On the choice of "geometric" thermodynamic models

A number of "geometric" models have been proposed for estimating the thermodynamic properties of a ternary solution from optimized data for its binary subsystems, Among the most common of these are the Kohler, Muggianu, Kohler/Toop, and Muggianu/Toop models. The latter two are "asymmetric" models in that one component is singled out and treated differently, whereas the first two models are "symmetric." it is shown that the use of a symmetric model when an asymmetric model is more appropriate can often give rise to large errors. Equations are proposed for extending the symmetric/asymmetric dichotomy inter N-component systems (N = 3), while still permitting the flexibility to choose either a symmetric or;an asymmetric model for any ternary subsystem. An improved general functional form for "ternary terms" in the excess Gibbs energy expression is also proposed. These terms are related to the effect of a third component upon the binary pair interaction energies. All the above considerations also apply when short-range ordering is taken into account by using the modified quasichemical model. Finally, some arguments in favor of the Kohler model over the Muggianu model are presented.