First Principles Calculation on Equilibrium Si Isotope Fractionation Factors and its Implementation on Si Isotope Distributions in Earth Surface Environments

Abstract:

Several important equilibrium Si isotope fractionation factors are calculated here. We use a so-called volume-variable-cluster-model (VVCM) method for solids and the “water-droplet” method for aqueous species for isotope fractionation calculation at the same quantum chemistry level. The calculation results show that several silicate minerals, such as quartz, feldspar, kaolinite, etc., all enrich heavy Si isotopes relative to aqueous H₄SiO₄ and can be up to 3.3‰ at 25°C, different from most field observations. Meanwhile stable organosilicon complexes can enrich even lighter Si isotopes than aqueous H₄SiO₄. For explaining the difference between the calculation results and field observations, we calculate the kinetic isotope effect (KIE) associated with the formation of amorphous silica, and find that amorphous silica will enrich extremely light Si isotopes. From amorphous silica to crystalline quartz, the structural adjustment & transition needs getting rid of small amount of Si to re-organize the structure. Light Si isotopes will be preferentially lost and let the final crystalline quartz with a little bit more heavy Si isotopes. However, such late-stage Si heavy isotope enrichment cannot erase the total isotopic signal, crystalline quartz still inherit much light Si isotopic composition from amorphous quartz. That is the reason for the discrepancy between the calculation results and the field observations, because the formation of amorphous quartz is under a non-equilibrium process but theoretical calculations are for equilibrium isotope fractionations. With accurate equilibrium fractionation factors provided here, Si isotope distributions in earth surface environments including soil, groundwater and plants can be further interpreted. We find that δ³⁰Si variations in soil are mainly driven by secondary minerals precipitation and adsorption. Also, bulk soil δ³⁰Si maybe have a parabolic distribution with soil age, with a minimum value at where allophane is completely dissolved and the total amount of sesqui-oxides and poorly crystalline minerals reach their maximum. Similarly, precipitation of clay minerals can explain δ³⁰Si variation in ground water profile.