Interpretable machine learning prediction of erbium-related thermodynamic parameters and experimental validation of Er2O3 phase stability in metallic melts

Rare earth elements play important roles in high-temperature metallic systems due to their strong oxygen affinity and influence on phase formation. However, thermodynamic parameters involving erbium remain limited, hindering quantitative evaluation of Er-containing oxide formation. In this work, an interpretable machine-learning framework was developed to predict erbium-related thermodynamic parameters by integrating dataset reconstruction, data augmentation, thermodynamic calculation, and experimental validation. A symmetry-consistent dataset of solute interaction coefficients was constructed and expanded, and key descriptors were identified through hierarchical feature selection. The optimized XGBoost model achieved the best performance (R² = 0.904, RMSE = 0.82659). SHAP analysis indicated that atomic size mismatch, electronegativity difference, and valence characteristics govern solute interactions. The predicted effective descriptors were converted into reciprocity-consistent direction-specific interaction coefficients before being incorporated into the Wagner interaction formalism to establish the equilibrium relationship for Er2O3 formation and construct the corresponding predominance diagram. Experimental observations in high-purity iron provided preliminary supporting evidence for Er2O3-containing particles and were consistent with the predicted Er2O3 stability trend. This work provides thermodynamic data for erbium-containing systems and a data-driven approach for analyzing rare-earth oxide stability in metallic melts.