Calculation of ternary mixing properties of melts and minerals from the bounding binaries

Among the several methods that have been used to predict thermodynamic properties of ternary alloys and oxides from three binary data, we used the models proposed by Kohler(1), Toop(2), and Muggianu (3) in order to evaluate the possibility of the application of these methods to geologically important systems, such as zeolites, clay minerals and silicate glasses. These models can represent the ternary excess Gibbs energy of the NaCl-KCl-H2O and Ca-Mg-Fe2+ garnet (Ca3Al2Si3O12 - Mg3Al2Si3O12 - Fe3Al2Si3O12) systems relatively well without a ternary correction term. The deviation from the reference data increases in the central region of the composition triangle. Toopʹs model with constant mole fractions of NaCl and Mg best simulated the ternary systems among the models. The path independent Muggianu model was applied to diopside (CaMgSi2O6) -jadeite (NaAlSi2O6) - acmite (NaFe3+Si2O6) ternary as an example. Although there exists intrinsic uncertainty in calculation without the ternary interaction term, these models, especially, Muggianu and Kohler can be good approximation methods for prediction of the ternary excess properties of the natural mineral solid solutions, devoid of ternary experimental thermodynamic data.