Entropy-dominated and alkali-enhanced scandium partitioning into clinopyroxene revealed by density functional theory and machine learning

Scandium holds significant importance in modern technology and is recognized as a strategic or critical metal in many countries. Scandium-rich clinopyroxene is important in forming various Sc resources, whereas the favorable conditions in forming Sc-rich clinopyroxene remain unclear. By compiling available experimental data on Sc partition coefficients between clinopyroxene and melt (DSccpx/melt), we demonstrate that DSccpx/melt values increase exponentially with the alkali contents in melts. Using first-principle calculations combined with a simple thermodynamic model, we propose that this trend arises from simultaneous competitive formation of AlM1AlT, NaM2AlM1 and NaM2ScM1 pairs in clinopyroxene. This mechanism differs from conventional models such as charge-coupled substitutions, which would increase Sc partitioning with Al through ScM1AlT pairing. The incorporation of Sc into clinopyroxene is highly energetically unfavorable compared to Al, suggesting that Sc uptake may be governed mainly by configurational entropy rather than enthalpic factors. Entropy-driven competition model predicts a pronouced temperature dependence of Sc partitioning, with lower temperature and alkali-richer melts tending to yield larger DSccpx/melt values, thereby potentially promoting Sc enrichment in clinopyroxene. Our model demonstrates that Sc partitioning may reflect a complex interplay of different components in both the melt and solid phases, and previous regressions of experimental data may have not fully captured these effects. To complement the thermodynamic approach, we develop a predictive machine-learning model trained on experimental data, achieving a high coefficient of determination (R2 = 0.98). Together, the thermodynamic framework and data-driven model quantify how melt alkalis and temperature regulate Sc partitioning, provide new constraints on the petrogenic conditions and magma compositions that promote Sc-rich clinopyroxene and, by extension, Sc enrichment in alkaline magmatic systems.