An active learning workflow for predicting misfit volume in body-centered cubic refractory high-entropy alloys

Refractory high-entropy alloys (RHEAs) exhibit exceptional high-temperature mechanical properties. However, a mechanistic understanding of their yield strength requires accurate determination of the misfit volume descriptor ($$\delta$$), which quantifies the local volume change due to the size and electronic heterogeneity of constituent elements in the solid solution. Traditional approximations, such as Vegard’s Law, fail to capture local atomic relaxation and electronic structure effects in these compositionally complex systems. An active learning workflow is developed that integrates density functional theory calculations with ensemble machine learning (ML) to efficiently predict the $$\delta$$-descriptor across 126 equiatomic quinary body-centered cubic (BCC) RHEAs. Partial dependence plots and symbolic regression reveal that atomic size mismatch directly influences the $$\delta$$-descriptor, while electronegativity variations provide electronic structure compensation. Incorporating ML-predicted $$\delta$$-values into the Maresca-Curtin mechanistic model achieves good correlation with experimental yield strengths across diverse BCC RHEA compositions.