Rebuilding the theory of isotope fractionation for evaporation of silicate melts under vacuum condition

Isotope effects are pivotal in understanding silicate melt evaporation and planetary accretion processes. Based on the Hertz–Knudsen equation, the current theory often fails to predict observed isotope fractionations of laboratory experiments due to its oversimplified assumptions. Here, we point out that the Hertz-Knudsen-equation-based theory is incomplete for silicate melt evaporation cases and can only be used for situations where the vaporized species is identical to the one in the melt. We propose a new model designed for silicate melt evaporation under vacuum. Our model considers multiple steps including mass transfer, chemical reaction, and nucleation. Our derivations reveal a kinetic isotopic fractionation factor (KIFF or α) α_{our model} = [m(¹species)/m(²species)]^0.5, where m(species) is the mass of the reactant of reaction/nucleation-limiting step or species of diffusion-limiting step and superscript 1 and 2 represent light and heavy isotopes, respectively. This model can effectively reproduce most reported KIFFs of laboratory experiments for various elements, i.e., Mg, Si, K, Rb, Fe, Ca, and Ti. And, the KIFF-mixing model referring that an overall rate of evaporation can be determined by two steps jointly can account for the effects of low P_H2 pressure, composition, and temperature. In addition, we find that chemical reactions, diffusion, and nucleation can control the overall rate of evaporation of silicate melts by using the fitting slope in ln(− lnf) versus ln(t). Notably, our model allows for the theoretical calculations of parameters like activation energy (E_a), providing a novel approach to studying compositional and environmental effects on evaporation processes, and shedding light on the formation and evolution of the proto-solar and Earth-Moon systems.