Statistical self-similarity in Rhines’ concept of unique multiphase diffusion paths on the ternary gibbs’ isotherm

Abstract

For ternary systems with infinite boundary values encompassing supersaturation, interface instability is inevitable with the emergence of internal microstructural order parameters that exhibit autonomy from the initial and/or boundary conditions in accord with tie-line degrees of freedom. A well-known description of statistical self-similarity in such a nonisotropic system following Rhine’s experiments is Wagner’s one-dimensional theory of dilute multidisperse internal oxidation and its generalization provided by the author and Morral and co-workers. These treatments yield unique self-similar or parabolic solutions transferable to the Gibbs isotherm for solute distribution and relative precipitate fraction. This article is concerned with the more general free-boundary dispersion problem involving both microstructure mode and wave number selection. It offers a vacancy-based argument within a scalar time-dependent, Ginzburg-Landau reaction formalism as to why observations of average parabolic relaxation extend to a much wider range of constitutions, morphology, and volume fractions than considered by Wagner. The idea of mode selection is introduced in some detail; a cusp catastrophe being explicitly identified with the triplet of virtual diffusion paths corresponding to special composition terminals. The possible role of dissipation principles in removing such complex degeneracies is briefly discussed. We present a semiquantitative analysis of Coates’ experiments in Cu-Zn-Ni together with an explanation of the observed plastic turbulence in terms of Curie’s theorem and the Kirkendall effect.