Pressure-Dependent Atomic Properties Extend Classical Hume–Rothery Descriptors for Binary Alloy Mixing Prediction

The Hume–Rothery rules have guided alloy design for nearly a century by evaluating atomic radius and electronegativity compatibility at ambient pressure. Here we extend these classical descriptors from static ambient values to pressure-dependent response functions spanning 0–300 GPa, testing whether the dynamic behaviour of atomic properties under compression contains predictive information for binary alloy mixing absent from single-point evaluation. Using 780 binary pairs from 40 elements with mixing enthalpies from the DFT calculations and pressure-dependent atomic data from the SHARC database, we constructed 83 features: 13 ambient-only (classical Hume–Rothery baseline) and 70 pressure-dependent (gradients, variabilities, and trajectory stabilities). Statistical hypothesis testing demonstrates that pressure-dependent features improve prediction of the mixing enthalpy sign by Δ = +11.5% over ambient-only descriptors (p = 0.0001, Cohen's d = 2.69). Pipeline-aware SHAP analysis attributes 84.6 ± 0.1% of predictive contribution to pressure-dependent features across three independent runs. The dominant descriptors—electronegativity variability and gradient under compression—directly extend the classical electronegativity-mismatch criterion: favourable mixing correlates not merely with small ambient Δχ, but with electronegativity trajectories that preserve electronic compatibility across the pressure domain. Similarly, atomic radius gradients extend the 15% size-mismatch rule by capturing differential compressibility. External validation on 29 lanthanum-containing pairs not included in training achieved 80% accuracy. These results establish that the logic of Hume–Rothery—evaluating atomic compatibility to predict mixing—gains substantial predictive power when extended from single ambient values to pressure-response trajectories.