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 O2–, F– and an array of silicate and fluorosilicate anions of general formula SinO3n+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.