Surface kinetic model for isotopic and trace element fractionation during precipitation of calcite from aqueous solutions |
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| Authors: | Donald J DePaolo |
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| Institution: | Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA |
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| Abstract: | A surface reaction kinetic model is developed for predicting Ca isotope fractionation and metal/Ca ratios of calcite as a function of rate of precipitation from aqueous solution. The model is based on the requirements for dynamic equilibrium; i.e. proximity to equilibrium conditions is determined by the ratio of the net precipitation rate (Rp) to the gross forward precipitation rate (Rf), for conditions where ionic transport to the growing crystal surface is not rate-limiting. The value of Rp has been experimentally measured under varying conditions, but the magnitude of Rf is not generally known, and may depend on several factors. It is posited that, for systems with no trace constituents that alter the surface chemistry, Rf can be estimated from the bulk far-from-equilibrium dissolution rate of calcite (Rb or kb), since at equilibrium Rf = Rb, and Rp = 0. Hence it can be inferred that Rf ≈ Rp + Rb. The dissolution rate of pure calcite is measureable and is known to be a function of temperature and pH. At given temperature and pH, equilibrium precipitation is approached when Rp (=Rf − Rb) ? Rb. For precipitation rates high enough that Rp ? Rb, both isotopic and trace element partitioning are controlled by the kinetics of ion attachment to the mineral surface, which tend to favor more rapid incorporation of the light isotopes of Ca and discriminate weakly between trace metals and Ca. With varying precipitation rate, a transition region between equilibrium and kinetic control occurs near Rp ≈ Rb for Ca isotopic fractionation. According to this model, Ca isotopic data can be used to estimate Rf for calcite precipitation. Mechanistic models for calcite precipitation indicate that the molecular exchange rate is not constant at constant T and pH, but rather is dependent also on solution saturation state and hence Rp. Allowing Rb to vary as  , consistent with available precipitation rate studies, produces a better fit to some trace element and isotopic data than a model where Rb is constant. This model can account for most of the experimental data in the literature on the dependence of 44Ca/40Ca and metal/Ca fractionation in calcite as a function of precipitation rate and temperature, and also accounts for 18O/16O variations with some assumptions. The apparent temperature dependence of Ca isotope fractionation in calcite may stem from the dependence of Rb on temperature; there should be analogous pH dependence at pH < 6. The proposed model may be valuable for predicting the behavior of isotopic and trace element fractionation for a range of elements of interest in low-temperature aqueous geochemistry. The theory presented is based on measureable thermo-kinetic parameters in contrast to models that require hyper-fast diffusivity in near-surface layers of the solid. |
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