Boundary Conditions for Atomistic Simulation of Material Defects

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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.