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Ground-State Structure Search of Defective High-Entropy Alloys Using Machine-Learning Potentials and Monte Carlo Sampling

Siya Zhu, Raymundo Arroyave

TL;DR

A Monte Carlo framework coupled with machine-learning interatomic potentials (MLIPs) that searches for ground-state atomic configurations in HEAs with defects and interstitials, providing a general and efficient framework for predicting atomic ordering, segregation, and interstitial behavior in complex, defective HEA systems.

Abstract

Resolving the atomic-scale structure of defective high-entropy alloys (HEAs) containing interstitial species remains a major computational challenge due to the vast configurational space and the limitations of existing methods. Here we introduce PAIPAI (Package for Alloy Interstitial Predictions using Artificial Intelligence), a Monte Carlo framework coupled with machine-learning interatomic potentials (MLIPs) that searches for ground-state atomic configurations in HEAs with defects and interstitials. PAIPAI employs a dual-worker architecture-fast workers for rapid configurational screening and slow workers for high-accuracy refinement-coordinated through a shared waiting pool, enabling efficient parallel sampling. We demonstrate PAIPAI through three case studies: (i) surface segregation in a Ti-V-Cr-Re slab; (ii) interstitial oxygen and boron aggregation in bulk BCC Nb-Ti-Ta-Hf; and (iii) coupled metallic and interstitial segregation at grain boundaries in Nb-Ti-Ta-Hf. In all cases, Monte Carlo-optimized structures are significantly lower in energy than any configuration obtained by random sampling, and MLIP energy rankings are validated against density functional theory calculations. PAIPAI provides a general and efficient framework for predicting atomic ordering, segregation, and interstitial behavior in complex, defective HEA systems.

Ground-State Structure Search of Defective High-Entropy Alloys Using Machine-Learning Potentials and Monte Carlo Sampling

TL;DR

A Monte Carlo framework coupled with machine-learning interatomic potentials (MLIPs) that searches for ground-state atomic configurations in HEAs with defects and interstitials, providing a general and efficient framework for predicting atomic ordering, segregation, and interstitial behavior in complex, defective HEA systems.

Abstract

Resolving the atomic-scale structure of defective high-entropy alloys (HEAs) containing interstitial species remains a major computational challenge due to the vast configurational space and the limitations of existing methods. Here we introduce PAIPAI (Package for Alloy Interstitial Predictions using Artificial Intelligence), a Monte Carlo framework coupled with machine-learning interatomic potentials (MLIPs) that searches for ground-state atomic configurations in HEAs with defects and interstitials. PAIPAI employs a dual-worker architecture-fast workers for rapid configurational screening and slow workers for high-accuracy refinement-coordinated through a shared waiting pool, enabling efficient parallel sampling. We demonstrate PAIPAI through three case studies: (i) surface segregation in a Ti-V-Cr-Re slab; (ii) interstitial oxygen and boron aggregation in bulk BCC Nb-Ti-Ta-Hf; and (iii) coupled metallic and interstitial segregation at grain boundaries in Nb-Ti-Ta-Hf. In all cases, Monte Carlo-optimized structures are significantly lower in energy than any configuration obtained by random sampling, and MLIP energy rankings are validated against density functional theory calculations. PAIPAI provides a general and efficient framework for predicting atomic ordering, segregation, and interstitial behavior in complex, defective HEA systems.
Paper Structure (9 sections, 2 equations, 6 figures, 1 table)

This paper contains 9 sections, 2 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Results
  3. Surface segregation in a Ti--V--Cr--Re alloy slab without interstitials
  4. Interstitial aggregation and solubility estimation in Nb--Ti--Ta--Hf alloys
  5. Coupled interstitial and grain boundary segregation in Nb--Ti--Ta--Hf alloys
  6. Discussion
  7. Methods
  8. Monte Carlo sampling framework
  9. MLIP and DFT calculation settings

Figures (6)

  • Figure 1: Monte Carlo process of Ti--V--Cr--Re slab. (a) Total energy of the slab versus Monte Carlo steps, with MLIP and DFT calculations; (b) initial random atomic structure; (c) atomic structure after $10^5$ accepted Monte Carlo steps with PAIPAI.
  • Figure 2: Energies of 100 fully relaxed random configurations of the Ti--V--Cr--Re slab. The Monte Carlo--optimized ground-state energy is marked with a dashed line.
  • Figure 3: Monte Carlo results of BCC Nb--Ti--Ta--Hf HEA with (a) no interstitials; (b) O interstitials; (c) B interstitials; (d) O and B interstitials. The metallic atoms are plotted with reduced radii to better visualize the configuration.
  • Figure 4: Grain boundary structure of Nb--Ti--Ta--Hf. (a) 200-atom structure with $\Sigma$5(120) grain boundaries in the middle and at both ends; (b) GB structure without interstitials after Monte Carlo; (c) GB structure with B interstitials after Monte Carlo; (d) GB structure with B and O interstitials after Monte Carlo. The metallic atoms are plotted with reduced radii to better visualize the configuration.
  • Figure 5: Benchmark of random perturbations applied to the MC-optimized Nb--Ta--Ti--Hf + B grain boundary structure. Three sets of 100 configurations are generated by randomly perturbing (i) both metallic and interstitial atoms; (ii) metallic atoms only; (iii) interstitial atoms only. The box plots show the energy difference relative to the MC-predicted ground state.
  • ...and 1 more figures