Equation of State for Natural Almandine, Spessartine, Pyrope Garnet: Implications for Quartz-In-Garnet Elastic Geobarometry

Elissaios Stavrou,Thomas D. Hoisch,Alexander G. Smith,Oliver Tschauner,Suzanne R. Mulligan,Michael L. Wells,Ashkan Salamat,Stella Chariton,Vitali Prakapenka

doi:10.3390/min11050458

Abstract

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 Grüneisen 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. Grüneisen tensors produce apparent higher pressures relative to the hydrostatic method, but with large uncertainties.

Highlights

Garnets are a family of mineral structures with the formula X3Y2[ZO4]3
An equation of state (EoS) fitted to experimental data for this natural garnet of composition Alm74Sps13Prp10Grs3 follows ideal solid solution mixing
The determined EoS and an EoS produced using an ideal solid solution mix of V0, B0, and B0 of the garnet compositional end-members are within uncertainty (Figure 1)

Summary

Introduction

Garnets are a family of mineral structures with the formula X3Y2[ZO4]3. Most silicate garnets have cubic symmetry forming dodecahedral crystals in the space group Ia3d with an 8-coordinated X-site, 6-coordinated Y-site, and 4-coordinated Z-site [1]. Substitution of different cations into the X-site defines common compositional end-members of the garnet group in metamorphic rocks [2]. This study is restricted to crustal aluminosilicate garnets (Z = Si; Y = Al), that are common metamorphic and igneous minerals in the Earth’s crust. These garnets are dominated by the compositional end-members pyrope (Mg3Al2[SiO4]3), almandine (Fe3Al2[SiO4]3), spessartine (Mn3Al2[SiO4]3), and grossular (Ca3Al2[SiO4]3). They form in a variety of rock types and participate in key metamorphic reactions allowing them to be used to model geologic pressures and temperatures, important for understanding mountain building processes, tectonic histories, and metamorphic reactions. Discrepancies between garnet solid solution mixing volumes derived from calorimetry are often inconsistent with results from X-ray diffraction depending on the EoS model used [5,6,7,8,9]

Methods

Results

Discussion

Conclusion