Thermodynamic Theory of Single-Crystal Lead Titanate with Consideration of Elastic Boundary Conditions

A phenomenological free-energy function including the effects of elastic boundary conditions was presented and used to investigate the single-domain, single-crystal properties of the ferroelectric perovskite, PbTiO₃. In particular, the effects of tensile and compressive hydrostatic stress on the spontaneous polarization, Curie point, dielectric susceptibility, and piezoelectric property coefficients were examined. The calculated shift of the Curie point with hydrostatic stress, along with the entropy and enthalpy of the ferroelectric-paraelectric phase transition, was found to be in good agreement with experimental measurements. The isothermal variation of the relative dielectric susceptibility and piezoelectric coefficients with hydrostatic stress exhibited the expected behavior near the ferroelectric-paraelectric phase transition.