The Gorsky, Bragg and Williams model

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). 

We are going to look at these models in the simple case of an alloy where the molar ftactions of A and B are equal to V2 and the fractions of sites are also equal to Vi (that is x = y = Vz in the notation used in Table 2.3) - this is the Gorsky expansion. The calculations are carried out in the same way for any given values of x and y, but the expansions are, naturally, more complex. 

In the same way, we calculate the number of pairs B-B, which gives us the same result. The number of A-B pairs will thus be given by the difference between the total number of pairs (which is NzH) and the number of pairs A-A and B-B  

Let us now examine how to calculate the statistical weight. We said earlier that the atoms of A and B were distributed at random, and 

By switching to logarithms and using Stirling s approximation, we obtain  

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