Efficient compositional exploration for sluggish interstitial diffusion in FeNiCrCoCu high-entropy alloys using machine learning-kinetic Monte Carlo and Bayesian optimization

The study of sluggish diffusion in high-entropy alloys (HEAs) remains underexplored largely due to their extensive compositional space. In particular, self-interstitial diffusion exhibits a non-monotonic compositional dependence, necessitating an efficient search to identify optimum compositions. This work presents three kinetic Monte Carlo (KMC)-based methods to simulate complex $〈100〉$ interstitial dumbbell diffusion of 15 dumbbell types with 125 distinct migration paths in a model FeNiCrCoCu HEA system over a large compositional space: conventional KMC (C-KMC), random-sampling KMC (RS-KMC), and machine learning KMC (ML-KMC). Our results demonstrate that ML-KMC, with its ability of efficiently predicting dumbbell formation energies on the fly, can effectively capture key diffusion patterns, as validated by independent molecular dynamics (MD) simulations. This ML-KMC method provides a promising high-throughput approach (about 3500 times faster than MD) for studying the complex dumbbell diffusion in HEAs. The controversial percolation effect by faster diffusing elements (Cr+Cu) is also analyzed, suggesting no universal percolation threshold in HEAs. To efficiently explore the compositional space and pinpoint HEA compositions with slower interstitial diffusivities, ML-KMC is integrated within a Bayesian optimization (BO) framework. This approach successfully identifies HEA compositions with diffusivities over an order of magnitude slower than the equiatomic HEA at 800 K within only a few ten iterations, circumventing the inefficiency of conventional brute-force compositional enumeration. The identified optimal composition (Fe₃₅Ni₁₄Cr₆Co₃₅Cu₁₀) is further verified by independent MD simulations, confirming the effectiveness of the ML-KMC-BO methodology. This work can advance the understanding of compositional-dependent diffusion mechanisms and provide valuable insights for HEA design.