Fractal structure of the equilibrium crystal shape

Abstract

The equilibrium crystal shape of the classical crystal at zero temperature is found in the framework of the model suppressing the atomic distortions. In this model the interaction between two atoms of a pair is supposed to decrease at large distances more rapidly than r-4. The crystal surface is shown to have a fractal structure : it consists of an infinite number of facets and of solitary edges and corners, which form the Cantor set. The crystal is completely faceted (i.e. there is no rounded area), but there is no sharp edge (i.e. the slope is continuous). The boundary of a facet is shown to have a fractal structure too. It consists of an infinite number of « smooth » edges and of the Cantor set. The microscopic configuration of steps and kinks on every facet is also found