Exploration for the physical origin and impact of chemical short-range order in high-entropy alloys: Machine learning-assisted study

Atomic-level chemical short-range order (CSRO) in high-entropy alloys (HEAs) has ever garnered increasing attention. However, the mechanisms underlying the effects of CSRO remain poorly understood. Material informatics, through a machine learning (ML) algorithm, can fit the high-dimensional correlation between features well and provide a new approach for elucidating complex mechanisms. In this study, we introduced a set of interpretable ML workflows and successfully determined the best algorithm (kernel ridge regression (KRR)) for predicting the atomic stress in HEAs, which can deepen the understanding of the formation mechanism of CSRO. Based on first-principles calculations and Monte Carlo methods, we first obtained information on each atom at atomic and electronic levels to establish features. By systematically studying these features, we found that the Shapley additive algorithm indicated that the t2g orbitals are fundamental factors that dominate atomic stress, which is critical in the CSRO landscape. Additionally, we discovered that the elemental t2g-eg orbital relationship, like Ti, greatly influences the characteristics of atomic coordination. Moreover, the closely packed configuration efficiently promotes the ideal strength of the short-range order (SRO) HEA compared to its fully random counterpart. We posit that this endeavor provides a theoretical bedrock for grappling with experimental quandaries and theoretical conundrums.