Microscopical Justification of the Winterbottom problem for well-separated Lattices

Abstract

We consider the discrete atomistic setting introduced in [25] to microscopically justify the continuum model related to the Winterbottom problem, i.e., the problem of determining the equilibrium shape of crystalline film drops resting on a substrate, and relax the rigidity assumption considered in [25] to characterize the wetting and dewetting regimes and to perform the discrete to continuum passage. In particular, all results of [25] are extended to the setting where the distance between the reference lattices for the film and the substrate is not smaller than the optimal bond length between a film and a substrate atom. Such optimal film-substrate bonding distance is prescribed together with the optimal film-film distance by means of two-body atomistic interaction potentials of Heitmann-Radin type, which are both taken into account in the discrete energy, and in terms of which the wetting-regime threshold and the effective expression for the wetting parameter in the continuum energy are determined.