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.

中文翻译：

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天然金刚烷，斯倍沙汀，石榴石石榴石的状态方程：对石榴石中弹性弹性气压计的影响

天然金刚烷胺₇₄ spessartine ₁₃ pyrope ₁₀总体₃的状态方程（EoS）在室温等温压缩下，利用单晶同步加速器X射线衍射法获得了在地壳变质岩石中发现的典型成分的石榴石。将三阶Birch-Murnaghan EoS拟合到PV数据，并将结果与​​已发布的铁，锰，镁和钙石榴石组成端基的EoS进行比较。该比较表明，理想的固溶体混合可以为石榴石的这种中间成分重现EoS。此外，这种新的EoS还用于计算来自同一颗岩石的石榴石样品的地质气压，该岩石是从爱达荷州南部的阿尔比恩山脉采集的。石榴石中的石英弹性地压法用于使用石榴石混合的替代方法以及静水和Grunëisen张量方法来计算石英夹杂物的截留压力。使用纯底端金刚烷胺的EoS，端基EoS的加权平均值和本研究中提出的EoS进行计算时，QuiG大气压力在不确定性内重叠。相对于静水压法，Grunëisen张量产生明显更高的压力，但不确定性很大。