M. Nagamori et al., THE GRAND PARTITION-FUNCTION OF DILUTE BIREGULAR SOLUTIONS, Metallurgical and materials transactions. B, Process metallurgy and materials processing science, 25(5), 1994, pp. 703-711
It has been demonstrated that the grand partition function (GPF) of bi
regular solutions contains in one single equation such thermodynamic p
rinciples as Henry's law, Raoult's law, the Gibbs-Duhem relation, Raou
ltian activity coefficients and their finite power series, Wagner's re
ciprocity, Schenck-Frohberg-Steinmetz's interchange, Lupis-Elliott's a
dditivity, Mori-Morooka's disparity, and Darken's quadratic formalism.
The logarithm of the Raoultian activity coefficient of species i, 1n
gamma(i), should not be expressed by the Taylor series expansion, lest
its truncation infringe the Gibbs-Duhem equation. The GPF methodology
establishes that In yi is not a vector but a scalar point function, f
ree from any path dependence. While Darken's quadratic formalism emplo
ys three parameters to describe a ternary solution, the present biregu
larity approximation offers an alternative using seven empirical param
eters, in case better accuracy is needed.