Abstract
We address the question of whether three-dimensional crystals are minimizers of classical many-body energies. This problem is of conceptual relevance as it presents a significant milestone towards understanding, on the atomistic level, phenomena such as melting or plastic behavior. We characterize a set of rotation- and translation-invariant two- and three-body potentials V 2, V 3 such that the energy minimum of
over all \({Y \subset \mathbb{R}^3}\), #Y = n, converges to the energy per particle in the face-centered cubic (fcc) lattice as n tends to infinity. The proof involves a careful analysis of the symmetry properties of the fcc lattice.
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Flatley, L.C., Theil, F. Face-Centered Cubic Crystallization of Atomistic Configurations. Arch Rational Mech Anal 218, 363–416 (2015). https://doi.org/10.1007/s00205-015-0862-1
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DOI: https://doi.org/10.1007/s00205-015-0862-1