Calculus of Variations and Geometric Measure Theory

P. Piovano - I. Velčić

Microscopical justification of the Winterbottom problem for well-separated lattices

created by piovano on 02 Dec 2021
modified on 19 May 2023


Published Paper

Inserted: 2 dec 2021
Last Updated: 19 may 2023

Journal: Nonlinear Analysis
Volume: 231
Pages: 32
Year: 2023

ArXiv: 2111.13604 PDF


In this manuscript we address the classical problem of determining the equilibrium shape formed by crystalline film drops resting upon rigid substrates possibly of a different material, which is often referred to as the Winterbottom problem. Moving forward from the specific discrete atomistic setting introduced in a previous paper by the authors to microscopically justify such model, we relax the rigidity assumption considered in that paper to characterize the wetting and dewetting regimes and to perform the discrete to continuum passage. In particular, all results 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 found.