Thermodynamics of Ferroelectric Solid Solutions with Morphotropic Phase Boundaries

Abstract

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.

Strain Mechanisms in Lead-Free Ferroelectrics for Actuators

“…10,29,150,151,154,155 The origin of maximized properties at interferroelectric phase boundaries has been commonly attributed to a FD transverse instability of that ease its reorientation due to increased multiplicity of polarization states, reduced free energy anisotropy, and softening of the crystal lattice. 42,150,[156][157][158][159][160] Transverse instabilities have been pointed out in several works as the key for the enhancement of dielectric and electromechanical properties. 157,[159][160][161][162][163][164][165][166][167] Based on the soft-mode theory of ferroelectricity 168 , crystal softening is a result of an optical phonon that dramatically reduces its frequency down to zero during phase transitions.…”

“…This results in a reduced free energy anisotropy, which aids polarization mobility leading to a transverse instability of the and thus lower retention of the . 156 The MPB region marked with point in Figure 2.16 has been generically characterized as O or Monoclinic (M) phases. [170][171][172][173][174][175][176] This interleaving region was proposed to be a bridge phase between the nearby phases B and C, as there is no group-subgroup relation between the commonly found 4 / 4 and 3 symmetries.…”

“…39 Therefore, their experimental determination is quite difficult. 156 The coincidence of a tricritical point with a triple point such as the one marked with in Figure 2.16, will only occur in the hypothetical case that the critical points in the temperature-electric field and electric field-pressure phase diagrams intersect at the same temperature-composition coordinates of the triple point (at zero electric field and atmospheric pressure). The exceptionally large electromechanical properties of some BT-based materials were previously attributed to the presence of tricritical points.…”

“…Recent computations demonstrated that two triple points are expected in this region, although they may be difficult to access experimentally due to their close proximity. 156 Synchrotron studies determined that the R phase is characterized by a 3 symmetry, while the T phase depicts a 4 symmetry. 331,333 Both symmetries originate from a prototype cubic structure with 3 ̅ symmetry.…”

“…Recent calculations demonstrated that a broad region of the pseudobinary phase diagram features diminished free energy anisotropy and was ascribed to tilted PPBs. 156 Recent reports also highlighted the importance of studying elastic properties of the system, as they couple with piezoelectric properties. 318,341,349 Figure 3.6 displays (a) ´ and (b) 33 as a function of composition.…”