Sound velocity change in doped displacive ferroelectrics

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.