The coordination cluster theory: Extension to multicomponent systems
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I.
INTRODUCTION
T H E O R I E S for predicting the thermodynamic behavior of dilute solutes in multicomponent solvents are necessary for a full description of many scientifically and technologically important systems, which include alloys, metallurgical slags, magmas, and molten salts. In this paper, we discuss a theory that leads to such predictions based on data for the lower-order unary and binary solvents. The coordination cluster theory (CCT) for the activity coefficients of a dilute solute, S, in a binary solvent ~ has been shown to accurately represent thermodynamic data for solutions of oxygen and sulfur in binary alloys. This theory requires use of a single unknown parameter. 2 Prior theories of Alcock and Richardson, 3'4 Jacob and Alcock, 5 and Wagner 6 have been shown to be special cases of the CCT. The generality of the CCT stems from the fact that it simultaneously takes into account all the different types of energetic effects accompanying the dissolution of a solute atom in a solvent. The original derivation of the CCT used statistical mechanical calculations, which included all the different kinds of interactions existing in solution, namely, (i) the solventsolute atom interactions, (ii) the solvent-solvent atom interactions for atoms located in the first coordination sphere of a solute atom, and (iii) the interactions between solvent atoms that are not near neighbors to a solute and all other solvent atoms. The only interactions not considered were those between solute atoms; this simplification was justified since the theory deals only with dilute solutions, where the probability of configurations in which solute atoms are close is negligible. This paper reports an extension of the CCT based on a simple "chemical" method of calculation previously outlined by Blander and Saboungi. 7 In Section II, a fundamental rationale is given for the prediction of the thermodynamic properties of a solute in a multicomponent solvent, based solely upon the properties of the solute in the pure components and in the subsidiary binaries. In Section III, M A R I E - L O U I S E S A B O U N G I , Senior C h e m i s t , IRA B L O O M , Chemist, and MILTON BLANDER, Group Leader, are with Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439-4837. DEANNA CAVENY is Participant m the Argonne Division of Educational Programs from the University of Southern Mississippi, Hattiesburg, MS. Manuscript submitted November 10, 1986.
METALLURGICAL TRANSACTIONS A
the solubility of oxygen in Ag-Cu-Sn is calculated from the CCT equations. The values thus obtained are compared with measurements. Finally, the differences between calculations based on the CCT and prior theory and experiments are discussed.
II.
THE COORDINATION CLUSTER THEORY
The dissolution of a solute S in a binary solvent A-B leads to the formation of coordination clusters S(Az-,, B,), where S is coordinated by Z solvent atoms of which i are B atoms and the remainder are A atoms. The statistical mechanical calculation I leads to an expression for
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