Diamond–garnet geobarometry: The role of garnet compressibility and expansivity

Abstract

We report P–V and T–V Equations of State (EoS) for synthetic single crystal pyrope (Py, Mg3Al2Si3O12) and the P–V EoS for synthetic single crystals of almandine (Alm, Fe3Al2Si3O12) as well as an intermediate composition (Py60Alm40) as measured by in-situ high-pressure and high-temperature X-ray diffraction experiments. The unit-cell volumes of the three samples were measured at room temperature and different pressures and up to about 8GPa in a diamond-anvil cell. The high-temperature experiment was carried out using a micro-furnace. The pressure-volume data were fitted to a third order Birch–Murnaghan EoS giving the following coefficients: V0=1506.15(16)Å3, KT0=163.7(1.7)GPa and K′=6.4(4) for pyrope, V0=1533.52(10)Å3, KT0=172.6(1.5)GPa and K′=5.8(5) for almandine and V0=1516.32(13)Å3, KT0=167.2(1.7)GPa and K′=5.6(5) for the intermediate Py60Alm40 composition. The unit-cell volume along the pyrope–almandine join changes linearly within the error of measurement indicating ideality in the volume of mixing behaviour for the solid solution. The first pressure derivative, K′, for all three garnets is similar within experimental uncertainty with an average value of K′=6.0(4). The thermal expansion parameters for end-member pyrope, as described using to the Kroll-type EoS, with the Einstein temperature, θE, fixed to 320K, are α(303K, 1bar)=2.543(5)∗10−5K−1 and V0=1504.64(4)Å3. The determined thermoelastic parameters were combined in a thermal-pressure type EoS (thermal-P type EoS) to calculate the entrapment pressures, Pe, for natural garnet inclusions in diamonds at mantle temperatures. A calculated pressure of 5.8GPa at T=1500K using our newly determined thermoelastic parameters appears to be more consistent with diamond-forming conditions compared to the higher pressures that range up to 6.8GPa at T=1500K, which are obtained using thermoelastic data in the literature.