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

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
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isbn: 9781119594963
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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).

      1.4.1. 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)upper J Subscript i Baseline equals minus rho upper D Subscript i Superscript upper E Baseline left-parenthesis StartFraction partial-differential upper X Subscript i Baseline Over partial-differential x EndFraction plus sigma Subscript i Baseline upper X Subscript i Baseline upper X Subscript j Baseline StartFraction partial-differential upper T Over partial-differential x EndFraction right-parenthesis

      where upper D Subscript i Superscript upper E is the effective binary diffusion coefficient of i in a mixture of components i and j, ρ is the density of the mixture, Xi and Xj are the mass fractions of i and j, and σ i is the Soret coefficient. In a steady state Ji = 0 and the Soret coefficient becomes sigma Subscript i Baseline equals StartFraction negative 1 Over upper X Subscript i Baseline upper X Subscript j Baseline EndFraction StartFraction partial-differential upper X Subscript i Baseline Over partial-differential upper T EndFraction . Lesher and Walker (1986) determined Soret coefficients for the major components of silicate liquids using an approximate version of σ i determined as sigma Subscript i Baseline equals StartFraction negative 1 Over upper X Subscript i Baseline overbar left-parenthesis 1 minus upper X Subscript i Baseline overbar right-parenthesis EndFraction StartFraction partial-differential upper X Subscript i Baseline Over partial-differential upper T EndFraction, where upper X Subscript i Baseline overbar 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.

Schematic illustration of the black squares that 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. Schematic illustration 


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