Guggenheim’s quasi-chemical

Essentially, we are looking at the solubility of metals in other metals - i.e. monophase metal alloys. The most commonly used solution models are the models with similar atomic volumes, which give us the perfect solution, the infinitely-dilute solution and the strictly-regular solution. Thus, we will then look at Guggenheim s quasi-chemical model, which includes the notion of short-distance order. 

Fowler and Guggenheim s quasi-chemical model of the solution... 

In order to evaluate the functions g(5) and E s), we need to know the distribution of the atoms on the lattice for the given value of s. Two models have been developed the Gorsky, Bragg and Williams model and the quasi-chemical model. The hypotheses upon which these models are based are similar, respectively, to those used for the model of a strictly-regular solution (see section 2.3.3) and those used for Fowler and Guggenheim s quasi-chemical solution model (see section 2.3.5). 

Figure 3.3 shows the variations of Warren and Cowley s order parameter for Fowler and Guggenheim s quasi-chemical model, for the following values of the parameters T = 800 K, NaWAB = 30 kJ and z = 12. The result obtained respects the symmetry of the model with a minimum for the composition Xa = Xb = 0.5. 

Figure 3.3. Variation of the degree of order as a function of the composition ofa binary solution in Fowler and Guggenheim s quasi-chemical model (reproducedfrom [DBS 10], p.87)...

Then, we move on to the second phase, searching for the so-called r -order approximation or Guggenheim s quasi-chemical approximation, characterized by the relation ... 

The UNIQUAC (Universal Quasi-Chemical) model was introduced by Abrams and Prausnitz (1975), using Guggenheim s quasi-chemical model and applying the concepts of conformation with Staverman s relation and Wilson s local-composition model. 

We shall express the canonical partition function of mixing by using Guggenheim s quasi-chemical method (see section 3.3), applied with Staverman s athermic model as a reference, where the excess entropy is given by relation [3.137],... 

Abrams and Prausnitz (1975) combined Guggenheim s quasi-chemical tiieory with the concept of local compositions to develop the Universal Quasi-Chemical (UNIQUAC) expression for the excess Gibbs free energy. [The equation can be also developed from the two-fluid theory (Maurer and Prausnitz, 1978).]... 

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