Thermodynamic description of generation of the second acoustic harmonics induced by an electric field in ferroelectrics

The temperature behavior of the generation of the second acoustic harmonics induced by an electric field during the transition of a crystal to the ferroelectric state has been considered based on the thermodynamic approach in the framework of the Landau model. It has been shown that the appearance of the contribution to polarization quadratic in the electric field leads to a change in the sign of the second acoustic harmonics and a change in its magnitude as compared to the paraphase. The results of the calculation are presented for the first-order and second-order transitions and in the tricritical point.