Thermodynamic properties and phase equilibria in the CaF2-SiO2-Al2O3-CaO system:: II.: Thermodynamic modeling of CaF2-SiO2-Al2O3-CaO melts

A model is developed for describing the composition and temperature dependences of the thermodynamic properties in the CaF2-SiO2-Al2O3-CaO melt system within the associated-solution approximation. The model predicts that, along with the C-1, S-1, A(1), and Fl(1) monomeric units (Fl = CaF2, S = SiO2, A = Al2O3, C = CaO) CA, C(2)A, CS, and C2S associates; and S-2, S-3, ..., S-k, ... polymeric species of arbitrary length and configuration, as found earlier in studies of the CaF2-Al2O3-CaO and CaF2-SiO2-CaO ternary melt systems, the melts also contain AS, CAS, C(2)AS, and CAS(2) groups and AS(j)(1 < j < infinity) and CAS(i) (2 < i < infinity) polymeric units of arbitrary length and configuration. The equilibrium constant of reactions resulting in the attachment of a silicon-oxygen group to S-k, AS(j), and CAS(i) (1 < k < infinity, 1 < j < infinity, 2 < i < infinity) polymeric units was assumed to be independent of the size and configuration of the polymeric complex formed. The model parameters, found by minimizing the sum of the squares of the differences in the calculated and measured component activities, allow one to describe the composition and temperature dependences of component activities to within the experimental accuracy (1-2%). The calculated parameters of silica polymerization coincide with those found for the MnO-SiO2, CaO-SiO2, and CaF2-SiO2-CaO melt systems, suggesting that our model of silica polymerization in silicate melts is of general nature.