Structure, short-range order, and phase stability of the Al$_x$CrFeCoNi high-entropy alloy: Insights from a perturbative, DFT-based analysis

TL;DR

This study uses a perturbative, DFT-based approach to analyze phase stability and short-range order in Al$_x$CrFeCoNi high-entropy alloys, revealing temperature-dependent ordering and phase decomposition behaviors.

Contribution

It introduces a novel perturbative, DFT-based method combined with atomistic simulations to predict ordering tendencies and phase stability in high-entropy alloys.

Findings

Predicted $ ext{L}1_2$ or $ ext{D}0_{22}$ ordering in fcc alloys below 1000 K.

Found $ ext{B}2$ ordering in bcc alloys occurs above melting temperature.

Identified atomic ordering patterns with Al on one sublattice, Ni and Co on the other, Cr and Fe disordered.

Abstract

We study the phase behaviour of the Al$_x$CrFeCoNi high-entropy alloy. Our approach is based on a perturbative analysis of the internal energy of the paramagnetic solid solution as evaluated within the Korringa-Kohn-Rostoker formulation of density functional theory, using the coherent potential approximation to average over disorder. Via application of a Landau-type linear response theory, we infer preferential chemical orderings directly. In addition, we recover a pairwise form of the alloy internal energy suitable for study via atomistic simulations, which in this work are performed using the nested sampling algorithm, which is well-suited for studying complex potential energy surfaces. When the underlying lattice is fcc, at low concentrations of Al, depending on the value of $x$, we predict either an $\mathrm{L}1_2$ or $\mathrm{D}0_{22}$ ordering emerging below approximately 1000 K. On the other hand, when the underlying lattice is bcc, consistent with experimental observations, we predict $\mathrm{B}2$ ordering temperatures higher than the melting temperature of the alloy, confirming that this ordered phase forms directly from the melt. For both fcc and bcc systems, chemical orderings are dominated by Al moving to one sublattice, Ni and Co the other, while Cr and Fe remain comparatively disordered. On the bcc lattice, our atomistic modelling suggests eventual decomposition into $\mathrm{B}2$ NiAl and Cr-rich phases. These results shed light on the fundamental physical origins of atomic ordering tendencies in these intriguing materials.