Isotopic Constraints on Earth System Processes. Группа авторов

with a model curve calculated using an effective binary diffusion coefficient for magnesium that depends on the evolving SiO2 content of the melt. The lower panel on the left uses open circles with two sigma error bars to show the δ²⁶Mg‰ of thin slabs cut perpendicular to the long axis of the glass recovered from experiment GBM‐2. The two black diamonds in this panel show the δ²⁶Mg‰ of the mafic and felsic powders used to make the diffusion couple. The dashed curve is from a chemical diffusion calculation with δMg = 0.040 while the continuous black curve is from a calculation with δ = 0.040 but which also took into account the thermal isotope fractionation associated with the temperature profile shown in Fig. 1.5. The panels on right the show the weight percent MgO and the magnesium isotopic fractionation across an exposed contact between felsic and mafic rock in the Vinalhaven igneous complex in Maine, USA. The model curves in the panels on the right were calculated in the same way as those on the left except that the isotopic fractionation was fit using δMg = 0.045. The δ²⁶Mg‰ is reported relative to the magnesium isotope standard DSM3 of Galy et al. (2003).

1.4. ISOTOPE FRACTIONATION BY SORET DIFFUSION

It is well known that sustained temperature differences in gases and liquids can measurably fractionate elements and isotopes. The existence of this phenomenon in gases was described theoretically by Enskog (1911) and later confirmed by the experiments of Chapman and Dootson (1917). In the case of liquids, thermal diffusion was first demonstrated experimentally by Soret (1879) who found that ionic salts dissolved in water became measurably enriched at the cold end of an imposed temperature gradient. There have also been studies involving silicate liquids (see, for example, Lesher & Walker, 1986), in which Soret diffusion caused some components (e.g., CaO, MgO, FeO) to become enriched in the colder end of a temperature gradient, while other components (e.g., SiO₂ and alkali oxides) became enriched in the hot end. The earliest evidence of thermal isotope fractionation in a silicate liquid appears to be the study by Kyser et al. (1998), who reported oxygen isotope fractionation in some of the diffusion couples from the Lesher and Walker (1986) experiments.

      1.4.1. The Soret Coefficient

      As mentioned in Section 1.2, the flux equation for a component i in a system that is inhomogeneous in both concentration and temperature can be represented by a pseudo‐binary equation

      (1.8)

      where is the effective binary diffusion coefficient of i in a mixture of components i and j, ρ is the density of the mixture, X_i and X_j are the mass fractions of i and j, and σ _i is the Soret coefficient. In a steady state J_i = 0 and the Soret coefficient becomes . Lesher and Walker (1986) determined Soret coefficients for the major components of silicate liquids using an approximate version of σ _i determined as , where is the average mass fraction of i in the starting composition of their experiments.

      1.4.2. Soret Isotope Fractionation in Silicate Liquids

      The importance of laboratory experiments documenting kinetic isotope fractionation by temperature differences in silicate liquids is not so much because of potential applications to geologic problems (see reference to Bowen later in this section), but rather that certain features of the isotopic fractionation of samples recovered from piston cylinder experiments appear to have been significantly affected by thermal effects. A possible example of this was already noted in connection with the ⁴⁴Ca/⁴⁰Ca fractionation of about 3‰ in the basaltic part of the RB‐2 diffusion couple shown in Fig. 1.4. The suggestion that this “unexpected” isotopic fractionation might be the result of thermal isotope fractionation prompted the quantitative question of whether a few tens of degrees of temperature difference, which Watson et al. (2002) had shown was common for samples run in a piston cylinder apparatus, can explain isotopic fractionations of several per mil. This question was addressed in a series of experiments by Richter et al. (2008; 2009b; 2014a) that quantified the isotope fractionation of all the major elements, plus lithium and potassium, by a sustained temperature difference across a basalt melt.

The thermal isotope fractionation experiments by Richter et al. (2008; 2009b; 2014a) were run in piston cylinder assemblies like the one shown schematically in Fig. 1.5, except that the sample was initially a homogeneous basalt melt that was intentionally offset from the hot spot of the piston cylinder assembly (as shown schematically in Fig. 1.7) in order for there be a temperature difference of about 150°C across the basalt. Fig. 1.8 shows the results of two such experiments from Richter et al. (2008) in terms of the steady‐state distribution of the MgO and SiO₂, and the isotopic fractionation of magnesium, as a function of the local temperature. Other experiments by Richter et al. (2009b; 2014a) showed that CaO and FeO, like MgO, migrate to the cold end, Al₂O₃ remains relatively unchanged, while SiO₂, K₂O, and Na₂O become enriched at the hot end. The Soret coefficients derived from the three Richter et al. experiments are not significantly different from what had been previously reported by Lesher and Walker (1986). However, the main objective of the Richter et al. studies was not the Soret coefficients per se but rather to determine the thermal isotope fractionation of elements in a basalt melt.

Figure 1.7 The black squares in this figure show the temperature derived from the spinel thickness at places above and below the molten basalt (shown schematically by the grey rectangle) where MgO and Al₂O₃ were in contact in the piston cylinder assembly used by Richter et al. (2008) for Soret experiment SRT4. The temperature profile shown by the thin black line was fit to the spinel‐thickness temperature data points and extrapolated into the sample based on temperature measurements that Watson et al. (2002) had previously made in a sample run in a similar piston assembly.

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