Predicting activation energies for vacancy-mediated diffusion in alloys using a transition-state cluster expansion

TL;DR

This paper introduces a transition-state cluster expansion model to accurately predict vacancy-mediated diffusion activation energies in alloys, outperforming simpler models as training data increases.

Contribution

The study develops and evaluates a transition-state cluster expansion model that improves prediction accuracy for diffusion activation energies in alloys.

Findings

Cluster expansion has similar error to other models with small training sets.

With larger training sets, cluster expansion significantly outperforms other models.

A weighted average of cluster expansion and Marcus theory-based models yields the lowest prediction error.

Abstract

Kinetic Monte Carlo models parameterized by first principles calculations are widely used to simulate atomic diffusion. However, accurately predicting the activation energies for diffusion in substitutional alloys remains challenging due to the wide variety of local environments that may exist around the diffusing atom. We address this challenge using a cluster expansion model that explicitly includes a sublattice of sites representing transition states and assess its accuracy in comparison with other models, such as the broken bond model and a model related to Marcus theory, by modeling vacancy-mediated diffusion in Pt-Ni nanoparticles. We find that the prediction error of the cluster expansion is similar to that of other models for small training sets, but with larger training sets the cluster expansion has a significantly lower prediction error than the other models with comparable execution speed. Of the simpler models, the model related to Marcus theory yields predictions of nanoparticle evolution that are most similar to those of the cluster expansion, and a weighted average of the two approaches has the lowest prediction error for activation energies across all training set sizes.