Accurate phenomenological models for all four phases of BaTiO3via semi-infinite optimization

Abstract

Abstract For the first time, an accurate model for all the 4 phases of single crystal barium titanate (BaTiO3) is obtained via semi-infinite optimization formulation that determines the temperature-dependent coefficients of an appropriately truncated elastic Gibbs function. Functional-inequality constraints characterize the changing crystal structure; equality constraints enforce the phase transition temperatures. Solution techniques and their intricacies are clearly discussed. The resulting model accurately predicts the ferroelectric properties of single crystal BaTiO3 such as phase transitions, together with spontaneous polarization and permittivity at any temperature. The proposed methodology is applicable to ferroics in general.