented with higher order anharmonic terms. The defect and anharmonic contributions to the attenuation constant are discussed separately. An anomalous increase in attenuation constant is predicted in the vicinity of Curie temperature. The soft mode is held responsible for this effect. The effect of defect and anharmonicity on stabilization of the soft mode frequency is also studied. With addition of defect (concentration <i>x</i>) in Ba_xSr_1-x TiO₃, the soft mode frequency continuously decreases and hence the attenuation constant (α) increases. The results agree with those obtained by Tani & Tsuda, <i>J Phys Soc Japan</i>, 26 (1969) 113 and Heuter & Neuhaus, <i>J Acoust Soc Am</i>. 27 (1955) 292.