| Abstract: |
| A discrete-to-continuum analysis for free-boundary problems related to crystalline materials deposited on crystalline substrates is performed by employing the notion of $\Gamma$-convergence and rigidity estimates. The discrete models take into account the possibility of a mismatch between the lattice parameters of the film and the substrate at the crystalline equilibrium. In view of a proper scaling regime the resulting continuum limiting model is characterized by a configurational energy that includes both the surface and the bulk elastic energy. As such, it well describes the two competing mechanisms responsible for the profile shape of epitaxially-strained thin films on substrates. On the one hand, the lattice mismatch may generate large stresses in the film forcing film atoms to move in order to release the elastic energy, thus possibly generating profile corrugations. On the other hand, more regular profiles may be preferable to minimize the surface energy. |
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