Bragg-Williams treatment of convergent ordering in solid solutions

Bragg-Williams treatment of convergent ordering in solid solutions 

Let us assume that there are N sites in the two lattices a and b. Thus Na + Nb = 2N and there are a total of z,N interactions between nearest neighbours. The energy of the system in the disordered state is for a given composition given by eq. (9.17)  

Taking into account thatiVAA = /VBB and Nm =zN - /VAA - NBB the energy of the disordered solid solution becomes 

Since the enthalpy of the fully ordered state corresponding to cr = 1 is zNuAB, the enthalpy for the disordering process is 

The configurational entropy on the b lattice is given by an identical equation. For the perfect long-range ordered modification the configurational entropy is zero, and the entropy change due to disorder is thus 

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