Atomistic modeling of β-Sn surface energies and adatom diffusivity

Energies for low number Miller index surfaces of β-Sn (b.c.t. structure) were computed and the (1 0 0) plane was found to have the lowest un-relaxed energy of 0.0497 eV/Å ² . We then used the Dimer method to find mechanisms and corresponding activation energies, E _A , for a Sn adatom moving on a β-Sn (1 0 0) surface. After extensive dimer searches and comparison to long molecular dynamics simulations, we conclude that two simple hopping mechanisms dominate transitions on this surface. For each, we determined hopping rates of the adatom using transition state theory and computed its tracer diffusivity. A hop of the adatom in the lattice c-direction gives D _{300 K} = 1.893 × 10 ^-06 cm ² /s (E _A = 0.1493 eV), while in the lattice a-direction D _{300 K} = 3.994 × 10 ^-06 cm ² /s (E _A = 0.1138 eV). When compared to studies on the existence of low energy multi-atom adatom diffusion on Cu and Al (1 0 0), we assert that β-Sn's successive (2 0 0) plane layering in the [1 0 0] direction provides for significantly lower activation energies and may contribute to the inability to locate any concerted atomic motion mechanisms.