Microscopical justification of the Winterbottom problem for well-separated lattices. (English) Zbl 1517.82018
Summary: We consider the discrete atomistic setting introduced in [the authors, J. Nonlinear Sci. 32, No. 3, Paper No. 32, 55 p. (2022; Zbl 1489.82023)] 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 [loc. cit.] to characterize the wetting and dewetting regimes and to perform the discrete to continuum passage. In particular, all results of the authors [loc. cit.] 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.
MSC:
| 82B24 | Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 81V45 | Atomic physics |
Keywords:
island nucleation; wetting; dewetting; Winterbottom shape; discrete-to-continuum passage; \(\gamma\)-convergence; atomistic models; surface energy; anisotropy; adhesion; capillarity problems; crystallizationCitations:
Zbl 1489.82023References:
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