Some binary and ternary silicate solution models

Four different solution models, the two-parameter Margules, the quasi-chemical (QC), the Wilson and the non-random two-liquid (NRTL) model, have been used for fitting the calorimetric excess enthalpy of solution for the following four binary silicate systems: anorthite-albite, pyrope-grossular, diopside-enstatite and diopside-Ca-Tschermak. All models except the Wilson model yield a satisfactory fit to the data but the NRTL model generally results in the lowest residuals. The use of NRTL and QC facilitates the study of the configurational and non-configurational parts of the excess entropy of mixing.Three different methods, namely those of Kohler, Wohl, and Hillert, have been used to combine binary solution properties to predict ternary solution properties. Comparison of computed excess free energy of mixing in a hypothetical solution shows that all the three methods are viable but the Kohler and Wohl methods are similar to each other and are significantly different from the Hillert method. The Kohler method with one or a combination of different binary models is recommended for predicting multicomponent solution properties.Abbreviations G^ex excess free energy of mixing - H^ex excess enthalpy of mixing - S^ex total excess entropy of mixing - S_ex^c configurational excess entropy of mixing - W_ij interaction energy parameter between speciesi andj - X_i mole fraction of speciesi - QC quasi-chemical - NRTL non-random two-liquid - M Margules formulation - W Wohl's formulation - RK Redlich-Kister - K Bertrand-Kohler - H Hillert - Di diopside (CaMgSi₂O₆) - En enstatite (Mg₂Si₂O₆) - Py pyrope (MgAl_2/3SiO₄) - Gr grossular (CaAl_2/3SiO₄) - CaTs Ca-Tschermak (CaAl₂SiO₆) - Ab albite (NaAlSi₃O₈) - An anorthite (CaAl₂Si₂O₈)