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

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isbn: 9781119594963
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(see Supplemental Information 2.A). Regardless, for a given transient profile of SiO2, there exists an associated hypothetical “quasi‐equilibrium” profile for the equilibrium concentration of the component of interest, Ce, that scales with 1/ γ as well as the concentration of SiO2. Assuming that diffusion of SiO2 can be characterized by a concentration‐independent EBD, Db, and that diffusion of SiO2 does not reach either end of the diffusion couple, the “equilibrium” concentration profile for Ce is an error function:

      which leads to the one‐dimensional diffusion equation (Eq. 9a in Zhang, 1993):

Schematic illustration of the Zhang model and its parameters are based on the concept of elemental partitioning in an SiO2 gradient.

       Model Validation and Behavior

      The Zhang (1993) model deviates significantly from the EBD model when the component of interest diffuses significantly faster than SiO2. In this situation, which is common in silicate liquids, the component of interest will not reach homogeneity quickly, but rather, will partition along the compositional continuum between the high‐ and low‐silica liquids and reach compositional homogeneity only as fast as SiO2 diffuses.

Schematic illustration of model behavior showing concentration, activity, and transient equilibrium concentration profiles for C negative = 6 wt%, C plus = 8 wt%, D over Db = 8, and variable Cf.

       Model Applied to the Rhyolite‐Phonolite Couples

      The rhyolite‐phonolite diffusion couple spans a broad range of melt compositions. Although the diffusion coefficients are expected to be sensitive to melt composition across this range, we assume script upper D and Db are constant. We also treat the diffusion couple as infinite with respect to SiO2 even though we see some uphill diffusion of SiO2 at the ends of the couple in the 2.5 hour run. This, however, may just be due to mass balance and dilution effects caused by the faster diffusing components. For the faster diffusing K2O and CaO components, the diffusion couple is not treated as infinite; i.e., C/∂x = 0 at the boundaries.