An interacting pair model for alkaline binary and ternary liquid silicates: Application to the systems Na 2 O-K 2 O-SiO
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I.
INTRODUCTION
NUMEROUS thermodynamic models of oxide melts are available in the literature. In particular, for molten silicates, a review of these structural models has been published by Gaskell in 1981.[1] Chronologically, the theoretical representations developed by Toop and Samis,[2] Gaskell, Masson and co-workers,[3,4,5] Kapoor et al.,[6,7,8]. Yokokawa and Niwa,[9,10] and then Lin and Pelton[11] can be mentioned. The models describing the liquid as polymerized silicate anions represent correctly the viscosity of the melts. For most of the descriptions, the basic idea is the gradual depolymerization of the three-dimensional network of pure silica by the modifying oxides. Following the pioneers Fincham and Richardson,[12] the polymerization-depolymerization reactions can be reduced to the simplest equilibrium O0 1 O22 5 2 O2, where the double bounded O0 atom represents the bridging oxygens between the silicon atoms in the tetrahedral network of silica, O22 the free oxygens provided by the modifying oxide, and O2 the nonbridging oxygens resulting from the depolymerization reaction. Although no structural details are initially introduced, the model of Lin and Pelton[11] permits description of the distribution of the chain lengths in the entire concentration range and in agreement with the results of structural models. This model is particularly efficient to represent the thermodynamic quantities of silicate melts, and its mathematical simplicity can be considered as a quality. The enthalpy of mixing is then described by the following expression: DH 5 nO2 /2 (AxSi 1 BxM 1 CxSixM) in which xSi denotes the silica concentration and xM the modifying oxide M2O concentration in the melt; nO2 is the number of singly bounded oxygen O2 per mole of binary silicate M2O-SiO2. The three adjustable parameters A, B, and C are fitted to experimental data and thus do not a priori hold any physical significance. In this work, the model that differs from that of Pelton in the expression of the enthalpy is developed F. BENNOUR, Thesis Student, M. GILBERT, Engineer CNRS, J. ROGEZ and J.C. MATHIEU, Directors of Research, are with the Centre de Thermodynamique et de Microcalorimetrie du CNRS, 13331 Marseille, Cedex 3, France. Manuscript submitted June 18, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS B
for ternary systems by giving a statistical meaning to the parameters.
II.
BINARY SYSTEMS
A. Model It is supposed that only configurational properties act in the mixing process. In addition, neither volume nor accommodation effects have been taken into account. The introduction of the modifying ionized oxide 2M+, O22 in the pure silica network breaks the -Si-O0-Si- bonds, which transform into two ionic entities -Si-O2. Two singly bonded oxygen O2 appear instead of one bridging oxygen O0. Let nSi be the number of silicon atoms and nM the number of M2O molecules. The resulting enthalpies and entropies of reaction vary significantly with the nature of the cation M+. It is assumed that the melt contains the anions O22 and O2, the dival
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