Estimation of complex concentration in a regular associated solution
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the given solution to short-range nearest neighbor interactions. The interaction energies and the concentrations of the two unassociated atoms and the complex were expected to determine the ternary activity coefficients through equations similar to those suggested by Prigogine and Defay ~3for ternary solutions. Jordan termed solutions obeying such conditions as regular associated solutions and demonstrated the utility of such an approach in arriving at the equations for liquids in the Zn-Te and Cd-Te systems where A B-type associations (CdTe and ZnTe) were anticipated. Jordan, 7 however, assumed that both the unassociated species interact equally strongly with the complex. Osamura and PredeP 2 applied Jordan's analysis to the In-Sb system but solved the necessary equations by ignoring the higher order terms in the concentration of the complex. The present communication illustrates how the concentration of A pB-type complexes can be determined from activity data without any assumptions whatsoever. The equilibrium constant for the dissociation reaction, heat of dissociation, enthalpy of mixing and other thermodynamic parameters have been estimated for liquid Mg-Sn and In-Sb alloys which are known to be associated. R E G U L A R ASSOCIATED S O L U T I O N S The presence of A pB complexes in an associated solution results in a depletion of the concentration of free atoms (or monomers) of components 1 and 2. Considering a solution of n t atoms of component 1 and n 2 atoms of component 2, the formation of nA, s complexes requires that n~ = n A + PnA.B; n2 = n s + nA,, for conservation of mass in the partiafly associated solution where n A and n 8 represent the numbers of unassociated components 1 and 2 respectively. As a result of association, the thermodynamic behavior of the components 1 and 2 in the solution is governed by their true mole fractions x A and x s (referred to the total number of species) rather than their gross mole fractions x Rand x 2 (referred to the total number of atoms). Thus, we require two frames of reference, the total number of atoms (n~ + n2) for defining x I and x 2 [x I = n l / ( n I + n2) and x 2 = n 2 / ( n ~ + n2)] and the total number of species
ISSN 0360-2141/81 / 1211-0659500.75/0 9 1981 AMERICAN SOCIETY FOR METALS AND VOLUME 12B, DECEMBER 1981--659 THE METALLURGICAL SOCIETY OF AIME
(nA + nn + hA,B) for estimating x A, x n and x A,a [xA = nA/(nA + nB + nA,n) and so forth]. The two sets of fractions are related to each other. Prigogine and Defay ~3have shown that in an associated solution, the gross chemical potentials of components 1 and 2 are equal to the chemical potentials of the monomeric species A and B. Jordan has suggested that to a first approximation, the deviation from ideality in an associated solution can be considered in terms of activity coefficients 7A, 7s and YA B of the monomers and complex respectively in aPstricly regular ternary solution. Following Jordan, 7 these activity coefficients can be expressed in terms of pairwise interaction energies through R T In 7A =
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