Lattice ground states for Embedded-Atom Models in 2D and 3D

TL;DR

This paper investigates the mathematical minimization of the Embedded-Atom Model energy among lattice configurations in 2D and 3D, analyzing various interaction potentials through analytical and numerical methods.

Contribution

It provides new analytical and numerical insights into lattice ground states for EAM with different potentials in two and three dimensions.

Findings

Identification of lattice configurations minimizing EAM energy

Analysis of Gaussian, inverse-power, and Lennard-Jones interactions

Numerical results supporting analytical findings

Abstract

The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic interactions and nonlocal effects due to the corresponding electronic clouds. The purpose of this paper is to mathematically investigate the minimization of the EAM energy among lattices in two and three dimensions. We present a suite of analytical and numerical results under different reference choices for the underlying interaction potentials. In particular, Gaussian, inverse-power, and Lennard-Jones-type interactions are addressed.