An analysis of clustering and ordering in multicomponent solid solutions—II fluctuations and kinetics

Abstract

The free energy of a multicomponent substitutional solid solution is rederived on the basis of a more rigorous averaging procedure than the one used in I. The resulting expression is a quadratic form in the Fourier transforms of the concentration variables. Application of the Landau theory of fluctuations then leads to a set of formulas for the expectation values of concentration fluctuation intensities, which are the extension to multicomponents of the Clapp and Moss formulas for binary systems. Coupled discrete-space diffusion equations are derived and solved by diagonalization of the diffusion matrix. Principal directions in composition space and static and kinetic eigen vectors are defined. The effect of the positive definite mobility matrix is to rotate the directions of fastest and slowest initial concentration changes (kinetic directions) away from the principal free energy directions but in such a way that asymptotic directions are never crossed. Examples of ternary systems are given and asymptotic directions in quaternary systems are discussed qualitatively.