From the simplest chemical system to the natural one: garnet peridotite barometry

The available experimental data on garnet-bearing-assemblages for synthetic chemical systems (MAS, FMAS, CMAS) have been used to calibrate consistent models for the Al-solubility in orthopyroxene coexisting with garnet, on the basis of equilibrium reaction Py(opx) ? Py(gt). The alternative reaction En(opx)+MgTs(opx) ? Py(gt) is discarded as it yields larger a-posteriori uncertainties. To provide a reliable equation, directly applicable to natural garnet lherzolites, each successive synthetic-system calibration is tested against Mori and Green's (1978) natural-system reequilibration data. For the MAS system, an ideal solution model with constant ΔH°, ΔV° and ΔS° based on 12-oxygen structural formulae for aluminous pyroxenes yields the best fit (GPa, K), $${text{25,134 + 9,941 }}P - 23.177{text{ }}T{text{ + }}RT{text{ ln (}}X_{{text{Al}}}^{TB'} {text{) = 0}}$$ . The MAS synthetic-system calibration can be directly applied to the FMAS system by adding an empirical correction term (20,835 [X _Fe ^gt ]²) independent of either pressure and temperature. However, this correction term is not important because of the limited Fe content of mantle peridotites. When calcium is added to the MAS system, the equilibrium constant is calculated as: $$K_{{text{CMAS}}} = {{[(1 - X_{{text{Ca}}}^{M2} )^2 (X_{{text{Al}}}^{TB'} )]} mathord{left/ {vphantom {{[(1 - X_{{text{Ca}}}^{M2} )^2 (X_{{text{Al}}}^{TB'} )]} {[(1 - X_{{text{Ca}}}^X )^3 (X_{{text{Al}}}^Y )^2 ]}}} right. kern-nulldelimiterspace} {[(1 - X_{{text{Ca}}}^X )^3 (X_{{text{Al}}}^Y )^2 ]}}$$ where M2 and TB′ are pyroxene sites and X and Y are garnet sites. Up to 5 GPa, X _Ca ^X ～ and the CMAS experimental data agree well with the MAS model, but for Yamada and Takahashi's (1983) higher pressure experiments (up to 10 GPa), this no longer holds. Indeed, the garnet solid solution does not behave ideally and an asymmetric regular solution model is needed for application to the deepest natural samples available (>7GPa). Calibration based on new high pressure data yields, $$begin{gathered} Delta G_{{text{CMAS}}}^{XS} = (X_{{text{Ca}}}^X )(1 - X_{{text{Ca}}}^X )(0.147 - X_{{text{Ca}}}^X ) hfill {text{ }} cdot {text{(6,440,535 - 1,490,654 }}P{text{)}} hfill end{gathered}$$ . According to tests of the inferred solution model, the CFMAS system is a good analogue of natural systems in the pressure, temperature and composition ranges covered by the natural-system reequilibration data (up to 1,500° C and 4 GPa). Simultaneous application of this thermobarometer and of the two-pyroxene mutual solubility thermometer (Bertrand and Mercier 1985) to the phases of the garnet-peridotite xenoliths from Thaba Putsoa, Lesotho, yields a refined paleogeotherm for southern Africa strongly contrasting with previous results. The “granular” nodules yield a thermal gradient of about 8 K/km characteristic of a lithospheric-type environment, whereas the “sheared” ones show a lower gradient of about 1 K/km. This is a typical geotherm expected for a steady thermal state with an inflexion point at the depth of about 160 km corresponding to the lithosphere/asthenosphere boundary.