We share a weekly seminar series with the Warwick Centre for Predictive Modelling (WCPM). Seminars are held from 1-2 pm on Mondays during the university term. Nominations for speakers are welcome. Please contact James Kermode or Peter Brommer with suggestions.
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Mon, Aug 20, '18
13:00 - 14:00
Computing mass transport in solids
Mass transport controls both materials processing and properties, such as ionic conductivity, in a wide variety of materials. While first-principles methods compute activated state energies, upscaling to mesoscale mobilities requires the solution of the master equation. For all but the simplest cases of interstitial diffusivity, calculating diffusivity directly is a challenge. Traditionally, modeling has taken two paths: uncontrolled approximations that map the problem onto a simpler (solved) problem, or a stochastic method like kinetic Monte Carlo, which is difficult to converge for strong correlations. Moreover, uncertainty quantification or derivatives of transport coefficients are complicated without analytic or semianalytic solutions. An automated Green function approach for transport both determines the minimum set of transition states to calculate from symmetry and computes the dilute-limit transport without additional approximations. I will also present an alternative derivation of the transport coefficients, and show that it can be recast as a variational problem, where the true transport coefficients are minimal against variations in state position. This expression for transport coefficients involves a thermal average over the states, making it amenable to Monte Carlo algorithms rather than kinetic Monte Carlo. The result encompasses previous computational methods for diffusion, as well as providing a framework for the development of new approximation methods.