Decoding high-temperature activity coefficients in magnesium alloys through interpretable data-driven thermodynamics

To investigate the high-temperature thermodynamic properties of magnesium alloys, this study calculates the activity coefficients of alloying elements in the Mg matrix phase for the Mg-1X-1Y ( at.% ) ternary system at 500°C based on the Pandat thermodynamic database. Employing correlation analysis, random forest algorithm, and SHAP interpretation methods, the relationships between the activity coefficients and both intrinsic elemental features (atomic radius, electronegativity, melting point, boiling point, electron affinity, atomic mass, crystal structure) and interaction features are systematically analyzed. The results indicate that electron affinity, melting point, boiling point, atomic mass, and crystal structure characteristics exhibit strong correlations with the activity coefficients. On this basis, random forest prediction models are constructed for two categories of alloying elements: those with a full range of activity coefficients (Y-model) and those with activity coefficients less than 1 (X-model). SHAP analysis reveals the contribution mechanisms of each feature to the prediction outcomes. Among them, the absolute difference in electron affinity between Mg and Y plays a dominant role in predicting the full-range activity coefficients, while atomic mass features and the interaction between atomic radius and electronegativity contribute most significantly to the system where activity coefficients are less than 1. Thermodynamic calculations show that Sc, Y, and rare earth elements significantly enhance the activity coefficients of highly active elements (Ca, Sr, Zn, Al). In the Mg-Gd/Sn/Sc/Si-X systems, the addition of most alloying elements increases the activity coefficients of Gd, Sn, Sc, and Si, whereas Sc, Al, and Sr reduce the activity coefficients in some systems. This work extends machine learning methods to ternary Mg-1X-1Y systems, systematically revealing the dominant role of binary Mg-X and Mg-Y interactions in ternary dilute solution systems, as well as the negligible nature of X-Y solute-solute interactions. It innovatively establishes two predictive models: one for the full range of activity coefficients (Y-model) and another specifically for γ < 1 (X-model). The computational data provided in this work offer a theoretical basis for the composition design and process optimization of magnesium alloys, and the established machine learning model provides a concise and effective method for obtaining high-temperature activity data of magnesium alloys.