The equation of state (EoS) of a natural almandine74spessartine13pyrope10grossular3 garnet of a typical composition found in metamorphic rocks in Earth’s crust was obtained using single crystal synchrotron X-ray diffraction under isothermal room temperature compression. A third-order Birch-Murnaghan EoS was fitted to P-V data and the results are compared with published EoS for iron, manganese, magnesium, and calcium garnet compositional end-members. This comparison reveals that ideal solid solution mixing can reproduce the EoS for this intermediate composition of garnet. Additionally, this new EoS was used to calculate geobarometry on a garnet sample from the same rock, which was collected from the Albion Mountains of southern Idaho. Quartz-in-garnet elastic geobarometry was used to calculate pressures of quartz inclusion entrapment using alternative methods of garnet mixing and both the hydrostatic and Grunëisen tensor approaches. QuiG barometry pressures overlap within uncertainty when calculated using EoS for pure end-member almandine, the weighted averages of end-member EoS, and the EoS presented in this study. Grunëisen tensors produce apparent higher pressures relative to the hydrostatic method, but with large uncertainties.

Mulligan, Suzanne R.; Stavrou, Elissaios; Chariton, Stella; Tschauner, Oliver; Salamat, Ashkan; Wells, Michael L.; Smith, Alexander G.; Hoisch, Thomas D.; Prakapenka, Vitali. 2021. “Equation of State for Natural Almandine, Spessartine, Pyrope Garnet: Implications for Quartz-In-Garnet Elastic Geobarometry” Minerals 11, no. 5: 458. abstract

Pressure-volume data for the Alm74Sps13Prp10Grs3 garnet analyzed in this study with SXD plotted as black squares. Experimental errors are smaller than the data symbols. The black line is the third-order Birch-Murnaghan EoS fitted to the experimental data. EoS for end-member almandine [14], end-member pyrope [10], and end-member spessartine [13] are plotted for comparison. The green line is an EoS created using a weighted average of the V0, B0, and B0 of the end-members.