Isotopic Constraints on Earth System Processes. Группа авторов. Читать онлайн. Newlib. NEWLIB.NET

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alt="script upper D"/> ), the modified EBD model is capable of reproducing the sign and magnitude of uphill diffusion in the K2O and CaO profiles (Fig. 2.7a–f). The positive Cf for CaO implies that CaO partitions into mafic liquids whereas the negative Cf for K2O implies that K2O partitions into felsic liquids, which is consistent with the known partitioning behavior of these two oxide components (Ryerson & Hess, 1978; Watson, 1976). The misfit on the ends of the CaO profiles suggest that the activity of CaO depends on melt components in addition to SiO2. The next level of complexity would be to include the alkali components in the activity‐composition model for CaO.

      The goodness‐of‐fit for the K2O profile is even less satisfying due to the unusual shape of the measured K2O profile, which is nearly flat on the mafic side and linear to nearly convex on the felsic side. This shape cannot be reproduced using the simplified EBD models discussed herein. Nevertheless, the inferred script upper D Subscript normal upper K 2 normal upper O is a reasonable average value, being somewhat overestimated on the rhyolite side and somewhat underestimated on the phonolite side. A better fit could be obtained by casting script upper D Subscript normal upper K 2 normal upper O as a function of SiO2 concentration (Richter et al., 2003, 2009; Watkins et al., 2009) or by introducing some other additional ad hoc complexity into the model. We did not undertake such efforts because the calculated concentration profiles provide an adequate description of the K2O fluxes to be used as a baseline for modeling the isotope ratio profiles.

Schematic illustration of the modified EBD model applied to the data.

       Model for the Isotope Ratio Profiles

      (2.9)StartFraction script upper D 44 Over script upper D 40 EndFraction equals left-parenthesis StartFraction m 40 Over m 44 EndFraction right-parenthesis Superscript beta Baseline equivalent-to left-parenthesis StartFraction 40 Over 44 EndFraction right-parenthesis Superscript beta Baseline comma

      where β is a dimensionless empirical parameter. Here, m refers to the isotopic mass and not the mass of an isotopically substituted molecule such as, for example, CaAl2O4. This functional form is based on principles from the kinetic theory of gases, but it’s also convenient because it normalizes out the fractional mass difference between isotopes, thereby allowing for direct comparison between different isotopic systems.

      To model the isotope ratio profiles, we assume the rhyolite and phonolite have the same isotopic composition since they are within error of each other with respect to δ 44Ca. Although we did not directly measure the δ 41K of either starting material, the assumption that they are the same can be justified on the basis that the global range in δ 41K of igneous rocks and minerals is < 1‰ (Morgan et al., 2018). We assume further that the equilibrium isotope ratio profile is uniform at all times; i.e., Ce, 44 is defined to be proportional to Ce, 40 such that the ratio Ce, 44/Ce, 40 is constant, which implies that there is no equilibrium isotopic partitioning between the liquids. Hence, any isotopic fractionations in the model arise solely from diffusive fluxes and the difference in isotopic diffusion coefficients.

      Model isotopic profiles are compared to the data in the bottom panels of Fig. 2.7. For Ca isotopes, no single set of parameters (script upper D Subscript upper C a upper O , Db, Cf, and β ) can explain the full profile or its time evolution reflected in the 2.5‐ and 6‐hour runs. Nevertheless, the fits are qualitatively no worse than those used to estimate β factors and associated uncertainties in other natural silicate liquid diffusion couple experiments (Richter et al., 2003; Watkins et al., 2009). By plotting model curves corresponding to different values of β against the data, we estimate β = 0.10 ± 0.02. This is a somewhat crude estimate, however, and appears to be on the low side for the rhyolite while fitting the phonolite in the 2.5‐hour run, and on the low side for the phonolite while fitting the rhyolite in the 6‐hour run. For K isotopes, we estimate β = 0.25 ± 0.03, which is comparable to the value for Li ( β = 0.21–0.23) in basalt‐rhyolite and rhyolite‐rhyolite diffusion couples (Holycross et al., 2018; Richter et al., 2003).

      2.5.3. Comparison to Previous Studies

Schematic illustration of beta factors from this study (points with an asterisk) compared to literature values.

      The ratio script upper D Subscript upper C a upper O /DSi is inferred to be about 20, and the β factor for Ca is offset from the overall trend. The ratio script upper D Subscript normal upper K 2 normal upper O /DSi is inferred to be about 35 and the β factor for K is the highest value yet determined for diffusion in silicate liquids. Despite K2O being present in major quantities, it behaves like a trace element insofar as its diffusion is kinetically decoupled from the motion of the slower‐moving aluminosilicate structures (cf. Dingwell, 1990). The high β factor suggests that large