This paper applies Kirkwood's method for calculating the configurational free energy E of a solid solution to a solid solution AB3 inhabiting a face-centred cubic lattice. In this method, the free energy F is expressed as a series in (kT)A-1, and our calculation goes as far as the coefficient of (kT)-4. If the order of the solid solution is denoted by S and the free energy on neglecting 0(kT)-n by Fn, the relation between Fn and S are found to depend on n in a marked manner. In particular, F3 and F5, have always a minimum at S=0, implying no superlattice may exist. The foregoing is actually nothing but an indication of the slow convergence for the expansion of F in (kT)-1. On expressing F as a series in η≡exp{-(VAA+VBB-2VAB)/kT}-1 where VAA, VBB and VAB are interaction energies between AA, BB and AB pairs of nearest neighbours and denoting by Fn′ the free energy on neglecting O(ηn) , we find that F2′ and F3′ do not give us any superlattice, but F4′, F5′ do. In fact, from F4′, F5′, we get a sudden change of S accompanied by a latent heat, just as in the earlier theories. F4′, F5′ behave similarly, so we may hope they approximate the actual free energy.
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