Lattice Stability for Atomistic Chains Modeled by Local Approximations of the Embedded Atom Method

TL;DR

This paper compares lattice stability predictions for atomistic chains using the embedded atom method and local approximations, highlighting differences in critical strain estimates and error magnitudes.

Contribution

It provides a theoretical comparison of local Cauchy-Born models with atomistic EAM models, analyzing their accuracy in predicting critical strains for lattice instability.

Findings

Both local models can produce O(1) errors in critical strain predictions.

Volume-based local model overestimates critical strain compared to atomistic model.

Reconstruction-based local model can overestimate or underestimate critical strain.

Abstract

The accurate approximation of critical strains for lattice instability is a key criterion for predictive computational modeling of materials. In this paper, we present a comparison of the lattice stability for atomistic chains modeled by the embedded atom method (EAM) with their approximation by local Cauchy-Born models. We find that both the volume-based local model and the reconstruction-based local model can give O(1) errors for the critical strain since the embedding energy density is generally strictly convex. The critical strain predicted by the volume-based model is always larger than that predicted by the atomistic model, but the critical strain for reconstruction-based models can be either larger or smaller than that predicted by the atomistic model.