Multiscale Modeling and Simulation of Ferroelectric Materials

材料建模的最新技术为特定长度和时间尺度提供了精确的模拟方法，从原子尺度的电子结构计算和分子力学到宏观尺度的连续体配方。然而，计算成本限制了原子模拟技术的长度和时间尺度。作为一个值得注意的例外，准连续体（QC）方法降低了计算成本，而不会在需要的区域丢失原子细节。因此，它减少了自由度的数量，通过引入运动学约束，这内插晶格位点的位置从一组减少的代表性原子的位置。除了运动学约束，求和规则被引入到有效地减少要考虑的能量和力的计算中的晶格位点的数量。QC方法已被证明是有用的，在多尺度材料建模，如纳米压痕，晶格缺陷与纳米尺寸的裂纹和纳米空隙的相互作用等问题的研究。然而，建立QC方法有两个中心的局限性。首先，它不能令人满意地扩展到多晶格晶体以捕获单位晶胞或分子内的非均匀行为。其次，更重要的是，它不延伸到离子晶体，因为长程库仑相互作用对QC方法提出了额外的挑战。QC求和规则利用了典型的短程原子间势，它允许对感兴趣的量进行局部评估。当长程相互作用变得重要时，这样的概念就不再适用了。传统QC方法对原子级相互作用性质的这种限制排除了它对一大类材料的应用;因此，QC方法不能应用于研究典型功能材料的丰富的介电行为，而这些典型功能材料是能量存储，感测/致动，因此，开发和扩展离子晶体的QC方法是扩大该方法适用性的重大飞跃。因此，通过这个项目，我们提出了一种新的扩展QC方法，适用于多晶格晶体和离子晶体，从而克服了现有QC方法的局限性。在LTM使用内部开发和实施的QC软件进行的初步工作显示了有希望的结果，并表明所提出的扩展QC方法确实将有效地应用于离子晶体。因此，总的来说，这个项目的目标是（i）QC方法扩展到多晶格晶体材料，（ii）QC方法扩展到处理长程库仑相互作用，（iii）实现这些扩展并提供第一个用于三维QC模拟的开源库，以及（iv）使用扩展的QC方法研究铁电行为。

The state of the art in material modeling offers accurate simulation methods for specific length and time scales, spanning from electronic structure calculations and molecular mechanics at atomistic scales to continuum formulations at the macroscale. However, computational costs limit the length and time scales accessible to atomistic simulation techniques. As a noteworthy exception, the quasicontinuum (QC) method reduces computational costs without losing atomistic detail in regions where it is required. Thereby it reduces the number of degrees of freedom by introducing kinematic constraints, which interpolate lattice site positions from the positions of a reduced set of representative atoms. In addition to kinematic constraints, summation rules are introduced to efficiently reduce the number of lattice sites to be considered in the computation of energies and forces. The QC method has proven useful to study exemplary problems in multiscale material modeling such as nanoindentation, interaction of lattice defects with nanosized cracks and nanovoids, etc.However, the established QC method has two central limitations. First, it does not extend satisfactorily to multi-lattice crystals to capture non-uniform behavior within a unit cell or a molecule. Second, and more importantly, it does not extend to ionic crystals, since long-range Coulomb interactions present an additional challenge for the QC method. The QC summation rules take advantage of typical short-range interatomic potentials, which admit the local evaluation of quantities of interest. When long-range interactions gain importance, such a concept no longer applies. This restriction on the nature of atomic-level interactions for the conventional QC method excludes its application to a large class of materials; all dielectrics, polarizable solids, and ionic solids.The QC method, therefore, does not find application to study the rich dielectric behavior of typical functional materials that are central to modern technologies in energy storage, sensing/actuation, etc. Developing and extending the QC method for ionic crystals is thus a significant leap in broadening the applicability of the method. Therefore, through this project we propose a novel extended QC method that is applicable to multi-lattice crystals and ionic crystals thereby overcoming limitations of the established QC method. The preliminary work undertaken at LTM using a QC software developed and implemented in-house shows promising results and indicates that the proposed extended QC method will indeed apply effectively to ionic crystals. Thus in summary, the goals of this project are (i) extension of the QC method to multi-lattice crystalline materials, (ii) extension of the QC method to handle long-range Coulomb interactions, (iii) implementation of these extensions and providing the first open-source library for three-dimensional QC simulations, and (iv) the study of ferroelectric behavior using the extended QC method.