Semi-infinite optimization formulation to obtain accuratephenomenological models for all phases of ferroelectric-ferroelasticcrystals

摘要

A formulation based on semi-infinite optimization is proposed tonobtain accurate thermodynamic phenomenological models over all phases ofnferroelectric and ferroelastic materials. The formulation is illustratednwith barium titanate (BaTiO3) single crystals. Analogous tonthe Devonshire theory, the elastic Gibbs function is expressed as antruncated Taylor series in terms of the polarization vector components,nwhose coefficients are unknown functions of temperature. Employing anmethodology based on semi-infinite optimization, the unknownncoefficients are determined using experimental measurements. In contrastnto all existing methods in the literature, the methodology proposednherein yields models that accurately predict the ferroelectricnproperties such as phase transitions, spontaneous polarization, andnpermittivity over a large temperature range. The objectivenfunction-which is a measure of the relative error in thenphenomenological model-for the optimal model shows a difference of morenthan 500% over the models obtained using previously proposed methods