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We consider a system of $N$ hard spheres sitting on the nodes of either the$\mathrm{FCC}$ or $\mathrm{HCP}$ lattice and interacting via a sticky-diskpotential. As $N$ tends to infinity (continuum limit), assuming the interactionenergy does not exceed that of the ground-state by more than $N^{2/3}$ (surfacescaling), we obtain the variational coarse grained model by$\Gamma$-convergence. More precisely, we prove that the continuum limitenergies are of perimeter type and we compute explicitly their Wulff shapes.Our analysis shows that crystallization on $\mathrm{FCC}$ is preferred to thaton $\mathrm{HCP}$ for $N$ large enough. The method is based on integralrepresentation and concentration-compactness results that we prove for generalperiodic lattices in any dimension.

Emergence of Wulff-Crystals from atomistic systems on the FCC and HCP lattices