A phase-field approach to studying the temperature-dependent ferroelectric response of bulk polycrystalline PZT

Abstract Ferroelectric ceramics are of interest for engineering applications because of their electro-mechanical coupling and the unique ability to permanently alter their atomic-level dipole structure (i.e., their polarization) and to induce large-strain actuation through applied electric fields. Although the underlying multiscale coupling mechanisms have been investigated by modeling strategies reaching from the atomic level across the polycrystalline mesoscale to the macroscopic device level, most prior work has neglected the important influence of temperature on the ferroelectric behavior. Here, we present a phase-field (diffuse-interface) constitutive model for ferroelectric ceramics, which is extended to account for the effects of finite temperature by considering thermal lattice vibrations based on statistical mechanics and by modifying the underlying Landau-Devonshire potential to depend on temperature. Results indicate that the chosen interpolation of the Landau energy coefficients is a suitable approach for predicting the temperature-dependent spontaneous polarization accurately over a broad temperature range. Lowering the energy barrier at finite temperature by the aforementioned methods also leads to better agreement with measurements of the bipolar hysteresis. Based on a numerical implementation via FFT spectral homogenization, we present simulation results of single- and polycrystals, which highlight the effect of temperature on the ferroelectric switching kinetics. We observe that thermal fluctuations (at the phase-field level realized by a thermalized stochastic noise term in the Allen-Cahn evolution equation) promote the nucleation of needle-like domains in regions of high heterogeneity or stress concentration such as grain boundaries. This, in turn, leads to a faster polarization reversal at low electric fields and a simulated domain pattern evolution comparable to experimental observations, stemming from the competition between nucleation and growth of domains. We discuss the development, implementation, validation, and application of the temperature-dependent phase-field framework for ferroelectric ceramics with a focus on tetragonal lead zirconate titanate (PZT), which we demonstrate to admit reasonable model predictions and comparison with experiments.