The pressure-temperature-compositional (P-T-X) dependence of the solubility of Al2O3 in orthopyroxene coexisting with garnet has been experimentally determined in the P-T range 5–30 kilobars and 800–1200 °C in the system FeO—MgO—Al2O3—SiO2 (FMAS). These results have been extended into the CaO—FeO—MgO—Al2O3—SiO2 (CFMAS) system in a further set of experiments designed to determine the effect of the calcium content of garnet on the Al2O3 contents of coexisting orthopyroxene at near-constant Mg/(Mg + Fe). Starting materials were mainly glasses of differing Mg/(Mg + Fe) or Ca/(Ca + Mg + Fe) values, seeded with garnet and orthopyroxene of known composition, but mineral mixes were also used to demonstrate reversible equilibrium. Experiments were performed in a piston-cylinder apparatus using a talc/pyrex medium. Measured orthopyroxene and corrected garnet compositions were fitted by multiple and stepwise regression techniques to an equilibrium relation in the FMAS system, yielding best-fit, model-dependent parameters δGoy= −5436 + 2.45T cal mol−1, and WM1FeA1= −920 cal mol−1. The volume change of reaction, δVo, the entropy change, δSo970 and the enthalpy change δHo1,970, were calculated from the MAS system data of Perkins et al. (1981) and available heat capacity data for the phases. Data from CFMAS experiments were fitted to an expanded equilibrium relation to give an estimate of the term WgaCaMg = 1900 ± 400 cal/mole cation, using the other parametric values already obtained in FMAS. This geobarometer is applicable to both pelitic and metabasic granulites containing garnet orthopyroxene, and to garnet peridodite and garnet pyroxenite assemblages found as xenoliths in diatremes or in peridotite massifs. It is limited, however, by the necessity of an independent temperature estimate, by errors associated with analysis of low Al2O3 contents in orthopyroxenes in high-pressure or low-temperature parageneses, and by uncertainties in the composition of garnet in equilibrium with orthopyroxene. An analysis of errors associated with this formulation of the geobarometer suggests that it is subject to great uncertainty at low pressures and for Fe-rich compositions. The results of application of this geobarometer to natural assemblages are presented in a companion paper.
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Simon L. Harley (1984) studied this question.