Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures

A revised regular solution-type thermodynamic model for twelve-component silicate liquids in the system SiO₂-TiO₂-Al₂O₃-Fe₂O₃-Cr₂O₃-FeO-MgO-CaO-Na₂O-K₂O-P₂O₅-H₂O is calibrated. The model is referenced to previously published standard state thermodynamic properties and is derived from a set of internally consistent thermodynamic models for solid solutions of the igneous rock forming minerals, including: (Mg,Fe²⁺,Ca)-olivines, (Na,Mg,Fe²⁺,Ca)^M2 (Mg,Fe²⁺, Ti, Fe³⁺, Al)^M1 (Fe³⁺, Al,Si)₂ ^TETO₆-pyroxenes, (Na,Ca,K)-feldspars, (Mg,Fe²⁺) (Fe³⁺, Al, Cr)₂O₄-(Mg,Fe²⁺)₂ TiO₄ spinels and (Fe²⁺, Mg, Mn²⁺)TiO₃-Fe₂O₃ rhombohedral oxides. The calibration utilizes over 2,500 experimentally determined compositions of silicate liquids coexisting at known temperatures, pressures and oxygen fugacities with apatite ±feldspar ±leucite ±olivine ±pyroxene ±quartz ±rhombohedral oxides ±spinel ±whitlockite ±water. The model is applicable to natural magmatic compositions (both hydrous and anhydrous), ranging from potash ankaratrites to rhyolites, over the temperature (T) range 900°–1700°C and pressures (P) up to 4 GPa. The model is implemented as a software package (MELTS) which may be used to simulate igneous processes such as (1) equilibrium or fractional crystallization, (2) isothermal, isenthalpic or isochoric assimilation, and (3) degassing of volatiles. Phase equilibria are predicted using the MELTS package by specifying bulk composition of the system and either (1) T and P, (2) enthalpy (H) and P, (3) entropy (S) and P, or (4) T and volume (V). Phase relations in systems open to oxygen are determined by directly specifying the f _{o 2} or the T-P-f _{o 2} (or equivalently H-P-f _{o 2}, S-P-f _{o 2}, T-V-f _{o 2}) evolution path. Calculations are performed by constrained minimization of the appropriate thermodynamic potential. Compositions and proportions of solids and liquids in the equilibrium assemblage are computed.