Semi-infinite optimization formulation to obtain accurate phenomenological models for all phases of ferroelectric-ferroelastic crystals

A formulation based on semi-infinite optimization is proposed to obtain accurate thermodynamic phenomenological models over all phases of ferroelectric and ferroelastic materials. The formulation is illustrated with barium titanate (BaTiO/sub 3/) single crystals. Analogous to the Devonshire theory, the elastic Gibbs function is expressed as a truncated Taylor series in terms of the polarization vector components, whose coefficients are unknown functions of temperature. Employing a methodology based on semi-infinite optimization, the unknown coefficients are determined using experimental measurements. In contrast to all existing methods in the literature, the methodology proposed herein yields models that accurately predict the ferroelectric properties such as phase transitions, spontaneous polarization, and permittivity over a large temperature range. The objective function-which is a measure of the relative error in the phenomenological model-for the optimal model shows a difference of more than 500% over the models obtained using previously proposed methods.