Thermodynamics of multicomponent pyroxenes: II. Phase relations in the quadrilateral

The model for the thermodynamic properties of multicomponent pyroxenes (Part I) is calibrated for ortho- and clinopyroxenes in the quadrilateral subsystem defined by the end-member components Mg₂Si₂O₆, CaMgSi₂O₆, CaFeSi₂O₆, and Fe₂Si₂O₆. This calibration accounts for: (1) Fe-Mg partitioning relations between orthopyroxenes and augites, and between pigeonites and augites, (2) miscibility gap features along the constituent binary joins CaMgSi₂O₆-Mg₂Si₂O₆ and CaFeSi₂O₆-Fe₂Si₂O₆, (3) calorimetric data for CaMgSi₂O₆-Mg₂Si₂O₆ pyroxenes, and (4) the P-T-X systematics of both the reaction pigeonite=orthopyroxene+augite, and miscibility gap featurs, over the temperature and pressure ranges 800–1500°C and 0–30 kbar. The calibration is achieved with the simplifying assumption that all regular-solution-type parameters are constants independent of temperature. It is predicated on the assumptions that: (1) the Ca-Mg substitution is more nonideal in Pbca pyroxenes than in C2/c pyroxenes, and (2) entropies of about 3 and 6.5 J/K-mol are associated with the change of Ca from 6- to 8-fold coordination in the M2 site in magnesian and iron C2/c pyroxenes, respectively. The model predicts that Fe²⁺-Mg²⁺ M1-M2 site preferences in C2/c pyroxenes are highly dependent on Ca and Mg contents, with Fe²⁺ more strongly preferring M2 sites both in Ca-rich C2/c pyroxenes with a given Fe/(Fe+Mg) ratio, and in magnesian C2/c pyroxenes with intermediate Ca/(Ca+Fe+Mg) ratios.The proposed model is internally consistent with our previous analyses of the solution properties of spinels, rhombohedral oxides, and Fe-Mg olivines and orthpyroxenes. Results of our calibration extend an existing database to include estimates for the thermodynamic properties of the C2/c and Pbca pyroxene end-members clinoenstatite, clinoferrosilite, hedenbergite, orthodiopside, and orthohedenbergite. Phase relations within the quadrilateral and its constitutent subsystems are calculated for temperatures and pressures over the range 800–1700°C and 0–50 kbar and compare favorably with experimental constraints.