Isotopic Constraints on Earth System Processes. Группа авторов

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Isotopic Constraints on Earth System Processes - Группа авторов

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target="_blank" rel="nofollow" href="#fb3_img_img_7728f71b-0d92-5b6e-915a-3e605093c9e2.png" alt="StartFraction upper J Subscript i Baseline Over upper J Subscript j Baseline EndFraction equals left-parenthesis StartFraction Ï’ Subscript i v Baseline Over Ï’ Subscript j v Baseline EndFraction StartRoot StartFraction upper M Subscript j Baseline Over upper M Subscript i Baseline EndFraction EndRoot right-parenthesis StartFraction upper N Subscript i Baseline Over upper N Subscript j Baseline EndFraction"/>

      The quantity left-parenthesis StartFraction Ï’ Subscript i v Baseline Over Ï’ Subscript j v Baseline EndFraction StartRoot StartFraction upper M Subscript j Baseline Over upper M Subscript i Baseline EndFraction EndRoot right-parenthesis, which we will call α ij, is the kinetic isotope fractionation of the evaporation flux relative to the isotopic ratio of the evaporating material. Prior to having results from vacuum evaporation experiments it was often assumed that StartFraction upper J Subscript i Baseline Over upper J Subscript j Baseline EndFraction equals StartRoot StartFraction upper M Subscript j Baseline Over upper M Subscript i Baseline EndFraction EndRoot, (i.e., the inverse square root of the mass “law”) but as we will see, this is not correct.

      1.6.2. Rayleigh Fractionation

      (1.12)StartFraction d upper N Subscript i Baseline Over d upper N Subscript j Baseline EndFraction equals StartFraction upper J Subscript i Baseline Over upper J Subscript j Baseline EndFraction equals left-parenthesis StartFraction Ï’ Subscript i v Baseline Over Ï’ Subscript j v Baseline EndFraction StartRoot StartFraction upper M Subscript j Baseline Over upper M Subscript i Baseline EndFraction EndRoot right-parenthesis StartFraction upper N Subscript i Baseline Over upper N Subscript j Baseline EndFraction equals alpha Subscript i j Baseline StartFraction upper N Subscript i Baseline Over upper N Subscript j Baseline EndFraction

      which when rearranged becomes

      (1.14)ln left-parenthesis StartFraction upper N Subscript i Baseline Over upper N Subscript i comma 0 Baseline EndFraction right-parenthesis equals alpha Subscript i j Baseline ln left-parenthesis StartFraction upper N Subscript j Baseline Over upper N Subscript j comma 0 Baseline EndFraction right-parenthesis

      Applying the exponential function to both sides of this equation it becomes left-parenthesis StartFraction upper N Subscript i Baseline Over upper N Subscript i comma 0 Baseline EndFraction right-parenthesis equals left-parenthesis StartFraction upper N Subscript j Baseline Over upper N Subscript j comma 0 Baseline EndFraction right-parenthesis Superscript alpha Super Subscript i j, which dividing by StartFraction upper N Subscript j Baseline Over upper N Subscript j comma 0 Baseline EndFraction and rearranging gives left-parenthesis StartFraction upper N Subscript i Baseline Over upper N Subscript j Baseline EndFraction right-parenthesis equals left-parenthesis StartFraction upper N Subscript i comma 0 Baseline Over upper N Subscript j comma 0 Baseline EndFraction right-parenthesis Superscript left-parenthesis alpha Super Subscript i j minus 1 Superscript right-parenthesis . Writing the isotope ratios as StartFraction upper N Subscript i Baseline Over upper N Subscript j Baseline EndFraction as Ri, j and StartFraction upper N Subscript i comma upper O Baseline Over upper N Subscript j comma 0 Baseline EndFraction as Ro one arrives at the Rayleigh fractionation equation for the evaporation residue

      1.6.3. High‐Temperature Vacuum Evaporation Experiments

      The experiments involving the evaporation of CAI‐like liquids described in this section were run at the University of Chicago in a high‐temperature vacuum furnace (pressure < 10–6 Torr) that was designed and constructed by Akihiko Hashimoto (see Hashimoto, 1990, for a description of the furnace). The experimental methods for evaporating molten samples in this furnace are described in the first paper documenting high‐temperature isotopic fractionations of evaporation residues from a silicate liquid (molten fayalite) by Davis et al. (1990). For CAI evaporation experiments powders of CAI‐like CMAS composition (CaO+MgO+SiO2+Al2O3) were loaded onto small iridium wire loops (1–6 mm in diameter) that were then placed for different lengths of time in the hot spot of the vacuum furnace at temperatures between 1600°C and 1900°C and pressure less than 10–6 Torr. The objective of the evaporation experiments was to determine the evaporation coefficients γ Mg and γ Si for calculating

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