Energy-minimization studies of twist grain boundaries in diamond

We study the zero-temperature energy and atomic structure of twist grain boundaries (GB’s) in diamond, using a semiempirical potential due to Tersoff. The (111) twist GB energies are similar to predictions of an empirical tight-binding potential. For the previously unstudied (001) twist boundaries in diamond, both the energy and the excess volume are insensitive to misorientation at large twist angles, although small energy cusps exist for the so-called Σ5 GB’s. The (001) twist GB energies are typically ≊ 6 J/${\mathrm{m}}^2$. Significant atomic relaxation occurs only in the two atomic layers nearest the grain boundary. Atoms in these contact layers are predominantly threefold coordinated. For (001) twist GB’s, in-plane translations significantly affect the Σ5(001) energies, but not the ${\mathrm{\Sigma }}_{\mathit{n}}$ energies, with n large.