Internally consistent recalibrations of mineral equilibria for geothermobarometry involving garnet-orthopyroxene-plagioclase-quartz assemblages and their application to the South Indian granulites

Three reactions are calibrated as geothermobarometers for garnet-orthopyroxene-plagioclase-quartz assemblages, namely: ½ ferrosilite + 1/3 pyrope ± ½ enstatite + 1/3 almandine (A): ferrosilite + anorthite ± 2/3 almandine + 1/3 grossularite + quartz (B); and enstatite + anorthite ± 2/3 pyrope + 1/3 grossularite + quartz (C). The internally consistent geothermobarometers based on reactions (A), (B) and (C) are calibrated from experimental data only. The thermodynamic parameters of reaction (A) are derived from published experimental data in the FMAS system (n= 104) in the range 700-1400°C and 5-50 kbar, while those for reaction (B) are derived by summation of the existing reversed experimental data of the mineral equilibria: ferrosilite ± fayalite + quartz (D) and anorthite + fayalite ± 2/3 almandine + 1/3 grossularite (E). The retrieved thermodynamic parameters for reactions (A), (B) and (C) are, respectively: (ΔH0, cal) -3367 ± 209, -2749 ± 350 and +3985 ± 545; (ΔS0, cal K-1) -1.634 ± 0.163, -8.644 ± 0.298 and -5.376 ± 0.391; and (ΔV01,298, cal bar-1) -0.024, -0.60946 and -0.5614. On a one-cation basis, the derived Margules parameters of the ternary Ca-Fe-Mg in garnet are: WFe-Mg= -1256 + 1.0 (~0.23) T(K), WMg-Fe= 2880 -1.7 (~0.13) T(K), WCa-Mg= 4047 (~77) -1.5 T(K), WMg-Ca= 1000 (~77) -1.5 T(K), WCa-Fe= -723 + 0.332 (~0.02) T(K), WFe-Ca= 1090, (cal) and the ternary constant C123= -4498 + 1.516 (~0.265) T(K) cal (subregular solution model of non-ideal mixing); and Fe-Mg-Al in orthopyroxene: WFe-Mg= 948 (~200) -0.34 (~0.10) T(K), WFe-Al= -1950 (~500) and WMg-Al= 0 (cal) (regular solution model of non-ideal mixing). The anorthite activity in plagioclase is calculated by the 'Al-avoidance'model of subregular Ca-Na mixing commonly used for geobarometry based on reactions (B) and (C). When the geothermobarometers are applied to garnet-orthopyroxene-plagioclase-quartz assemblages (n= 45) of wide compositional range from the Precambrian South Indian granulites, temperature ranges of 690-860°C (X= 760 ± 45°C) and pressure ranges of 5-10 kbar were obtained. The P-T values were estimated simultaneously and there is no difference in the pressure calculated from PMg (reaction C) and PFe (reaction B). In the existing calibrations this difference is 1 kbar or more. Furthermore, there is no compositional dependence of the ln K of the experimental data in the FMAS (n= 104) and the CFMAS (n= 78) systems at different temperatures and the estimated temperatures of the South Indian granulites