Chemical diffusion is a fundamental process in the evolution of planets. Equilibration within and among phases in response to changes in physical conditions requires the comprising chemical species to be spatially rearranged, over distances comparable to the grain size. Quantitative description of such processes demands diffusivities of these chemical species to be accurately known, while detailed insight into the mechanisms of diffusion at the atomic scale elucidate their dependence on pressure, temperature and composition. By applying our understanding of chemical bonding in condensed systems to numerically simulate diffusivity over a range of pressures and temperatures of planetary interest, we can obtain direct constraints on diffusivities at these extreme conditions, and self consistently assess the models used to extrapolate experimental data. Such computations further serve as a proving ground for testing the robustness of the various levels of theory applied in the characterization of bonding and dynamics of a material. The mathematical description of diffusion was first developed in the context of thermal transport by Fourier (1822). Its applicability to chemical transport was recognized by Fick (1855), who cast Fourier’s law of thermal conduction in terms of chemical transport and applied it to experiments on the diffusion of salt in a column of water. In an anisotropic system of n components, Fick’s description is most generally given by \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\frac{{\partial}\mathit{c}\_{\mathit{A}}}{{\partial}\mathit{t}} = {{\sum}\_{\mathit{i},\mathit{j}}^{3}}{{\sum}\_{\mathit{B}}^{\mathit{n} {-} 1}} {-} \mathit{D}\_{\mathit{AB}}^{\mathit{ij}}\frac{{\partial}^{2}\mathit{c}\_{\mathit{B}}}{{\partial}\mathit{x}\_{\mathit{i}}{\partial}\mathit{x}_{\mathit{j}}}\] \end{document}(1) where c A is the concentration of species A , and D AB ij is the relevant component of the diffusivity matrix (e.g., Crank 1975; Lasaga 1998; Zhang 2010). However, this description of diffusion is entirely in the continuum limit, and does not give any insight into the mechanisms by which chemical transport occurs at the atomic level. The description of chemical diffusivity was cast in an atomistic context by studies of Brownian motion (Einstein 1905; Smoluchowski …
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