A self-consistent model for predicting interaction parameters in multicomponent alloys
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NTRODUCTION
THE interaction parameters are frequently used for representing the effect of an alloying element on the activity of another alloying element in multicomponent alloys. Due to their important applications in thermodynamics of alloys and physical chemistry of extractive metallurgy, a great deal of work has been done on the experimental measurements of interaction parameters. Considering the great number of interaction parameters that are required and the complexity of measurements, one may expect that most interaction parameters should come from theoretical predictions rather than directly from measurements. Among all theoretical methods for predicting interaction parameters, the most attractive method is to predict from the physical characteristics of the constituent elements of alloys. Recently, several models of that sort have been proposed.[1–4] The reasonable agreement between the experimental data and the values calculated by these models is encouraging, with a reliability of 80 pct or higher in predicting the correct sign of interaction parameters. However, all these models have a common problem from theoretical consideration. It is well known that the reciprocal relation between interaction parameters as expressed by Eq. [1], which was first derived by Wagner,[5] exists. « ij 5 « ji
[1]
This reciprocal relation can be derived through the Gibbs– Duhem equation or the Maxwell relationship for metallic solutions, all of which obey Henry’s law at infinite dilution.[6] Furthermore, Lupis has demonstrated that the reciprocal relation is really a result of a comparison of configuration states for solutes in infinitely dilute metallic solutions based on the qualitative atomistic interpretation of interaction parameters in metallic solutions.[6] Thus, any theoretical model for predicting interaction parameters should satisfy the reciprocal relation. Unfortunately, none of these current models can meet this basic requirement automatically, which will be
PENG FAN, Associate Professor, is with the Department of Inorganic Materials, Sichuan University, Chengdu, 610065, People’s Republic of China. KUO-CHIH CHOU, Professor, is with the Department of Physical Chemistry, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China. Manuscript submitted November 10, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
demonstrated in the Appendix. The calculated value of « ij is always different from that of « ji using the same model; even the signs of calculated « ij and « ji are opposite to each other in some cases. One of the two different values calculated using the same model has to be selected for representing the value of both « ij and « ji so as to make the reciprocal relation satisfied by the model. This somewhat arbitrary choice is theoretically unreasonable. Thus, it may be said that none of these models is self-consistent. In the present article, a new model for predicting interaction parameters is proposed by coupling Chou’s geometric solution model on predicting excess ther
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