Effects of the Electron Concentration, d‐Orbital Energy Level, and Atomic Mismatch on Quantitative Phase Prediction in Complex Concentrated Alloys (CCAs): Empirical Criteria and Machine Learning Insights

ABSTRACT Dual‐phase high‐entropy alloys (DPHEAs) exhibit superior strength‐ductility synergy compared to single‐phase counterparts, with properties strongly governed by phase fraction. This necessitates robust quantitative phase prediction, as most prior studies remain qualitative. In this study, we develop and evaluate two complementary frameworks for quantitative phase prediction in DPHEAs: a threshold‐based approach and a machine learning (ML) approach. Both methods incorporate key descriptors of electronic structure and atomic size mismatch, including valence electron concentration (VEC), atomic size difference (δ), d‐orbital energy level (Md), and a newly introduced critical mismatch factor (δ c ). Amongst the threshold‐based approach, VEC + δ c showed the highest accuracy (81%), while in the ML approach, the random forest (RF) achieved 88% accuracy. The Md and VEC have similar predictive capability within the framework of threshold‐based modeling, owing to the high linear correlation between VEC and Md (Pearson coefficient of 0.97). Whereas δ c , which shows minimal correlation with electronic descriptors, emerged as the dominant parameter in threshold‐based modeling. In contrast, feature importance analysis from the RF regression identified Md as the dominant predictor, surpassing the commonly used VEC. The study demonstrated that electronic structure descriptors and atomic mismatch measures are complementary in nature for reliable phase prediction.