Stochastic Continuum Models for High--Entropy Alloys with Short-range Order

TL;DR

This paper develops stochastic continuum models for high-entropy alloys that incorporate short-range atomic order, derived from atomistic models, and validated as Ornstein-Uhlenbeck processes for both elastic and defected states.

Contribution

It introduces a rigorous derivation of stochastic continuum models for HEAs with short-range order from atomistic interactions, extending previous phenomenological approaches.

Findings

Continuum models retain atomic-level randomness and short-range order characteristics.

Models are validated as Ornstein-Uhlenbeck processes.

Applicable to elasticity with and without dislocations.

Abstract

High entropy alloys (HEAs) are a class of novel materials that exhibit superb engineering properties. It has been demonstrated by extensive experiments and first principles/atomistic simulations that short-range order in the atomic level randomness strongly influences the properties of HEAs. In this paper, we derive stochastic continuum models for HEAs with short-range order from atomistic models. A proper continuum limit is obtained such that the mean and variance of the atomic level randomness together with the short-range order described by a characteristic length are kept in the process from the atomistic interaction model to the continuum equation. The obtained continuum model with short-range order is in the form of an Ornstein--Uhlenbeck (OU) process. This validates the continuum model based on the OU process adopted phenomenologically by Zhang et al. [Acta Mater., 166 (2019), pp. 424--434] for HEAs with short-range order. We derive such stochastic continuum models with short-range order for both elasticity in HEAs without defects and HEAs with dislocations (line defects). The obtained stochastic continuum models are based on the energy formulations, whose variations lead to stochastic partial differential equations.