Boundary Conditions for Atomistic Simulation of Material Defects

原子模拟是现代材料科学、固态物理和化学不可或缺的工具，因为它们使科学家能够以实验室实验中不可能的方式研究单个原子和分子。理解原子过程为在原子尺度上操纵物质开辟了道路，以便在科学和工程中获得上级材料特性。原子材料建模的最常见任务之一是确定晶体缺陷的特性，包括它们的原子结构、形成、活化和电离能，从化学反应的电子和原子机制，电荷迁移率等，可以被直接发现，并且介观材料性质或粗粒度模型（例如，在动力学蒙特-卡罗、离散位错动力学、连续断裂定律、输运模拟中使用）。缺陷使周围的主晶格变形，产生长范围的弹性（也可能是静电）场。由于实际方案必须在小的计算域中工作，因此它们不能明确地解决这些远场，而是必须采用人工边界条件（例如，周期性边界条件）以模拟弹性体。这种近似引起必须被控制的模拟误差，并且与其他模型和/或离散化误差理想地平衡。例如，对于包含所有（中性）点缺陷和直位错的广泛类别的缺陷，Ehrlacher，Ortner和Shapeev（2016）表明几何误差以通用速率O（N^{-1/2}）衰减，其中N表示计算单元中的原子数。对于立方尺度计算化学模型，这种缓慢的速率特别严重。对于裂缝，事实证明，标准模型甚至产生在N上发散的方案。这种极慢的收敛速度甚至发散速度代表了理论和计算上的挑战，我们建议在本项目中解决这个问题。具体来说，我们将开发一个层次的高精度边界条件的四种常见的缺陷：电荷中性点缺陷，位错，裂纹和带电缺陷。这项研究的核心是开发一系列新的分析工具，以描述晶体固体中的弹性场和偏振场，以及它们如何与缺陷核耦合。分析结果将通过新的算法和开源软件直接反馈到材料模拟方法中。这些新算法的效果将是提高材料原子模拟的可靠性和效率，并使迄今为止无法使用传统工具的特别复杂的缺陷结构的模拟成为可能。

Atomistic simulations are an indispensable tool of modern materials science, solid state physics and chemistry, as they allow scientists to study individual atoms and molecules in a way that is impossible in laboratory experiments. Understanding atomistic processes opens up avenues for the manipulation of matter at the atomic scale in order to achieve superior material properties for applications in science and engineering.One of the most common tasks of atomistic materials modelling is to determine properties of crystalline defects, including their atomic structure, formation, activation and ionisation energies, from which electronic and atomistic mechanisms of chemical reactivity, charge mobility, etc., can be directly discovered, and mesoscopic material properties or coarse-grained models (e.g., employed in kinetic Monte-Carlo, discrete dislocation dynamics, continuum fracture laws, transport simulations) can be derived.Defects distort the surrounding host lattice, generating long-ranging elastic (and possibly also electrostatic) fields. Since practical schemes necessarily work in small computational domains they cannot explicitly resolve these far-fields but must employ artificial boundary conditions (e.g., periodic boundary conditions) to emulate the elastic bulk. This approximation gives rise to a simulation error that must be controlled and ideally balanced against other model and/or discretisation errors. For example, for a wide class of defects encompassing all (neutral) point defects and straight dislocations it is shown by Ehrlacher, Ortner and Shapeev (2016) that the geometry error decays with a universal rate O(N^{-1/2}) where N denotes the number of atoms in the computational cell. For a cubic scaling computational chemistry model, this slow rate is particularly severe. For cracks, it turns out that the standard models even yield schemes that are divergent in N.This extremely slow rate of convergence or even divergence represents both a theoretical and computational challenge, which we propose to address in this project. Specifically, we will develop a hierarchy of high-accuracy boundary conditions for four common classes of defects: charge neutral point defects, dislocations, cracks, and charged defects. At its core, this research involves the development of a range of new analytical tools to describe elastic and polarisation fields in crystalline solids and how they are coupled to defect cores. The analytical results will feed directly back into materials simulation methodology through new algorithms and open source software. The effect of these new algorithms will be to enhance both the reliability and efficiency of atomistic simulation of materials, and enable simulation of particularly complex defect structures that have so far been inaccessible with conventional tools.