The Molar Volume of FeO-MgO-Fe2O3-Cr2O3-Al2O3-TiO2 Spinels

A new model of molar volume has been calibrated in the spinel supersystem (Mg,Fe²⁺)(Al,Cr,Fe³⁺)₂O₄ - (Mg,Fe²⁺)₂TiO₄. A total of 832 X-ray and neutron diffraction experiments performed on spinels at ambient and in situ high-P, T conditions (from the American Mineralogist Crystal Structure Database (Downs and Hall-Wallace, 2003) and other sources) were used 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 allowed 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 states of the various spinel end members were 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 model has a total of 31 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 (Ghiorso and Sack, 1995; Ghiorso et al., 2002) spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure. Our primary motivation in this work is the development of a comprehensive spinel molar volume model for use in calibration of activity-composition models of garnet and pyroxene solid solutions. The thermodynamic models, along with a new silicate liquid equation of state, will be incorporated into the next generation MELTS model, xMELTS. The new solid solution models will include some minor components, including Ti⁴⁺ and Cr³⁺. Because most constraints on the activity of garnet and pyroxene at high-P are derived from experiments with coexisting spinel, we must be confident in the ability of our spinel model to realistically reproduce thermodynamic behavior over all applicable compositions. Additionally, producing a spinel molar volume model calibrated with recent in situ high-P, T diffraction data is crucial to our ability to accurately model the spinel-garnet transition in Earth's upper mantle. For example, we recently calibrated Cr-Al exchange equilibria for garnet and spinel. When this new calibration is used with the current MELTS model, a region of garnet-spinel coexistence in lherzolites is predicted with width in pressure comparable to experimental constraints. The transition occurs, however, at the unexpectedly low pressure of ~1.7 GPa. The improved model of spinel molar volume presented here, along with a new garnet molar volume model in the system FeO-MgO-CaO-Fe₂O₃-Cr₂O₃-Al₂O₃-TiO₂-Na₂O-SiO₂ currently being calibrated, will enable coupled recalibration of the garnet and pyroxene models to match both the absolute pressure and width of this key transition in mantle lithology.