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2 Ca and K Isotope Fractionation by Diffusion in Molten Silicates: Large Concentration Gradients Are Not Required to Induce Large Diffusive Isotope Effects
James M. Watkins1, John N. Christensen2, Donald J. DePaolo2,3, and Frederick J. Ryerson4
1 Department of Earth Sciences, University of Oregon, Eugene, Oregon, USA
2 Earth and Environmental Science Area, Energy Geosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, USA
3 Department of Earth and Planetary Science, University of California, Berkeley, California, USA
4 Atmospheric, Earth, and Energy Division, Lawrence Livermore National Laboratory, Livermore, California, USA
ABSTRACT
Laboratory experiments were used to investigate diffusive isotopic fractionation of calcium and potassium in phonolite‐rhyolite diffusion couples. The starting compositions have very different SiO2 and K2O, but similar CaO. These were juxtaposed and held in a completely molten state at 1450°C and 1.0 GPa for durations of 2.5 or 6 hours in a piston cylinder apparatus. The resulting major‐element diffusion profiles exhibit many complexities, including uphill diffusion of all major oxide components. The diffusive fluxes for SiO2, K2O, and CaO were modeled using a published modified effective binary diffusion model, whereby diffusion is driven by activity gradients that are solely a function of the time‐evolving SiO2 concentration. Both Ca and K exhibit large diffusive isotope effects that can be explained by imposing a mass dependence on the diffusion coefficients used to model the major‐element profiles. The mass dependence is parameterized in terms of the inverse ratio of the isotope masses raised to an empirically determined exponent β (i.e., Di/Dj = [mj/mi] β ). Our results confirm that β factors vary depending on the element as well as liquid composition, and that large diffusive isotope effects can arise even in the absence of a large initial concentration gradient. The retrieved β factor for Ca (0.10 ± 0.02) is typical of Ca in natural silicate liquids, whereas the β factor for K (0.25 ± 0.03) is the highest value yet reported, suggesting that large diffusive K isotope effects may yet be found in high‐T environments.
2.1. INTRODUCTION
Igneous and metamorphic rocks exhibit stable isotope variations in excess of what can reasonably be attributed to mixing processes or equilibrium partitioning during partial melting and (re)crystallization. Experimental studies have shown that diffusion is capable of generating measurable (sub‐permil) to large (tens of permil) kinetic isotopic fractionations that can account for some of this variability, and detailed knowledge of these effects can yield unique insights into the molecular level controls on diffusive transport and the role of kinetics in the formation of minerals in high temperature settings (Antonelli et al., 2019b; Barrat et al., 2005; Beck et al., 2006; Chen et al., 2018; Chopra et al., 2012; Dauphas, 2007; Dauphas et al., 2010; Gallagher & Elliott, 2009; Gao et al., 2011; Jeffcoate et al., 2007; Kil et al., 2016; Lundstrom et al., 2005; Marschall et al., 2007; Mueller et al., 2014; Oeser et al., 2015; Parkinson et al., 2007; Richter et al., 2009, 2014, 2016, 2017; Roskosz et al., 2006; Rudnick & Ionov, 2007; Sio et al., 2013; Su et al., 2016; Teng et al., 2006, 2011; Wu et al., 2018; Zhao et al., 2017).
Current knowledge of diffusive isotopic fractionations in molten silicates is based on a few elements (Ca, Fe, Mg, Li, and Si) and silicate melt compositions (cf. Watkins et al., 2017, for a review). The mass dependence on diffusion coefficients varies between cations and with liquid composition. In basalt‐rhyolite diffusion couples, for example, the stable isotopes of major elements (Ca, Fe, Mg) exhibit less mass discrimination ( β < 0.075) than the stable isotopes of trace element Li ( β ≈ 0.215) (Richter et al., 2003, 2009; Watkins et al., 2009). In simplified silicate liquids, it has been found that the β factor for Ca and Mg varies between 0.05 and 0.21, depending on liquid composition, and is correlated with the “solvent‐normalized” diffusivity (e.g., DCa/DSi), suggesting that faster diffusing elements exhibit greater mass discrimination because they move as single atoms or small moities whose diffusion is decoupled from that of the major melt structures/components (Goel et al., 2012; Watkins et al., 2009, 2011). This simple relationship provides a useful framework for choosing an appropriate value for β in diffusion models and
