Thermodynamics of polar anisotropy in morphotropic ferroelectric solid solutions

A classical 2-4-6 Landau polynomial is used to describe the generic pseudobinary composition-temperature (c-T) diagram of ferroelectric solid solutions that display a morphotropic boundary (MB). This polynomial is separated into an isotropic part that depends on the absolute value of the polarization and an anisotropic part that depends also on the direction of polarization. Composition and temperature are taken as external thermodynamic variables and the direction of the polarization vector is treated as an internal relaxing variable of the system. Conditions leading to the observation of stable rhombohedral (F-R), tetragonal (F-T) and orthorhombic (F-O) phases in the c-T plane are determined. In the lowest-order approximation, the isothermal composition change producing the F-R to F-T transition at the MB is dictated by the condition that the polarization anisotropy energy vanishes. A small lifting of the orientational degeneracy of the polarization leads to differing phase diagram topologies wherein a stable F-O phase may interleave the F-R and F-T phase fields along the MB line. The theory simultaneously accounts for disparate physical phenomena observed in morphotropic ferroelectric solid solutions, which include a sharp reduction in the ferroelectric domain size and the appearance of a dipole glass state connected with intermediate ferroelectric phases, and large extrinsic contributions to the electromechanical properties near the MB. The curving of the MB line, the nearly continuous transitions between adjacent ferroelectric phases and the change in the order of the paraelectric to ferroelectric transitions with composition also arise naturally in the theory.