# A modified formula for non-Arrhenius diffusion of helium in metals

## TL;DR

This paper introduces a modified diffusion formula for helium in metals, improving the accuracy of kinetic Monte Carlo simulations by accounting for low-energy barriers in helium diffusion.

## Contribution

A new stochastic model based on Brownian motion and cosine potential is derived to better predict helium diffusion rates in metals, surpassing traditional Arrhenius law limitations.

## Key findings

- Model predictions align with molecular dynamics simulations.
- The approach improves accuracy for low-energy barrier diffusion.
- Enhances KMC simulation of helium-vacancy cluster growth.

## Abstract

Helium diffusion in metals is the basic requirement of nucleation and growth of bubble, which gives rise to adverse degradation effects on mechanical properties of structural materials in reactors under irradiation. Lattice based Kinetic Monte Carlo approach is widely adopted to study the evolution of helium-vacancy clustering. However, the imple-mentation of Arrhenius law to prediction the event rate of single interstitial helium solute diffusion in metal is not always appropriate due to low-energy barrier. Based on a stochastic model, a modified formula is derived from the Brownian motion upon a cosine-type potential. Using the parameters obtained from molecular dynamics simulation for the diffusivity of single helium solute in BCC W, the prediction of our model is consistent with the results from dynamical simulation and previous model. This work would help to develop a more accurate KMC scheme for the growth of helium-vacancy clusters, as well as other low-energy reactions in materials science.