Polar Anisotropy and Inter-Ferroelectric Transitions in Barium Titanate and its Solid Solutions

A particular form of the Ginzburg-Landau-Devonshire theory of weak first-order transitions is applied to barium titanate and its solid solutions. The theory places emphasis on the crystallographic anisotropy of polarization and its relation to the inter-ferroelectric transitions between proper symmetry phases. It is shown that the dependences of the quartic anisotropy energy on external parameters of temperature and composition play dominant roles in controlling the phase diagram topologies of barium titanate-based systems. The theory is also applicable to morphotropic diagrams, and it provides a unified parameterization scheme useful for constructing constitutive models, phase field simulations, and first-principles derived thermodynamic theories.