Abstract
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 ${T}_{\mathrm{PR}}\ensuremath{\approx}{0.43T}_{R}$ 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.
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