A micromechanics-based model for temperature effect on piezoelectric and dielectric constants of ferroelectric crystals

A micromechanics-based thermodynamic model is applied to study the piezoelectric and dielectric constants of BaTiO3 crystals as a function of temperature upon the cooling from the Curie point. The formation of spontaneous polarization at the beginning of cooling provides dramatic change in symmetry of the system. This plays an important role for the sudden change in piezoelectric constant of d(31) at the beginning of the cooling. In this article, by considering such a heterogeneous nature of the crystal at the beginning of the cooling due to spontaneous polarization, the micromechanics-based model is able to evaluate the piezoelectric coefficient d(31). To verify this modified model, the dielectric constant k(33) of a BaTiO3 crystal in terms of temperature is also calculated and compared with the existing micromechanics-based model in the literature [Y. Su and G. J. Weng, J. Mech. Phys. Solids 53, 2071 (2005)]. It shows agreeable and improved result in dielectric constant k(33) of BaTiO3. Both dielectric and piezoelectric constants are also found to be consistent with the available experimental data.