To compute lnW in Boltzmann's equation, Stirling's approximation, lnN! = NlnN - N, is used.This converts the above equation to to:
The remaining empty sites after the A atoms have been placed on the lattice just accommodate the NB atoms of B. There is but one way that the rest of the sites can be filled with B atoms. Setting N = NAv (for a mole of solution), and dividing by NAv (to convert atom number to mole fraction) and substituting the above equation into Eq (7.35) yields Eq (7.10):
With this result in hand, substitution of Eqs (7.10) and (7.34) into Eq (7.33) gives:
Further progress requires expressing gex in terms of the composition.
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