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

We report P – V and T – V Equations of State (EoS) for synthetic single crystal pyrope (Py, Mg 3 Al 2 Si 3 O 12 ) and the P – V EoS for synthetic single crystals of almandine (Alm, Fe 3 Al 2 Si 3 O 12 ) as well as an intermediate composition (Py 60 Alm 40 ) 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 8 GPa 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: V 0 = 1506.15(16) Å 3 , K T 0 = 163.7(1.7) GPa and K ′ = 6.4(4) for pyrope, V 0 = 1533.52(10) Å 3 , K T 0 = 172.6(1.5) GPa and K ′ = 5.8(5) for almandine and V 0 = 1516.32(13) Å 3 , K T 0 = 167.2(1.7) GPa and K ′ = 5.6(5) for the intermediate Py 60 Alm 40 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, θ E , fixed to 320 K, are α (303 K, 1 bar) = 2.543(5) ∗ 10 − 5 K − 1 and V 0 = 1504.64(4) Å 3 . The determined thermoelastic parameters were combined in a thermal-pressure type EoS (thermal- P type EoS) to calculate the entrapment pressures, P e , for natural garnet inclusions in diamonds at mantle temperatures. A calculated pressure of 5.8 GPa at T = 1500 K using our newly determined thermoelastic parameters appears to be more consistent with diamond-forming conditions compared to the higher pressures that range up to 6.8 GPa at T = 1500 K, which are obtained using thermoelastic data in the literature. [ABSTRACT FROM AUTHOR]