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，因为它们允许科学家以一种在实验室实验中不可能实现的方式来研究单个原子和分子。原子材料模型最常见的任务之一是确定晶体缺陷的性质，包括它们的原子结构、形成、活化和电离能，由此可以直接发现化学反应、电荷迁移率等的电子和原子机制，并且可以推导出介观材料性质或粗晶模型(例如，在动力学蒙特卡罗、离散位错动力学、连续介质断裂规律、输运模拟中使用)。缺陷扭曲周围的主体晶格，产生长程弹性(也可能是静电)场。由于实用格式必须在较小的计算域中工作，所以它们不能显式地求解这些远场，而必须使用人工边界条件(例如，周期边界条件)来模拟弹性体。这种近似值会产生模拟误差，必须控制该误差，并与其他模型和/或离散化误差进行理想的平衡。例如，对于包括所有(中性)点缺陷和直位错的一大类缺陷，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，这种缓慢的速度尤其严重。对于裂缝，事实证明，标准模型甚至产生了在N中发散的格式。这种极慢的收敛速度甚至发散既是理论上的挑战，也是计算上的挑战，我们建议在这个项目中解决这一问题。具体地说，我们将为四类常见的缺陷开发一系列高精度的边界条件：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极化场，以及它们如何与缺陷核心耦合。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学中。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，并使模拟迄今为止用传统工具无法访问的特别复杂的缺陷结构成为可能。

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.