Application of polymer theory to silicate melts. The system MO + MF2+ SiO2

Abstract

Expressions are derived for activities of MO and MF₂ as functions of composition in MO + MF₂+ SiO₂ melts. The treatment is based on the assumption that the melts consist of M²⁺ cations and O^2–, F^– and an array of silicate and fluorosilicate anions of general formula Si_nO_3n+1–mF^{(2n+2–m)–}_m in thermodynamic equilibrium, where 1 ⩽n⩽∞ and 0 ⩽m⩽ 2n+ 2. As in previous treatments, the equilibrium between the oxide and silicate ions is described in terms of an equilibrium constant k, the value of which is independent of the chain length n of the polyions. The equilibrium between the fluoride, silicate, fluorosilicate and oxide ions is described in terms of a second equilibrium constant k′ the value of which is assumed to be independent of the degree of substitution of O^– by F on the silicate chains. Theoretical curves are shown for the activity of PbO as a function of composition in PbO + PbF₂+ SiO₂ melts for the simple case in which k′= 0, i.e., for the situation in which PbF₂ acts solely as a diluent. Comparison with experimental data shows that the value of k′ for this system is finite. Accurate determination of k′ requires a knowledge of the activities of both MO and MF₂. Knowledge of the value of k′ allows the ion fraction of any species to be evaluated approximately in the range of composition for which the theory is applicable.