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

Abstract

We present a forward prediction material screening framework designed to discover Pd-Cu alloys with improved B2 phase stability, thereby unlocking simultaneous $H_2$ generation and utilization. First, we trained CatBoost models with literature-derived Pd alloy data to predict $H_2$ permeability from composition and testing conditions. We evaluated fractional, composition-based, and physics-informed descriptors, individually and in combination, and showed that sequential Pearson filtering and fold-wise SHAP-based recursive feature elimination with cross-fold aggregation reduced errors while controlling complexity. Guided by the one-SE rule, a narrower domain-informed set of 13 features provided the best accuracy parsimony trade-off ($R^2=0.81$), only 0.01 below the max. $R^2$ achievable with 3x the number of features. SHAP analysis indicated that high permeability is promoted by elevated temperature, lattice expansion relative to Pd, atomic size mismatch, and favorable mixing tendencies. Second, the selected model was applied to screen $Pd_{(100-x-y)}Cu_{x}M_{y}$ spanning 16 co-dopants M for B2 stabilization. For each M system, we obtained the Pareto set of compositions that minimize Pd content and Miedema heat of formation and maximize the permeability, then picked three compounds, including that with the highest predicted permeability, the lowest Miedema heat of formation, and the lowest Pd content. With a final filter considering M concentration for single-phase Pd-M solution formation, we recommend Pd48.48Cu43.00Y8.52, Pd49.08Cu42.45Sc8.47, Pd56.09Cu33.70La10.21, and Pd52.68Cu40.44Mg6.88 for experimental validation. We predict those alloys to exhibit permeabilities 1.7 to 1.9 higher than B2 Pd60Cu40. Our framework provides plausible experimental targets and a scalable pathway for designing stable, high-temperature, H2-selective Pd-alloy membranes.