The self-diffusion properties of several $\beta \text{-Sn}$ symmetric tilt grain boundaries are examined using molecular dynamics simulations. The boundary types examined—(101), (201), (401), (310)-$\Sigma 5$, and (410)—are chosen from those observed in experiment and from arbitrary Miller planes, giving a variety of tilt angles and interface properties. Planar structure factor and diffusivity profiles for each boundary are computed and a grain-boundary width, ${\delta }_{GB}$, is measured from these profiles. Larger diffusive widths $\left({\delta }_{GB}\right)$ are exhibited by higher excess potential energy grain boundaries. Diffusivities $\left(D_{GB}\right)$ in the directions parallel to the interface plane are computed and activation energies are found with the Arrhenius relation. $D_{GB}$ (as ${\delta }_{GB}{D}_{GB}$ normalized by ${\delta }_{GB}$) is shown to agree well with experiment. We also investigate the anisotropic diffusive behavior of the (401) grain boundary and find that the low energy grain boundary exhibits very low activation energy diffusion, due to the development of diffusive channels.

• Received 19 January 2010

DOI:https://doi.org/10.1103/PhysRevB.81.134111