Representation of excess thermodynamic properties of ternary systems using interaction parameters
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INTRODUCTION
THE development of the
interaction parameter formalism Ll'2] is based on the expansion of the Maclaurin infinite series in terms of the partial property in the neighborhood of a solvent component of a system. Although the parameters are originally intended to be useful for interpretation of properties for dilute solutions, attempts have been made by several researchers to extend the approach to concentrated solutions.J3'4] Schuhmann t3j has shown that Wagner's original suggestion ~l is essentially valid if such an infinite series is not truncated. Since higher order interaction parameters are rarely available for systems of practical interest, activity coefficients of solutes at finite concentrations have so far been calculated using the first-order parameters. Two methods have been suggested by Srikanth and Jacob [7~ toward solution of the inexact differential equation: (a) through the introduction of the special relations of the interaction parameters and (b) by the use of suitable compositional paths. It should be mentioned that an extensive critical survey of the experimental data of the first- and second-order parameters has been compiled in the literature; r8-~21 their evaluation does not support the validity of the special relations between the first- and second-order parameters. A constant compositional path, such as x i = k or xi/x~ = k, may be employed, as suggested by them, tTj toward the solution of the problem. One cannot eliminate all of the compositional degrees of freedom by the application of a compositional path. Hence, the method remains inconsistent from a thermodynamic viewpoint as in the case of the use of the special relations between parameters. Two important aspects which emerge from the discussion are (a) thermodynamic consistency and (b) the capability of interpreting experimental data beyond the dilute solution range. It should be mentioned that the Maclaurin infinite series may either be expressed by an integral or a partial property in the neighborhood of a component of a system. Since a partial may be readily derived from the other using the Gibbs-Duhem relation for a binary system, the choice of an integral or a partial property for expressing J.P. HAJRA, Associate Professor, is with the Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India. Manuscript submitted June 1, 1990. METALLURGICAL TRANSACTIONS B
the Maclaurin series does not restrict the thermodynamic consistency due to truncation of the series. In the case of a ternary or a higher order system, the truncated Maclaurin series based on the partial property of the system has been shown to limit the thermodynamic consistency, f3,7] It should be mentioned that these observations are made with respect to the Maclaurin series which is expressed in the vicinity of a component of a system. Before one considers the applicability of a function beyond the dilute solution range, it must satisfy certain boundary conditions. For integral excess properties of a ternary system, these conditions are
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