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本文应用了Kirkwood方法去计算面心立方体的固溶体AB3的自由能。在这个方法中,自由能被表为(kT)-1的幂级数。我们的计算一直算到了(kT)-4的系数。如果称原子排列的秩为S,称忽略O(kT)-n的自由能为Fn,那末Fn与S的关系对于不同的n(n=2,3,4,5)是极不同的。事实上,F3,F5和S=0处始终为极小,使理论中看不到超点阵的结论。这说明自由能F对(kT)-1的展开的级数收敛极慢。将F表为η≡e(-(VAA+VBB-2VAB)/kT)-1的级数(式中VAA,VBB,VAB代表最近邻AA,BB,AB对的作用能)而称忽略O(ηn)的自由能为Fn′那末F2′,F3′依然不给我们超点阵的结论,但由F4′,F5′我们非但获得了超点阵,并也看到了S的突变及固溶体的潜热。F4′,F5′是极相似的,使我们相信它们近似于真正的F。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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