A thermodynamic model for hydrous silicate melts in the system NaAlSi3O8–KAlSi3O8–Si4O8–H2O

Computation of crystal–liquid equilibria in hydrous silicate systems requires a model of the free energy of the hydrous liquid that defines the activity of the melt components at given temperature, pressure and composition. We present in this study a parametrization of the free energy of the liquid in the haplogranite system NaAlSi3O8–KAlSi3O8–Si4O8–H2O based on the Margules approach. The excess free energy of the multicomponent melt is approximated from the binaries with the Kohler extrapolation method. Model parameters have been fitted to phase equilibrium data by mathematical programming techniques. A small but complex excess function of the anhydrous melt composition is necessary to reproduce reported liquidus phase relations. Using partial molar Cp data from the literature for the H2O melt component and a simple polynomial approximation for the molar volume, standard state enthalpy and entropy were refined close to −287 kJ/mol and 67.2 J/K mol, respectively. Calculated crystal–liquid phase relations are in good agreement with measurements to 5 kbar, and the modelled melt–fluid coexistence surface yields a valuable first order approximation of the H2O solubility at near liquidus temperatures. Thermodynamic assessment of solubility and liquidus data suggests that H2O mixing differs considerably in feldspar melts and in silica melts. Si4O8–H2O mixing contributes to a very minor degree to the haplogranite system.