Comparison of Diffusion Models: Transition State
Theory vs. Langevin Equation
Marc Dvorak
Department of Physics, Colorado School of Mines
Date: Oct. 24, 2011
I will outline the differences in theory and results for diffusion calculations based on
transition state theory (TST) and a Langevin equation approach. In the context of
impurity diffusion through a crystalline material, transition state theory assumes an
Arrhenius form for the jump rate of the impurity between two interstitial sites. The two
parameters for the Arrhenius form - activation energy and prefactor - can be estimated
with density functional theory (DFT). The more rigorous Langevin equation approach
explicitly includes a friction term between the impurity and the substrate, which can also
be estimated with DFT. It can be shown that TST is a particular limit of the Langevin
approach. Our goal is to compare diffusion rates predicted by the two theories, in
particular by studying the diffusion of hydrogen through diamond. Limited results for
this diamond system will be shown.