Compatibility of Geobarometers in the System CaO-FeO-Al₂O₃-SiO₂-TiO₂(CFAST): Implications for Garnet Mixing Models

In the system CaO-FeO-Al₂O₃-SiO₂-TiO₂ several barometers have been experimentally calibrated. hese include: Alm + 3 Ru = 3 Jim + Sil + Qtz (GRAIL), 2 Alm + Gr + 6 Ru = 6 Ilm + 3 An + 3 Qtz (GRIPS), 2 Alm + Gr = 3 Fa + 3 An (FAG), 3 An = Gr + 2 Ky + Qtz (GASP), 2 Fs = Fa + Qtz (FFQ), and Gr + Qtz = An + 2 Wo (WAGS). Because GRIPS, GRAIL, and GASP form a linearly dependent set, they provide a stringent test for the accuracy of a/X models for grossular/almandine solid-solutions. The Ganguly and Saxena garnet solution model yields a calculated position for GASP two kb above a best-fit to the available experimental reversals. Using these reactions to constrain mixing parameters for grossular/ almandine garnets (on a Ca + Fe⁺² = 1 cation basis) yields WHCaFe) = 6240 J, WH(FcCa) = 23800 J, and WS(CaFe) = WS(FeCa) = 11.4 J/K (Model 1), or WH(CaFe) = 628 J, WH(FeCa) = 17080 J (Model 2) using the measured pyrope/grossular value for WS(6.216 J/K). GRIPS can be further checked by adding Fa + 2 Ru = 2 Ilm + SiO₂ (FRIS) to FAG. Available thermodynamic data do not yield GRIPS in good agreement with available experiments, and a revised value for the Gibbs energy of fayalite has been calculated. These calculations yield the following values of ΔGᶜⁱʳᶜ₂₉₈ (elem) for almandine, fayalite, ferrosilite, grossular, and anorthite: -4940.8, -1377.1, -1116.2, -6282.3, and -4010.9 kJ/mol respectively.