Evaluation of interaction parameters in metallic solutions by the isoactivity method
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I. INTRODUCTION
INTERACTION parameters of elements in metallic solutions are basic components of the thermodynamic database. An accurate thermodynamic analysis for the relevant metallurgical reactions is important for improving the current producing process of various kinds of metals such as steel and ferroalloys. Interaction parameters of elements in metallic solutions have been gradually accumulated based on the Wagner formalism[1] during the past half-century, although other approaches have been developed[2–7] to describe the thermodynamics of metallic solutions for overcoming the shortcoming of the Wagner formalism, i.e., the thermodynamic inconsistency at high solute concentrations. It is the tendency to adopt the available interaction parameters to express thermodynamic properties of metallic solutions at high concentrated levels via different approaches.[8–13] The very simple and useful Wagner formalism is widely and frequently applied to evaluate interaction parameters of elements in dilute metallic solutions. However, the Wagner formalism is frequently misunderstood and/or misapplied in the literature, particularly for the isoactivity and solubility methods. The causes for the misapplication and the principles for evaluating interaction parameters are discussed.
where g i and g 0i are the activity coefficient of solute i at normal conditions and infinite dilution, respectively; « and r denote the first- and second-order interaction parameters, respectively, and their subscripts and superscripts are the same as designed by Lupis and Elliott[14]; xk represents the mole fraction of element k. The activity coefficient of i being a function of mole fractions of solutes is based on the phase rule of Gibbs[7] presented as F5n2p12
[3]
where n and p are the number of chemical species and phases, respectively, and F is the degrees of freedom, i.e., the number of independent variables. For a nonreacting system with one phase and n chemical species at fixed temperature and pressure, the degrees of freedom are n 2 1. That is to say ln gi should be a function of mole fractions of solutes, xk (k 5 2, 3, ???, n). Thus, Eqs. [1] and [2] are only valid under the conditions of fixed temperature and pressure and no independent chemical reactions within the system.
III. ISOACTIVITY METHOD II. WAGNER FORMALISM AND ITS BASIC REQUIREMENTS The well-known first- and second-order Wagner formalism for a dilute solution with n components 1-2-3- ??? -n, where 1 represents the solvent, can be written as n
ln g i 5 ln g 0i 1
o « ijxj j52
ln g i 5 ln g 0i 1
i xj xk o « ijxj 1 j52 o r ijx2j 1 j,k52 o r j,K j52
n
[1] n
n
[2]
(k.j)
ZHONGTING MA, Associate Professor, formerly with Beijing University of Science and Technology, is with the Institute of Iron and Steel Technology, Freiberg University of Mining and Technology, D-09599 Freiberg/Sa., Germany. Manuscript submitted August 18, 1998.
METALLURGICAL AND MATERIALS TRANSACTIONS A
The distribution method (between the liquid iron and liquid silver) first employed by Chipman[1
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