MSE Colloquium: Dallas Trinkle, Efficient mass transport calculations using a variational principle

Professor, Materials Science and Engineering Department, University of Illinois, Urbana-Champaign

Abstract

While first-principles methods can compute activated state energies using the nudged-elastic band method, upscaling to mesoscale mobilities requires the solution of the master equation. The general solution for mass transport coefficients involves the inversion of rate matrix: the Green function. However, while the rate matrix is typically sparse, its inverse is not; moreover, numerical algorithms for the Green function are currently only available for cases of dilute defect concentration. By recasting the calculation of transport coefficients as a variational problem, we can compute transport coefficients from thermal average quantities instead of trajectory-based calculations. The variational principle also ensures that our diffusivity calculations are upper bounds of the true diffusivities. Replacing kinetic Monte Carlo calculations with Monte Carlo averages, or approximations for thermal averages, also increases the efficiency of mass transport calculations. I'll discuss how this approach unifies different approaches to diffusivity, and leads to new methods for complex problems.

Bio

 

Dallas R. Trinkle is a Willett Faculty Scholar and Professor in Materials Science and Engineering at Univ. Illinois, Urbana-Champaign, and the Associate Head of Materials Science and Engineering. He received his Ph.D. in Physics from Ohio State University in 2003. Following his time as a National Research Council postdoctoral researcher at the Air Force Research Laboratory, he joined the faculty of the Department of Materials Science and Engineering at Univ. Illinois, Urbana-Champaign in 2006. He was a TMS Young Leader International Scholar in 2008, received the NSF/CAREER award in 2009, the Xerox Award for Faculty Research at Illinois in 2011, the AIME Robert Lansing Hardy Award in 2014, the TMS Brimacombe Medal in 2019, co-chaired the 2011 Physical Metallurgy Gordon Research conference, and became a Willett Faculty Scholar at Illinois in 2015, a Center for Advanced Study Associate and NCSA Faculty Fellow in 2017. His research focuses on computational methods for studying defects in materials at the atomic-scale using density-functional theory, and novel techniques to understand problems in mechanical behavior and transport. This has led to ab initio predictions of solid-solution softening in molybdenum, solute strengthening and softening in magnesium alloys, pipe diffusion of hydrogen in palladium, diffusion of oxygen in titanium and solutes in magnesium, among others.

https://dtrinkle.matse.illinois.edu/