Isotopic Constraints on Earth System Processes. Группа авторов

href="#ulink_71f9674b-8f8e-592b-8840-5c59725381c1">Fig. 1.1 is the result of the fluxes of MgO, CaO, FeO, and K₂O all being strongly coupled to the concentration gradient of SiO₂ via the off‐diagonal terms of the diffusion matrix. There are two reasons for this strong coupling with SiO₂. One reason is that the sum of volume fluxes of all the components must add up to zero and thus the fluxes are rate limited by the large and sluggish volume flux of SiO₂ that has to balance the fluxes of the other components. The second reason for the coupling is that the chemical potential gradients of the major oxides, which drive their diffusion, depend on the local SiO₂ content of the melt (see Liang et al., 1967 for a detailed discussion of the causes of diffusive coupling in silicate liquids).

      1.2.4. Thermal (Soret) Diffusion Coefficients

      The flux equation of a system that is inhomogeneous in both composition and temperature will have terms proportional to both the chemical gradient and the temperature gradient. Expanding the binary diffusion representation of the flux to include the effect of a temperature gradient results in a binary flux equation of the form (Tyrell, 1961)

Figure 1.1 Normalized concentration of CaO, MgO, K2O, FeO, and SiO2 measured across glass recovered from a molten rhyolite‐basalt diffusion experiment are superimposed to show the similarity of the effective diffusivity of all the major oxide components. For the purpose of this comparison, the concentration differences were normalized by (C‐CL)/(CH‐CL), where C is the concentration of a component along the profile, CL is its concentration in the low end‐member, and CH is its concentration in high end‐member.

      Figure taken from Richter et al. (2003).

      (1.6)

      where ρ is the bulk density,

is the effective binary diffusion coefficient of i in a mixture of components i and j, X_i and X_j are the mass fractions of i and j, and σ _i is the Soret coefficient. For present purposes, the term “Soret diffusion” will be used when the mass transport in a silicate liquid is due to fluxes driven by both chemical and temperature differences.

1.3. KINETIC ISOTOPE FRACTIONATION DURING DIFFUSION BETWEEN NATURAL MELTS

The earliest report of measurable differences in the mobility of isotopes of a major element in a silicate liquid was reported by Richter et al. (1999) based on the results of a diffusion experiment involving an isothermal and isochemical CaO‐Al₂O₃‐SiO₂ melt with an initial step with different concentration of ⁴⁸Ca and ⁴⁰Ca but with the same isotopic ratio of ⁴⁸Ca/⁴⁰Ca on both sides of the step. When annealed, this setup would cause ⁴⁸Ca and ⁴⁰Ca to race each other as they diffused into the low concentration side of the couple. A well‐resolved isotopic fractionation in the glass recovered from this experiment showed that ⁴⁰Ca had diffused measurably faster than ⁴⁸Ca. The relative mobility of the calcium isotopes was reported as D₄₈ /D₄₀ = (40/48) ^β with β = 0.075 ± 0.025. Subsequent laboratory experiments by Richter et al. (2003; 2008; 2009b; 2014a) addressed the question of whether the relative mobility of isotopes seen in isochemical experiments would also arise in molten systems where chemical potential gradients are present and where there can be significant coupling between the various diffusing components of the melt.

      1.3.1. Laboratory Experiments Documenting Ca Isotope Fractionation by Diffusion Between Molten Rhyolite and Basalt

The type of piston cylinder assembly used by Richter et al. (2003) to determine the isotopic fractionation of calcium and lithium in rhyolite‐basalt diffusion couples is shown schematically in Fig. 1.2.

      Fig. 1.3 shows the weight percent of major oxide components measured along five parallel lines along the long dimension of the glass recovered from experiment RB‐2. The data from all five lines fall along common smooth curves that are not symmetric with respect to the original interface between the rhyolite and basalt because the rate of diffusion is much faster in the lower SiO₂ content of the basalt side of the couple. The Al₂O₃ profile is a classic example of uphill diffusion in that the low concentration side of the couple became lower than the initial concentration. This uphill diffusion is an indication that the flux of Al₂O₃ is dominated by off‐diagonal terms in the diffusion matrix. Except for Al₂O₃, an effective binary diffusion coefficient D ^E can be derived from fits to the concentration data of all the other major oxides. Experiment RB‐2 was one of two that were run to determine whether calcium isotopes would become measurably fractionated as calcium diffused from the basalt into the rhyolite.

Figure 1.2 A schematic of the piston cylinder assembly used by Richter et al. (2003) to study isotope fractionation by diffusion between molten rhyolite and basalt.

Fig. 1.4 shows the ⁴⁴Ca/⁴⁰Ca fractionation measured by thermal ionization mass spectrometry of purified solutions derived by dissolving thin (~ 0.5 mm) slabs cut perpendicular to the long axis of the recovered glass from experiment RB‐2 run for 15.7 hours at 1450°C and 1.3 GPa, and from a second diffusion couple, RB‐3, run for 12 hours at 1450°C and 1.2 GPa. The calcium isotopic fractionation is reported in the usual per mil notation with the ⁴⁴Ca/⁴⁰Ca of a purified CaCO₃ salt used as the standard. The calcium isotopic composition of the rhyolite is within error (± 0.2), the same as that of the basalt, and therefore the initial δ⁴⁴Ca across the couple was effectively uniform. The locally negative δ⁴⁴Ca in that part of the couple where calcium diffused from the basalt into the rhyolite is evidence of ⁴⁰Ca having diffused measurably faster than ⁴⁴Ca.

      The model calculation for the evolution of the major oxide components and the calcium isotopes was formulated using effective binary diffusion coefficients. The conservation equations for total CaO, SiO₂, ⁴⁰CaO,