Calculating diffusivity

Diffusivity calculation in MD++

Yanming Wang

Sep 2015

This tutorial describes how to compute diffusivity in MD++ based on the random walk model. Here as an example, we will provide MD++ Tcl and Matlab scripts for calculating Si and Au diffusivities in a Au-Si binary liquid alloy system.

Theoretical background

We can assume the motion of each individual atom follows the random walk model. Thus we can find the following relation between the mean square displacement (MSD) $\sigma$ and the diffusivity $D$.

$D={\frac {\sigma }{6t}}$

This is the definition of MSD $\sigma =<r(t)-r_{0}>$, which can be easily obtained from the trajectories of the atoms in MD.