The confines of triple oxygen isotope exponents in elemental and complex mass-dependent processes

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© 2015 Elsevier Ltd. Small differences in triple isotope relationships, or δ17O in the case of oxygen, have been increasingly used to study a range of problems including hydrological cycles, stratosphere-troposphere exchange, biogeochemical pathways and fluxes, and the Moon's origin in the geochemical and cosmochemical communities. A δ17O value depends on the triple isotope exponent θ of involved reaction steps. However, the probabilistic distribution of the intrinsic and apparent θ values has not been examined for elemental processes and for processes that are out of equilibrium or bearing reservoir-transport complexities. A lack of knowledge on the confines of θ may hamper our understanding of the subtle differences among mass-dependent processes and may result in mischaracterization of a set of mass-dependent processes as being in violation of mass-dependent rules. Here we advocate a reductionist approach and explore θ confines starting from kinetic isotope effects (KIEs) within the framework of transition state theory (TST). The advantage of our KIE approach is that any elemental or composite, equilibrium or non-equilibrium process can be reduced to a set of KIEs with corresponding θKIE.We establish that the KIE between a reactant and a transition state (TS) is intrinsic. Given a range of KIEs known for Earth processes involving oxygen, we use a Monte Carlo calculation method and a range of oxygen-bonded molecular masses to obtain a distribution of θKIE values and subsequently that of θeq. Next, complexities are examined by looking into expected effects due to reaction progress, unbalanced fluxes, and reference frame. Finally, compounded reservoir-transport effects are examined using two simple processes - Rayleigh Distillation (RD) and Fractional Distillation (FD). Our results show that the apparent θ values between two species or two states of the same evolving species have much broader confines than the commonly used "canonical" confines of 0.51-0.53, particularly when the overall fractionation factors are close to 1.000. Equilibrium processes exhibit the narrowest α-θ value distribution. More complex processes or non-equilibrium further broaden the confines of the apparent θ values for reaction systems. The compounded reservoir-transport effects of RD and FD demonstrate that non-canonical apparent θ and large non-zero δ17O values are achievable even when all involved elemental steps are strictly mass-dependent. This study calls for a research effort to determine KIE and θKIE for important natural processes, and for cautions in interpreting a slope value drawn in a δ'17O-δ'18O space, as the slope is only a superficial manifestation of a set of complex reaction pathways and dynamics.

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Geochimica et Cosmochimica Acta

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