Thermodynamics of Ferroelectric Solid Solutions with Morphotropic Phase Boundaries

A thermodynamic analysis is presented for the diffusionless phase diagrams of ferroelectric solid solutions that display a morphotropic phase boundary (MPB) separating adjacent tetragonal and rhombohedral phases. Equations are developed for the shape of the MPB, the locations of triple and tricritical points, and for the line along which the anisotropy of polarization vanishes. The appearance of lower symmetry orthorhombic and monoclinic phases is considered and the topologies of energy surfaces in the region of the phase diagram where these phases may stabilize are illustrated. The theory is applied to the solid solution of lead zirconate with lead titanate (PZT) and relationships between polar anisotropy and the transformation strain, dielectric susceptibility and piezoelectric properties, are discussed. The analysis is used to reproduce phase boundary lines for solid solutions of lead titanate with lead magnesium niobate (PMN-PT) and lead zinc niobate (PZN-PT) and composition-temperature diagrams along isopleths in the ternary system PMN-PZT are estimated. The anisotropies of polarization in solid solutions based on lead titanate and barium titanate are contrasted. The results provide a thermodynamic framework useful for guiding experimental investigations of ferroelectric solid solutions and for generating energy functions used in constitutive modeling and phase field simulations of microstructure and properties.