A NEW METHODOLOGY TO OBTAIN ACCURATE MODELS FOR FERROELECTRICS WITH APPLICATION TO BATIO3

A new methodology based on semi-infinite optimization is proposed to o btain accurate yet simple phenomenological models for ferroelectric si ngle crystals. The phenomenological models for ferroelectrics start wi th a Taylor series expansion of the governing thermodynamic potential, the elastic Gibbs function, in terms of the independent variables. Th e coefficients of the appropriately truncated series are determined, b ased on the experimental properties of the crystal. However, there is to date no method to determine the coefficients for an accurate correl ation to the experimental measurements. To this end, a semi-infinite o ptimization problem is formulated, aiming at minimizing the error betw een the analytical model and experiments in terms of permittivity coef ficients and spontaneous polarization. A model in the cubic and the te tragonal phases for barium titanate (BaTiO3) single crystals for a par ticular choice of experimental measurements is used to demonstrate the workability of the proposed methodology. The resulting optimization p roblem has an infinity of inequality constraints. The optimal solution to the proposed semi-infinite optimization problem when used in the m odel, accurately predicts the ferroelectric properties of BaTiO3 singl e crystals such as phase transitions, spontaneous polarization, permit tivity, etc. over the range of temperature in the cubic and the tetrag onal phases. The proposed methodology is not limited by the complexity of the phenomenological model, or the choice of the experimental meas urements. Furthermore, the proposed methodology can be generalized to model ferroelastic materials.