Face-centered cubic crystallization of atomistic configurations

TL;DR

This paper proves that for certain classical many-body energies, the face-centered cubic lattice configuration minimizes energy per particle in the limit of large systems, advancing understanding of crystal formation.

Contribution

It characterizes specific two- and three-body energies for which the fcc lattice is the energy minimizer among large atomistic configurations.

Findings

The energy per particle converges to that of the fcc lattice as system size increases.

The proof relies on symmetry analysis of the fcc lattice.

The results provide a rigorous foundation for the stability of fcc structures.

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 energies such that the energy minimum per particle over all n-particle configurations converges to the energy per particle in the face-centered cubic (fcc) lattice as tends to infinity. The proof involves a careful analysis of the symmetry properties of the fcc lattice.