Analysis of interdiffusion and diffusion paths in multicomponent systems

A user-friendly computer program called MultiDiFlux has been developed for the analysis of multicomponent diffusion. Such analysis includes the evaluation of interdiffusion fluxes directly from the concentration profiles of an n-component diffusion couple and the determination of all (n-1) 2 interdiffusion coefficients. The interdiffusion coefficients are evaluated as average values over selected regions of the diffusion zone by the method of moments developed by Dayananda and Sohn. The program was assessed by determining the interdiffusion coefficients from a ternary test diffusion couple with known interdiffusion coefficients; the evaluated coefficients agreed within 1% of the known coefficients. The program was also used to analyze two sets of Cu-Ni-Zn single-phase diffusion couples annealed at 775°C; one set with intersecting diffusion paths and the other with overlapping diffusion paths. For the intersecting couples, the interdiffusion coefficients calculated at the common composition of the intersection from each individual couple agreed with those determined by the Boltzmann-Matano analysis within 2-39%. For the couples with overlapping diffusion paths, interdiffusion coefficients calculated for each couple over the overlapping path segments agreed within 0-30%. New expressions relating the concentration profiles, interdiffusion fluxes, and interdiffusion coefficients have been developed. The expressions were applied to one two-phase and several single phase Cu-Ni-Zn diffusion couples annealed at 775°C as well as one single phase Fe-Ni-Al couple annealed at 1000°C. Such applications showed that the ratio of the flux gradient to the concentration gradient of each component plotted against distance yielded overlapping straight lines with identical slopes. Effective interdiffusion coefficients for the individual components were also calculated at selected locations within the diffusion zones of the various diffusion couples. Additional expressions have also been developed to relate slopes of the diffusion path and ternary interdiffusion coefficients at selected locations. These expressions were used with calculated average ternary interdiffusion coefficients to estimate the diffusion path slopes at selected sections of the single phase Cu-Ni-Zn diffusion couples. The estimated diffusion path slopes were comparable to those determined from the concentration profiles. A preliminary method to predict the diffusion path of a ternary diffusion couple from ternary interdiffusion coefficients as functions of composition is also presented