Universal Jump of Gaussian Curvature at the Facet Edge of a Crystal

Novel universal behavior of the equilibrium crystal shape is reported: The Gaussian curvature, a product of two principal curvatures, assumes a universal jump across the facet contour at any temperature below the roughening temperature. This behavior is shown to be a consequence of a universal relation between the coefficients γₛ and B in the small-p expansion (p is the surface gradient) of the interface free energy, f(p)=f(0)+γₛ|p|+B|p|³+O(|p|⁴). Both exact results on a solvable model and Monte Carlo calculations support this behavior---universal Gaussian-curvature jump at the facet edge.