Hydrogen permeability prediction in palladium alloys and virtual screening of B2 phase-stabilized Pd(100-x-y)CuxMy ternary alloys using machine learning

Abstract

Ordered B2 phase Pd–Cu alloys are promising candidates for dense metallic membranes for high-temperature hydrogen purification, but their practical deployment is hindered by thermally induced disordering to the fcc phase, which degrades hydrogen permeability. Here, we develop a machine-learning–assisted materials-screening framework to identify hypothesis-generating Pd–Cu–M ternary alloys with improved B2-phase stability and competitive hydrogen transport properties. CatBoost regressors were trained on literature-derived hydrogen permeability data restricted to bulk diffusion–controlled regimes, using composition-based descriptors combined with operating conditions. Multiple descriptor families were evaluated through systematic ablation, and a feature-selection strategy integrating Pearson filtering with fold-wise SHAP-driven recursive feature elimination was employed. Guided by the one-standard-error rule, a compact, domain-informed set of 13 features achieved a favorable accuracy–parsimony balance (R2= 0.81), within 0.01 of the maximum performance obtained using 3 times more features. Model interpretability analysis indicates that high apparent permeability correlates with elevated temperature, lattice expansion relative to Pd, increased atomic size mismatch, and favorable alloy mixing tendencies. To enable responsible virtual screening, a k -nearest-neighbor applicability-domain analysis was combined with multi-objective Pareto optimization to distinguish interpolative predictions from extrapolative hypotheses. Within the model’s applicability domain, several Pd–Cu–M systems at low dopant concentrations exhibit predicted permeabilities (1.06 – 1.09 ×10–8 mol·m–1·s–1·Pa–0.5) comparable to the B2 Pd<inf>47.25</inf>Cu<inf>52.75</inf> benchmark. Post hoc density functional theory calculations on selected compositions further support the stabilizing influence of Nb and Cr at dilute levels, and Y at higher concentrations, through reduced ground-state formation enthalpy. Overall, this work provides experimentally relevant targets and a scalable, data-informed pathway for the rational design of thermally stable Pd-based hydrogen separation membranes. © 2026 The Authors.