Microscopical justification of the Winterbottom problem for well-separated lattices. (June 2023)

• Record Type: Journal Article
• Authors: Piovano, Paolo; Velčić, Igor
• Is Part Of: Nonlinear analysis. Volume 231(2023)
• Publication Date: 2023-06
• Subjects: 49JXX -- 82B24; Island nucleation -- Wetting -- Dewetting -- Winterbottom shape -- Discrete-to-continuum passage -- γ-convergence -- Atomistic models -- Surface energy -- Anisotropy -- Adhesion -- Capillarity problems -- Crystallization; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113113
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the discrete atomistic setting introduced in Piovano and Velčić (2022) 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 Piovano and Velčić (2022) to characterize the wetting and dewetting regimes and to perform the discrete to continuum passage . In particular, all results of Piovano and Velčić (2022) 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.