A thermodynamic model for multicomponent melts, with application to the system CAO-MGO-AL₂O₃-SIO₂

A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. Mineral-melt reactions are written in terms of liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a 'Margules solution' is derived in a generalized form which can be extended to systems of any number of components and to polynomials of any degree. Calibration of the model is achieved using the method of linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with available calorimetric measurements and phase equilibria data concerning liquidus relations, binary and ternary liquid immiscibility gaps, and solid-solid P-T reactions. Application of this model to the ternary CaO-Al₂O₃-SiO₂ system shows that a fourth degree polynomial equation for the excess free energy of the liquid solution is necessary to adequately reproduce phase relations. Successful reproduction of the liquidi of 24 minerals in the quaternary system CaO-MgO-Al₂O₃-SiO₂ requires no additional terms in the expansion for the excess free energy. For 69 invariant or piercing points on the joins used in calibration of the quaternary system, the average differences between calculated and experimentally determined invariant points are 0.24±14.5° and 0.52±0.55 oxide weight percent (owp). Calculated liquidus relations on the 5-35% Al₂O₃ and 5-10% MgO planes compare favorably with experimental data, and piercing points on 17 other quaternary joins not used in the calibration have average differences of -1.6±18.0° and 0.43±0.64 owp. Significant inconsistencies have been identified in several experimental studies and are most readily attributed to inhomogenous starting materials. All liquidus diagrams are recalculated by computer programs that trace univariant curves and isothermal sections while checking each point on a curve for metastability. Isobaric quaternary univariant curves have been calculated and are presented in stereographic projections. The intersections of these curves define the T, X positions of all quaternary invariant points at one atmosphere pressure. The model permits calculation of a variety of melt properties which can be used to supplement the limited data available from other sources. Calculated liquid activities, heats of fusion, and heats of mixing are compared with available experimental data.Science, Faculty ofEarth, Ocean and Atmospheric Sciences, Department ofGraduat