The thermodynamics of iron and magnesium partitioning between olivine and liquid: criteria for assessing and predicting equilibrium in natural and ... View Full Text


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Article Info

DATE

2005-03

AUTHORS

M. J. Toplis

ABSTRACT

The equations for the chemical potentials of fayalite and forsterite components in olivine and liquid may be used to derive a thermodynamic expression for the exchange coefficient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K^{{\;\;\;{\text{Mg - Fe}}}}_{{D{\text{Ol - Liq}}}} $$\end{document} (defined as the molar Mg/Fe2+ of the liquid divided by Mg/Fe of coexisting olivine). This expression, well known in the literature, shows that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K^{{\;\;\;{\text{Mg - Fe}}}}_{{D{\text{Ol - Liq}}}} $$\end{document} is a function of temperature, pressure, and compositions of the olivine and liquid. Quantitative application of this equation requires knowledge of the free energies and volumes of liquid and crystalline fayalite and forsterite, and a description of the non-ideality of Fe–Mg mixing in olivine. Independent measurements of these parameters reported in the literature have been used to constrain the influence of temperature, pressure and olivine composition on iron–magnesium partitioning. The other requirement for calculation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K^{{\;\;\;{\text{Mg - Fe}}}}_{{D{\text{Ol - Liq}}}} $$\end{document} is knowledge of the ratio of activity coefficients of Fe2+ and Mg in the liquid phase (γFe2+/γMg), but no independent predictive model for this exists. To assess and predict the variation of γFe2+/γMg as a function of liquid composition, a database of almost 400 olivine–liquid pairs at 1 bar and 200 experiments at pressures to the upper stability limit of olivine has been considered. Measured values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K^{{\;\;\;{\text{Mg - Fe}}}}_{{D{\text{Ol - Liq}}}} $$\end{document} in this data base vary from 0.17 to 0.45, and the data were chosen to cover wide ranges of temperature and olivine composition, in addition to liquid composition. Within the framework of the thermodynamic equation, γFe2+/γMg is found to be a function of silica content and alkali content of the liquid. Water is also inferred to have a direct influence at high pressure. A predictive model for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K_{D} {\kern 1pt} ^{{{\text{Mg}} - {\text{Fe}}}}_{{{\text{Ol}} - {\text{Liq}}}} $$\end{document} is proposed which recovers all input data at the 1σ level of uncertainty. It is used to assess equilibrium in published experimental studies of mantle melting and to illustrate the influence of individual parameters such as temperature and pressure. Application of the model to the field of melt inclusions is also discussed. More... »

PAGES

22-39

References to SciGraph publications

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    http://scigraph.springernature.com/pub.10.1007/s00410-004-0629-4

    DOI

    http://dx.doi.org/10.1007/s00410-004-0629-4

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    https://app.dimensions.ai/details/publication/pub.1003413829


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