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OX3 /IxI-Jxl---->I,x3---->O
[(0ln~'2t t \
= V12 + V23 - V31
N, q,
wU
0.5(E, + E~)] atomic fraction of atom i number of nearest neighbor atoms Wagnerian interaction parameter, Tables IV and V Raoultian activity coefficient " absolute activity of component i grand partition function (GPF) Lupisian interaction parameter, Tables IV and V.
= wdkT
x, z
Y Ai
E P
= z[E v -
The author expresses his gratitude to the Centre de Recherches Min6rales, Quebec Government, for permission to publish this note.
REFERENCES
:-V]2+V23-V3I
[11]
OX3 IIx2_]X2-..>O,x3--.~0
NOMENCLATURE k
temperature in Kelvin
[10]
Equations [10] and [11] clearly indicate that the partial derivative along the path of Xl = const converges to a value different from that along the path of x2 = const. Although Srikanth and Jacob used only the Wagnerian terms, namely their Eq. [23], the present Eqs. [10] and [11] are derived based on more rigorous expressions including both Wagnerian and Lupisian terms, as done earlier by Srikanth and Jacob in their Eqs. [9] and [10], for which the activity coefficient of solvent has already been given by Eq. [1.3] without any integration. This tremendous simplicity is a merit of the GPF method which obliterates all integrating operations from solution theories. Equation [1.3] does not depend on path, being valid for all compositions, dilute or concentrated, binary or ternary. It may be suggested that the activity coefficient of solvent is best assessed by regularity approximation, or Eq. [1.3], even if the solutes may not behave exactly regularly. In reference to Eqs. [10] and [11], it is of great importance to note that in a ternary solution 1-2-3 where the component 1 is the dominant solvent, the condition of (Xsolvent ~ 1), or (xl ~ 1, x 3 ~ 0 ) , is not the same as that of (x2 ~ 0, x3 ~ 0). Thus, the GPF formalism for regular solutions lends support to Srikanth and Jacob when they meant that some previous researchers and authors were misled due to the overlooking of the path dependence of interaction parameters. Incidentally, Wagner's original definition TM clearly designates the condition of (x2 ~ 0, x3 ~ 0) with categorical rejection of the other conditions such as (x~ ~ 1, x3 ~ 0), (xl ~ 1, x2 ~ 0), and ( x 2 / x 3 = const, xl ~ 1).
Eq
T
pairwise single bond energy between i and j Boltzmann constant number of atoms of metal i vibrational partition function of atom i
METALLURGICAL TRANSACTIONS B
1. S. Srikanth and K.T. Jacob: Metall. Trans. B, 1988, vol. 19B, pp. 269-75. 2. C.H.P. Lupis and J.F. Elliott: Acta Metall., 1966, vol. 14, pp. 529-38. 3. R. Fowler and E.A. Guggenheim: Statistical Thermodynamics, Cambridge University Press, London, 1965. 4. M. Nagamori: Metall. Review of MM1J, 1986, vol. 3, no. 3, pp. 26-41. 5. C. Wagner: Thermodynamics of Alloys, Addison-Wesley Pub. Co., Reading, MA, 1952, p. 51. 6. M.Z. Sukiennik and R.W. Olesinski: Metall. Trans. B, 1984, vol. 15B, pp. 677-80.
Authors' Reply S. SRIKANTH and K.T. JACOB Nagamori's discussion of our paper on the thermodynamic consist
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