A model for calculating interaction coefficients between elements in liquid and iron-base alloy
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INTRODUCTION
THE semiempirical formation enthalpy model for binary alloys suggested by Miedema and co-workers[1,2,3] in the early 1970s has been developed into a successful one which includes only three parameters: electronic density, atomic volume, and electronegativity. Based on a large number of experimental data, a formation enthalpy calculation formula for binary systems which contain almost all possible binary systems has been established. Recently, this model was applied to calculate ln g 0i and activity interaction coefficients ε ji.[4] The results obtained were in reasonable agreement with experimental data. In the preceding calculation, however, the excess entropy was assumed to be zero. In this case, it is possible for some alloys to cause a marked error. Tanaka et al.[5,6] estimated DSEM in liquid binary alloys by use of free volume theory and the Miedema model. The excess entropies they calculated were, for many binary alloy systems, very consistent with the experimental data. This article will establish a calculation model of ln g 0i and an activity interaction coefficient ε ji in liquid iron-base systems by use of free volume theory, the Miedema formation enthalpy model, and the Toop model. An investigation into the effect of excess entropy on ln g 0i and the activity interaction coefficients is presented and the results compared with those found in the literature.[4]. II.
ESTABLISHMENT OF A MODEL
The excess Gibbs energy for a binary system was obtained by use of the first approximation to the regular model, free volume theory, and the Miedema model. The calculation formula for the excess Gibbs energy of a ternary system was then derived from that for three relevant binary systems, based on the Toop model. A. Free Volume Theory[5,6] The basic physical picture of free volume theory assumes that each atom in a liquid metal vibrates harmonically in a cell made by its nearest-neighbor atoms. The partitions of pure liquid A and B, QAA and QBB, are F.M. WANG and X.P. LI, Postdoctoral Candidates, Q.Y. HAN, Professor, and N.X. ZHANG, Master Student, are with the Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, People’s Republic of China. Manuscript submitted December 5, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS B
given by the following equations: NA QAA 5 V f,AA exp (2
EAA ) RT
2 p LAA RT 3N /2 N U ) A exp (2 A AA ) UAA 2RT E B 5 V Nf,BB exp (2 BB ) RT 2 p LBB RT 3N /2 N U 5 (2 ) B exp (2 B BB ) UBB 2RT
[1]
5 (2 QBB
[2]
where Vf,xx is the free volume of atom x in pure liquid X, Lxx the distance which interatomic potential extends in a cell of atom x in pure liquid X, Uxx the depth of potential energy in a cell of atom x in liquid X, and Nx the number of atoms in pure liquid X. For a liquid binary alloy, the total partition function Q is expressed by NA NB Q 5 gV f,A V f,B exp (2
E ) RT
p L2A RT 3N /2 p LB2 RT 3N /2 ) A (2 ) B UA UB E exp (2 ) RT
5 g (2
[3]
where Vf,X(X5A,B) is the free volume of atom X in liquid A-B alloy, LX the distance wh
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