【摘要】 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F_n,那末F_n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⁽-(V_AA+V_BB - 2V_AB)/kT) - 1的级数(式中V_AA,V_BB,V_AB代表最近邻AA,BB,AB对的作用能)而称忽略O（ηⁿ）的自由能为F_n^′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。更多还原

【Abstract】 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 8 are found to depend on n in a marked manner. In particular, F³ and F³, 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）^-3.On expressing F as a series inwhere VAA, VBB and VAB are interaction energies between AA, BB and AB pairs of nearest neighbours and denoting by F’_n the free energy on neglecting 0（ηⁿ） , we find that F’2 and F’3 do not give us any superlattice, but F’4, F’5 do. In fact, from F’4, F’5, we get a sudden change of-S accompanied by a latent heat, just as in the earlier theories. F’4, F’5 behave similarly, so we may hope they approximate the actual free energy.更多还原