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The molar volume of FeO–MgO–Fe2O3–Cr2O3–Al2O3–TiO2 spinels

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Abstract

We define and calibrate a new model of molar volume as a function of pressure, temperature, ordering state, and composition for spinels in the supersystem (Mg, Fe2+)(Al, Cr, Fe3+)2O4 − (Mg, Fe2+)2TiO4. We use 832 X-ray and neutron diffraction measurements performed on spinels at ambient and in situ high-P, T conditions to calibrate end-member equations of state and an excess volume model for this system. The effect on molar volume of cation ordering over the octahedral and tetrahedral sites is captured with linear dependence on Mg2+, Al3+, and Fe3+ site occupancy terms. We allow standard-state volumes and coefficients of thermal expansion of the end members to vary within their uncertainties during extraction of the mixing properties, in order to achieve the best fit. Published equations of state of the various spinel end members are analyzed to obtain optimal values of the bulk modulus and its pressure derivative, for each explicit end member. For any spinel composition in the supersystem, the model molar volume is obtained by adding excess volume and cation order-dependent terms to a linear combination of the five end-member volumes, estimated at pressure and temperature using the high-T Vinet equation of state. The preferred model has a total of 9 excess volume and order-dependent parameters and fits nearly all experiments to within 0.02 J/bar/mol, or better than 0.5 % in volume. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure.

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Acknowledgments

We wish to thank Peter Luffi for identifying the garnet solid solution error in the original MELTS code, Ashley Nagle for pointing out the anomalously low spinel–garnet transition pressures obtained when the corrected garnet model is used, and Aaron Wolf for helpful discussions regarding statistical analysis. Comments by Associate Editor Jon Blundy are greatly appreciated, as are the reviews of two anonymous reviewers. This work was supported by the National Science Foundation and the American Recovery and Reinvestment Act through award 0838244.

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Authors and Affiliations

  1. Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, 91125, USA

    Emily A. Hamecher, Paula M. Antoshechkina & Paul D. Asimow

  2. OFM Research, 7336 24th Ave NE, Seattle, WA, 98115, USA

    Mark S. Ghiorso

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  1. Emily A. Hamecher
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  2. Paula M. Antoshechkina
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  3. Mark S. Ghiorso
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  4. Paul D. Asimow
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Correspondence to Emily A. Hamecher.

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Communicated by J. Blundy.

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Hamecher, E.A., Antoshechkina, P.M., Ghiorso, M.S. et al. The molar volume of FeO–MgO–Fe2O3–Cr2O3–Al2O3–TiO2 spinels. Contrib Mineral Petrol 165, 25–43 (2013). https://doi.org/10.1007/s00410-012-0790-0

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  • DOI: https://doi.org/10.1007/s00410-012-0790-0

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