[Paper Review] Modeling refractory high-entropy alloys with efficient machine-learned interatomic potentials: defects and segregation

Jesper Byggmästar, K. Nordlund+1 more|arXiv (Cornell University)|Jun 7, 2021

High Entropy Alloys Studies59 references130 citations

TL;DR

This study develops a highly accurate, computationally efficient machine-learned interatomic potential for the Mo–Nb–Ta–V–W refractory high-entropy alloy using a low-dimensional many-body descriptor approach. The potential enables large-scale molecular dynamics simulations revealing that vanadium segregates to compressed interstitial-rich regions like dislocation loops, while niobium prefers spacious void surfaces; unlike tungsten, interstitials in this alloy recombine efficiently due to enhanced vacancy mobility and limited interstitial migration, suppressing large dislocation loop formation and enhancing radiation tolerance.

ABSTRACT

We develop a fast and accurate machine-learned interatomic potential for the Mo-Nb-Ta-V-W quinary system and use it to study segregation and defects in the body-centred cubic refractory high-entropy alloy MoNbTaVW. In the bulk alloy, we observe clear ordering of mainly Mo-Ta and V-W binaries at low temperatures. In damaged crystals, our simulations reveal clear segregation of vanadium, the smallest atom in the alloy, to compressed interstitial-rich regions like radiation-induced dislocation loops. Vanadium also dominates the population of single self-interstitial atoms. In contrast, due to its larger size and low surface energy, niobium segregates to spacious regions like the inner surfaces of voids. When annealing samples with supersaturated concentrations of defects, we find that in complete contrast to W, interstitial atoms in MoNbTaVW cluster to create only small ($\sim 1$ nm) experimentally invisible dislocation loops enriched by vanadium. By comparison to W, we explain this by the reduced but three-dimensional migration of interstitials, the immobility of dislocation loops, and the increased mobility of vacancies in the high-entropy alloy, which together promote defect recombination over clustering.

Motivation & Objective

• To develop a fast and accurate machine-learned interatomic potential for the complex Mo–Nb–Ta–V–W quinary refractory high-entropy alloy system.
• To investigate atomic-scale defect behavior, including segregation and clustering, in bulk and damaged MoNbTaVW crystals.
• To understand the mechanisms behind radiation tolerance in high-entropy alloys by comparing defect evolution to pure tungsten.
• To overcome the challenge of high-dimensional descriptor spaces in multi-component alloys by using low-dimensional two- and three-body descriptors.
• To enable large-scale atomistic simulations of defect dynamics in complex HEAs using a tabulated, high-speed potential derived from DFT data.

Proposed method

• Trained a Gaussian Approximation Potential (GAP) using a hybrid descriptor combining repulsive pair potentials and machine-learned two- and three-body terms.
• Employed a low-dimensional, many-body descriptor based on interatomic distances (rij, rik) and bond angles (θijk) with 5 Å cutoffs to reduce overfitting and training data needs.
• Used a squared-exponential kernel with 1 Å length scale for regression, with optimized coefficients α and tabulated energy contributions for speed.
• Trained the potential on a diverse DFT dataset including bulk bcc crystals, random and ordered alloys, vacancies, self-interstitials, liquids, and surfaces across all compositions.
• Implemented a tabulated version (tabGAP) of the potential using an 80×80×80 grid for three-body terms and 5000 points for two-body terms, enabling fast, production-scale simulations.
• Validated accuracy via root-mean-square errors (RMSE) of ~1 meV/atom for energy and ~0.1 eV/Å for forces, with excellent agreement on mixing energies and defect properties.

Experimental results

Research questions

• RQ1 How does vanadium segregation behavior differ in radiation-damaged MoNbTaVW compared to pure tungsten?
• RQ2 What drives the preferential segregation of niobium to void surfaces and vanadium to interstitial-rich regions?
• RQ3 Why do interstitials in MoNbTaVW form only small, ~1 nm dislocation loops, unlike the large loops seen in pure W?
• RQ4 What role does enhanced vacancy mobility play in defect recombination and radiation tolerance in this high-entropy alloy?
• RQ5 Can a machine-learned potential trained on a limited DFT dataset accurately describe complex defect dynamics in quinary refractory HEAs?

Key findings

• Vanadium, the smallest atom in the system, preferentially segregates to compressed interstitial-rich regions such as radiation-induced dislocation loops.
• Vanadium dominates the population of single self-interstitial atoms, indicating a strong thermodynamic preference for interstitial sites.
• Niobium, due to its larger size and low surface energy, segregates to spacious regions like the inner surfaces of voids.
• Unlike pure tungsten, interstitials in MoNbTaVW do not form large dislocation loops; instead, they cluster into small (~1 nm) and experimentally undetectable loops enriched with vanadium.
• Defect evolution is dominated by recombination over clustering due to three-dimensional but reduced interstitial migration, immobile dislocation loops, and enhanced vacancy mobility.
• The high-entropy alloy exhibits superior radiation tolerance compared to pure W, as the defect recombination mechanism prevents the formation of large, hardening-inducing dislocation loops.