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

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.