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.

铁电陶瓷由于其机电耦合以及永久改变其原子级偶极结构（即其极化）并通过施加电场引起大应变致动的独特能力，因此在工程应用中受到关注。尽管通过建模策略研究了从根本上的多尺度耦合机制，这些策略从跨多晶中尺度的原子能级到宏观器件能级，但大多数先前的工作都忽略了温度对铁电行为的重要影响。在这里，我们介绍了铁电陶瓷的相场（扩散界面）本构模型，通过基于统计力学考虑热晶格振动并修改底层的Landau-Devonshire势能以依赖于温度，可以扩展到考虑有限温度的影响。结果表明，选择的Landau能量系数插值法是在较宽的温度范围内准确预测温度相关的自发极化的合适方法。通过上述方法降低有限温度下的能垒也导致与双极性磁滞的测量更好地吻合。基于通过FFT频谱均质化的数值实现，我们给出了单晶和多晶的仿真结果，突出了温度对铁电开关动力学的影响。我们观察到，热涨落（在Allen-Cahn演化方程中由热化随机噪声项实现的相场水平）促进了高异质性或应力集中（例如晶界）区域中针状畴的成核。反过来，这归因于畴的成核和生长之间的竞争，从而导致在低电场下极化反转更快，模拟的畴图案演变与实验观察结果相当。我们讨论了铁电陶瓷的温度相关相场框架的开发，实施，验证和应用，重点是四方钛酸锆钛酸铅（PZT），我们证明了该模型可以接受合理的模型预测并与实验进行比较。