Composite materials composed of multiferroelectric nanoparticles in dielectric matrixes have attracted enormous attention for their potential applications in developing future functional devices. However, the functionalities of ferroelectric nanoparticles depend on shapes, sizes, and materials. In this paper, a time-dependent Landau-Ginzburg method has been used and combined with a method as the coupled-physics finite-element-method-based simulations are used to illustrate the polarization behavior in isolated BaTiO3 or PbTiO3 octahedral nanoparticles embedded in a dielectric medium, like SrTiO3 (ST, high dielectric permittivity) and amorphous silica (a-SiO2, low dielectric permittivity). The equilibrium polarization topology of the octahedral nanoparticle is strongly affected by the choice of inclusion and the size of matrix materials. Also, there are three equilibrium polarization patterns, i.e., monodomain, vortex-like, and multidomain, because of the various sizes and material parameters combination. There is a critical particle size below which ferroelectricity vanishes in our calculations. This size of the PbTiO3 octahedral nanoparticle is 2.5 and 3.6 nm for high- and low-permittivity matrix materials, respectively. However, this size of the BaTiO3 octahedral nanoparticle is 3.6 nm regardless of the matrix materials.

中文翻译：

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铁电八面体纳米粒子的尺寸、形状和材料效应

由介电基质中的多铁电纳米粒子组成的复合材料因其在开发未来功能器件中的潜在应用而引起了极大的关注。然而，铁电纳米粒子的功能取决于形状、尺寸和材料。在本文中，使用了时间相关的 Landau-Ginzburg 方法并结合了一种方法，因为基于耦合物理的有限元方法模拟被用来说明嵌入在一个孤立的 BaTiO3 或 PbTiO3 八面体纳米粒子中的极化行为。介电介质，如 SrTiO3（ST，高介电常数）和无定形二氧化硅（a-SiO2，低介电常数）。八面体纳米粒子的平衡极化拓扑受夹杂物的选择和基质材料的大小的强烈影响。还，由于各种尺寸和材料参数组合，存在三种平衡极化模式，即单域、涡旋和多域。在我们的计算中，存在一个临界粒径，低于该粒径时，铁电性消失。对于高和低介电常数基质材料，PbTiO3 八面体纳米颗粒的这种尺寸分别为 2.5 和 3.6 nm。然而，无论基体材料如何，BaTiO3 八面体纳米颗粒的这种尺寸都是 3.6 nm。分别。然而，无论基体材料如何，BaTiO3 八面体纳米颗粒的这种尺寸都是 3.6 nm。分别。然而，无论基体材料如何，BaTiO3 八面体纳米颗粒的这种尺寸都是 3.6 nm。