By implementing a novel multiphase field model for ferroelectric systems, the phase coexistence of the tetragonal (T) and rhombohedral (R) phases in Pb-free BZT-40BCT was analyzed. Metastable coexistence of the T and R phases is predicted between a thermodynamic upper limit at $T_{C,\mathrm{R}}={49.90}^{\circ }\mathrm{C}$ and a kinetic lower limit determined by the time-temperature-transformation behaviour. Predicted domain microstructures exhibit faceted domain walls and curved T-R phase interfaces that are consistent with recent TEM studies in the vicinity of the polymorphic phase boundary (PPB). Further, miniaturization of the domain structure near the PPB is a result of the relatively low interfacial energies and a pinning effect caused by the large metastable phase fraction that originates from the vanishing macroscopic driving force for phase transformation. Particularly, the vanishing of rhombohedral domain wall energies as $T\to T_{C,\mathrm{R}}$ enables a phase transformation-induced polarization rotation mechanism and predicts a hierarchical domain morphology for the R phase. These results are in agreement with the higher piezoelectric response reported near the maximum temperature for R+T coexistence and the observations of a miniaturized nanodomains structure within micron-sized, wedge-shaped domains in the R phase for the BZT-$x$BCT system.

通过为铁电系统实现新颖的多相场模型，分析了无铅BZT-40BCT中四方（T）和菱形（R）相的共存。预测T和R相的亚稳态共存温度为${Ť}_{C，\mathrm{[R}}={49.90}^{\circ }\mathrm{C}$由时间-温度-转变行为确定的动力学下限。预测的畴微结构表现出多晶的畴壁和弯曲的TR相界面，这与近期在多态相边界（PPB）附近的TEM研究一致。此外，PPB附近的畴结构的小型化是相对较低的界面能和较大的亚稳相分数所引起的钉扎效应的结果，所述亚稳相分数源自消失的用于相变的宏观驱动力。特别是，菱面体畴壁能量的消失为$Ť\to {Ť}_{C，\mathrm{[R}}$启用相变诱导的极化旋转机制，并预测R相的分层域形态。这些结果与R + T共存的最高温度附近报道的更高的压电响应以及BZT-的R相中微米级楔形畴内的微型纳米畴结构的观察结果一致。$X$BCT系统。