Free Energy of an Inhomogeneous Binary Solid Solution in the Yang-Li Approximation. I. Inhomogeneity due to Concentration Fluctuation

Abstract

The free energy of a binary fcc metallic solid solution is calculated using the statistical approximation of Yang and Li. The analytic expression permits one to separate, in the free-energy contribution, the homogeneous part from any inhomogeneity due to an arbitrary one-dimensional concentration fluctuation. The extra free energy introduced by a nonuniform solid solution is shown to be completely equivalent to the gradient free-energy term introduced phenomenologically by Landau and Lifshitz. By comparison with the Bragg-Williams approximation, the gradient coefficient is no longer constant, but concentration dependent at low temperature in a solution with miscibility gap as well as in a system exhibiting ordering. The free energy obtained is consistent with the discontinuous order-disorder transition in a fcc structure of the CuAu type.