Effect of Thermoelastic Properties of the Pyrope-Almandine Solid Solutions on the Entrapment Pressure of Garnet-Related Elastic Geobarometer

Abstract

The pyrope (Prp)–almandine (Alm) solid solutions are the most fundamental garnet components on the Earth, and both the quartz inclusions in garnet (QuiG) barometry and the garnet inclusions in diamond barometry need to be constrained by the thermoelastic parameters of Prp-Alm solid solution garnets. Here, we report the thermoelastic properties of a series of synthetic Prp-Alm solid solutions based on the high-pressure and high-temperature (HP–HT) in situ synchrotron single-crystal x-ray diffraction (SCXRD) experiments up to ∼20 GPa and 700 K, using diamond anvil cell (DAC). Fitting the SCXRD data by the Birch-Murnaghan equation of state (BM-EoS) and the thermal-pressure EoS, we obtain the thermoelastic parameters of Prp-Alm solid solution garnets, including bulk modulus (K0), its pressure derivative (K′0), and the thermal expansion coefficient (α0). The K0 along the Prp-Alm solid solution changes linearly with Prp content within their uncertainties and can be expressed by K0 (GPa) = 181.0(8) – 0.11(1) Xprp (R2 = 0.91, Xprp is the Prp mole fraction and K′0 fixed at 4). Our result indicates that the compressibility of the Prp-Alm solid solution increases with the increasing Prp content. However, the thermal expansion coefficient of Prp-Alm solid solution at ambient pressure shows a non-linear trend with Prp content and can be expressed by α0 (10−5 K−1) = 2.7 (1) + 3.0 (5) XPrp− 3.2 (4) X2Prp (R2 = 0.985). It shows that the Prp-Alm solid solution with intermediate composition has a larger thermal expansion coefficient than those close to the endmembers at ambient conditions. Furthermore, we also evaluated the influence of thermoelastic properties of the Prp-Alm solid solution on the entrapment pressure (Pe) estimation for two types of elastic geobarometers. Our results indicate that the garnet component may significantly influence entrapment pressure, and among the thermoelastic parameters of garnet, the thermal expansion coefficient has the main effect on the estimation of Pe.