Applicability of central atoms models to binary silicate and aluminate melts
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I.
INTRODUCTION
T H E R E has been a continuing interest in the silicate and aluminate systems because of their importance in slag systems as also in glasses. Models proposed for these systems have had varying degrees of success in predicting the relationships between composition and structure. ~-8 The usefulness of these models has been recently reviewed by Gaskell. 9 The need for a model that should be conceptually and mathematically simple and be applicable to the entire composition range has been emphasized, 7 and the ease with which the model may be extended to ternary and multicomponent systems would determine its usefulness. It is the object of this paper to present a model based on the central atoms concept initially proposed for binary metallic solutions by Lupis and Elliot m and Hlcter et al u and later extended to multicomponent systems by Foo and Lupis.~2 The basic concept of the central atoms model for metallic solutions is to describe the partition function in terms of probabilities associated with different compositions of the nearest shells and in terms of the influence of these configurations on the field acting on the central atom under consideration. The advantage of this lies in the fact that while all other models assume the additivity of pairwise interaction, here it is only a special case since the entity of a cluster formed by a central atom and its neighbor shell replaces the entity of a pair, Pascal et al. ~3used a parabolic dependence and Lupis et al. ~4 a delta function approach to represent the interaction energies and predict the thermodynamic properties of metallic solutions. The authors proposed a central atoms model of silicate and aluminate melts that was useful only up to silica/ alumina saturation points. ~ A different model, using the same central atoms approach, is presented here which reproduces the entire phase diagram and the activities of both the components in the binary melt. The model is applied to silicate and aluminate melts though it is general enough to be applicable to most of the slag systems.
types of oxygen are considered: (1) O ~ surrounded by F, (2) O- surrounded by F or M, and (3) 0 2- surrounded by M; obviously F can be surrounded only by O ~ and O- and M only bv O- and 0 2 . Let pv represent the probability of an F central atom having i O ~ a n d . / O - neighbors (i + j = ZF, the coordination number of F for oxygen), pj)~ the probability of M central atom having j O- and k 0 2- neighbors (j + k = z~0, and 2z~ and 2z2 the coordination numbers of oxygen for F and M, respecnvely. Since the quantity of O must be the same with either F or M as central atoms, N~ ~ --
ZI
. F
N~I
m,, = --
I1
Z~
sl
El]
E m,~ IL
where NF and Nu are the number of F and M atoms in one mole of the solution. Also from mass balance considerations (see Appendix I) ZFX :,
=
[2]
- -
2v
--2 -
2M~l
[3]
2b
Equations [1] through [3] are adequate to satisfy the oxygen balance of the system. In the configuration whose probability is given by p~, let the central atom F be asso
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