Relaxation of surface atoms in NaCl: Influence on the equilibrium crystal shape

Ions at and near the surface of a NaCl crystal relax away from their bulk lattice positions. We have computed these ionic relaxations and the corresponding decrease in surface energy for simple edge and step configurations on an otherwise perfect {100} surface. These relaxed edge and step energies enter an expression obtained in an earlier paper (and rederived here) which predicts the temperature T0 at which the perfectly cubical low-temperature equilibrium crystal shape of NaCl first develops rounded corners. It turns out that relaxation decreases edge and step energies substantially, thus bringing the predicted corner-rounding temperature into the experimental range T0≊925 K. This agreement provides evidence in favor of a mechanism for corner rounding based on a thermally induced (mainly entropic) decrease in the step energy per unit length. The fact that relaxation reduces substantially the energies of these ideal surface features suggests more generally that the energies of the low-lying surface configurations which dominate the statistical mechanics of the NaCl surface below melting can be approximated by a term proportional to the microscopic area with successively smaller corrections for steps, edges, corners, and other more complex local structures.