Roughening and Preroughening of Diamond-Cubic{111}Surfaces

A solid-on-solid model for $\{111\}$ surfaces of diamond-cubic materials that correctly takes into account the diamond-cubic crystal structure has been developed for Monte Carlo simulation. In addition to a roughening transition at temperature $T_R$, a distinct preroughening transition at $T_{\mathrm{PR}}\approx {0.43T}_R$ is indicated by divergences in the surface specific heat and order-parameter susceptibility. Preroughening appears to arise naturally in our nearest-neighbor bond model from the entropic freedom available in the nontrivial crystal structure. Preroughening is shown to dramatically lower the nucleation barrier for growth and etching at low driving forces.