Comparison of solution models for nonmetallic solutes in binary liquid alloys: Nitrogen in Fe-Cr and Fe-Ni
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I.
INTRODUCTION
THE activity coefficient data of nonmetallic solutes in binary liquid alloys agree in essence with the values calculated from the Wagner ~ model. In that model it was assumed that the solute atoms occupy quasi-interstitial sites in a solvation shell formed by randomly distributed solvent atoms with one adjustable energy parameter. However, a quantitative agreement between experimental data and calculated values is obtained only when the model is extended2'3 to contain two adjustable energy parameters. The term "quantitative agreement" is used if the deviations between model and experimental data are smaller than the experimental error. Recently, the assumption of random distribution among the solvent atoms has been relaxed, 4 taking into consideration the nonideal behavior of the solvent metal atoms. This model with only one adjustable energy parameter 4 gives better descriptions of the oxygen activity coefficient data than the original Wagner ~equation. However, quantitative descriptions, as demonstrated by the two-parameter equation, 2 are not achieved. In the present study the available data for nitrogen in Ni-Fe and Fe-Cr alloys are evaluated in terms of the nonrandom equation 4 and in terms of other model equations for comparison. The two objectives of this study are to demonstrate: (i) that Wagner's original one-parameter equation is improved by incorporating the nonideal solvent behavior but that the maximum accuracy is attained with a two-parameter extension JEN-CHWEN LIN, Research Assistant, and Y. AUSTIN CHANG, Professor and Chairman, are with the Department of Metallurgical and Mineral Engineering, University of Wisconsin-Madison, Madison, WI 53706. RAINER SCHMID is with the Institut fiir Eisenhtittenkunde und Giesserelwesen Technische, Univers~t~it Clausthal. D-3392 Clausthal-Zellerfeld, West Germany. This paper is based on a presentation made at the G.R. Fitterer Symposmm on Nitrogen in Metals and Alloys held at the ll4th annual A1ME meeting in New York. February 24-28, 1985, under the auspices of the ASM-MSD Thermodynamic Activity Committee. METALLURGICAL TRANSACTIONS B
of Wagner's equation; (ii) that Wagner's general approach using the chemical equilibrium among solvation shells is also applicable to the substitutional dissolution of atoms.
II. DISCUSSION OF THE NONRANDOM MODEL EQUATION The meaning of the term "nonrandom" is illustrated in Figure 1. Two octahedral solvation shells, occupied by a solute atom (X), are depicted with z = 6 for the solvent atoms (A or B). The composition of both shells is given by j = 4 B-atoms. The shells are distinguished only by different configurations of A- and B-atoms and all of the configurations are assumed to have equal energy and
Fig. 1 - - Schematic view of two octahedral solvation shells with 4 B-atoms and 2 A-atoms, distinguished by a different configuration of solvent atoms VOLUME 17B. DECEMBER 1986--785
0
probability. Then the total number of configurations is given by the binomial term z!/[(z -j)!j!]. In other words, for given value
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