Role of electrostriction on domain switching near the morphotropic phase region in a ferroelectric solid solution: Thermodynamic analysis and phase-field simulations

Enhanced room-temperature electromechanical coupling in the equimolar lead-free ferroelectric solid solution of barium zirconate titanate and barium calcium titanate is attributed to the existence of an intermediate morphotropic phase region. Initial studies suggested that the existence of a polar orthorhombic phase in the morphotropic region between terminal solid solutions of rhombohedral barium zirconate titanate and tetragonal barium calcium titanate causes this enhancement. However, recent experiments suggest the coexistence of two or more of these phases in the morphotropic region. Such coexistence can often arise due to changes in anisotropy in electrostriction. To understand the effect of anisotropy in electrostriction on the stability of these phases and the consequent polarization switching characteristics in the equimolar solid solution, we performed systematic phase-field simulations of domain evolution to the steady state in this system under stress-free conditions as a function of anisotropy in electrostriction defined by Qz = 2Q44/(Q11- Q12), where Q11, Q12, and Q44 are the independent coefficients of the electrostriction tensor (expressed using Voigt notation). Our results show a systematic reduction in polarization anisotropy with increasing Qz. For example, a single-phase configuration consisting of orthorhombic variants corresponding to isotropic electrostrictive moduli (Qz = 1) transforms to a three-phase configuration containing tetragonal, orthorhombic, and rhombohedral variants when the moduli show strong anisotropy (Qz = 2.5). We use the effective in-plane and out-of-plane piezoelectric coefficients and their ratio as a measure of the electromechanical switching characteristics. Unlike polarization anisotropy behavior, these characteristics do not exhibit such monotonic behavior. The effective piezo coefficients depend not only on the number of coexisting polar phases but also on their spatial configuration with respect to the applied field. Our predictions pertaining to the coexistence of tetragonal and orthorhombic variants and the corresponding effective out-of-plane piezoelectric coefficient show good agreement with experimental findings. We also discuss how clamped or constrained conditions can modify the phase stability observed under stress-free conditions.