离子固体中长程静电相互作用的原子-连续多尺度模拟
Atomistic-to-Continuum Multiscale Modeling with Long-Range Electrostatic Interactions in Ionic Solids
摘要：
本文提出了一种研究含缺陷离子晶体的多尺度原子-连续方法。缺陷通常在离子和电子固体中起着核心作用，不仅限制了可靠性，更重要的是使这些材料具有至关重要的功能。实例包括通过带电点缺陷的运动传导电流的固体电解质，以及通过畴壁缺陷的运动显示多功能性的复合氧化物铁电体。因此，了解缺陷的结构及其对电场和机械场的响应非常重要。然而，一个中心障碍是离子固体中的相互作用包括短程原子相互作用以及长程静电相互作用。现有的原子-连续介质多尺度方法，如准连续介质方法，仅适用于原子间的短程相互作用。此外，量子力学到密度泛函模型的经验简化无法捕捉这些材料中感兴趣的关键现象。为了解决这个问题，我们发展了一种多尺度原子方法来粗粒化含缺陷离子晶体中的长程电相互作用。在这些设置中，电荷密度快速变化，但几乎是周期性的。其关键思想是使用的极化密度场作为多尺度调解人，使有效的粗粒化，利用几乎周期性的变化。在远离缺陷的区域，晶体接近完美，极化场作为代理，使我们能够避免考虑电荷变化的细节。我们结合这种方法为远程静电与标准的准连续体方法为短程相互作用，以实现一个有效的多尺度原子连续方法。
英文摘要：
We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that make these materials of critical importance. Examples include solid electrolytes that conduct current through the motion of charged point defects, and complex oxide ferroelectrics that display multifunctionality through the motion of domain wall defects. Therefore, it is important to understand the structure of defects and their response to electrical and mechanical fields. A central hurdle, however, is that interactions in ionic solids include both short-range atomic interactions as well as long-range electrostatic interactions. Existing atomistic-to-continuum multi-scale methods, such as the Quasicontinuum method, are applicable only when the atomic interactions are short-range. In addition, empirical reductions of quantum mechanics to density functional models are unable to capture key phenomena of interest in these materials. To address this open problem, we develop a multiscale atomistic method to coarse-grain the long-range electrical interactions in ionic crystals with defects. In these settings, the charge density is rapidly varying, but in an almost-periodic manner. The key idea is to use the polarization density field as a multiscale mediator that enables efficient coarse-graining by exploiting the almost-periodic nature of the variation. In regions far from the defect, where the crystal is close-to-perfect, the polarization field serves as a proxy that enables us to avoid accounting for the details of the charge variation. We combine this approach for long-range electrostatics with the standard Quasicontinuum method for short-range interactions to achieve an efficient multiscale atomistic-to-continuum method.
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