DIFFUSION IN MULTICOMPONENT METALLIC SYSTEMS: VII. SOLUTIONS OF THE MULTICOMPONENT DIFFUSION EQUATIONS WITH VARIABLE COEFFICIENTS

Abstract

Analytic solutions of the multicomponent diffusion equations are only available for constant diffusion coefficients, a situation which is unlikely in real systems. Using an extension of Boltzmann's treatment for binary diffusion, the multi-component diffusion equations with variable coefficients have been converted to an integral form which can be solved by iterative methods. For those multicomponent systems in which the off-diagonal Onsager L-coefficients may be approximated by zero, a simple numerical method of solution of the activity profile has been derived, which is applicable even if the D's are variable. A method is developed for designing and analyzing experimental diffusion couples to obtain the maximum amount of information about variable coefficients in ternary systems. The possibility of obtaining thermodynamic data from diffusion experiments is discussed.