Ternary Diffusion. Solutions with Diffusion Coefficients Linearly Dependent on Concentrations

Abstract

A numerical solution was devised for the set of differential equations characterizing interdiffusion in a ternary system in which the partial diffusion coefficients are linear functions of the concentrations. A one-step fourth order Runge-Kutta method was used in the computer program. The concentration-penetration curves obtained accurately reflect the behavior of an interdiffusing ternary ideal solid solution provided that the tracer diffusion coefficients are constant and the ratios of the latter are not very different from unity. A theorem was derived which specifies the conditions for which the points of inflection of the three concentration-penetration curves occur at the same position in the diffusion couple. Also, it was shown that in an ideal interdiffusing ternary solid solution, zero-flux plane positions cannot correspond exactly to the points of intersection of the diffusion path and iso-activity lines drawn through the terminal alloys of the diffusion couple, but approach the latter in the limiting case. Finally, a method was developed to calculate the partial interdiffusion coefficients at a composition point on the diffusion path of an ideal ternary solid solution diffusion couple through the use of information obtained only from that one diffusion couple.