Advances in high-index-oriented ferroelectric films offer the exciting possibility of utilizing strain engineering to tune the desired properties related to the nanostructures. Previous studies often considered ferroelectric films grown on cubic substrates (isotropic strain), while the effects of anisotropic strains introduced by orthorhombic substrates are still not well understood. In our recent work, we grew (111)-oriented PbTiO₃ (PTO) films on orthorhombic GdScO₃ substrates and studied the domain structure evolution with film thickness. However, the theoretical understanding is lacking. In this work, the physical mechanism of the formation and evolution of domain structures was clearly revealed from the viewpoint of energy competition. Moreover, through the stereographic projection (SP) analysis of polarization vectors, a wide variety of ferroelectric phases for (111)-oriented PTO films under anisotropic strains were identified, and the misfit strain-misfit strain domain stability diagram was then constructed at room temperature. It was indicated that anisotropic misfit strains not only lead to the separation of ferroelectric domain variants that could co-exist under isotropic strain states for tetragonal-like d and monoclinic ma phases, but also stabilize the monoclinic mb phase. Their representative domain morphologies with separated domain variants under different anisotropic strains were analyzed in detail. These results provide guidance for interpreting and understanding more experimental data as well as the designing of (111)-oriented epitaxial ferroelectrics under anisotropic strains.

高折射率取向的铁电薄膜的进步提供了利用应变工程技术来调节与纳米结构有关的所需性能的令人兴奋的可能性。先前的研究通常考虑在立方衬底上生长的铁电薄膜（各向同性应变），而对正交晶衬底引入的各向异性应变的影响仍然知之甚少。在我们最近的工作中，我们在正交晶的GdScO ₃上生长了（111）取向的PbTiO ₃（PTO）膜。并研究了膜厚度对畴结构演化的影响。但是，缺乏理论上的理解。在这项工作中，从能量竞争的角度清楚地揭示了域结构形成和演化的物理机制。此外，通过极化矢量的立体投影（SP）分析，确定了各向异性应变下（111）取向的PTO薄膜的多种铁电相，然后在室温下构建了失配应变-失配应变域稳定性图。结果表明，各向异性失配应变不仅导致铁电畴变体的分离，这些变体可以在各向同性应变状态下共存于四角形d和单斜晶马。相，但也稳定了单斜相mb相。详细分析了它们在不同各向异性应变下具有分离的结构域变体的代表性结构域形态。这些结果为解释和理解更多的实验数据以及各向异性应变下（111）取向外延铁电体的设计提供了指导。