Determination of eigenvalues, eigenvectors, and interdiffusion coefficients in ternary diffusion from diffusional constraints at the Matano plane

Abstract

New diffusional constraints interlinking interdiffusion fluxes, concentration gradients and concentrations of the components at the Matano plane are derived for an isothermal, solid-solid ternary diffusion couple. The derivations are based on the diagonalization of the interdiffusion coefficient matrices employed for the description of selected regions of the diffusion zone and on the integration of the decoupled concentration gradients and interdiffusion fluxes over those regions. By selecting two diffusion regions, one on either side of the Matano plane, the diffusional constraints are employed for the direct determination of eigenvalues, eigenvector parameters and a matched pair of interdiffusion coefficient matrices for the generation of concentration profiles over the two regions. For a diffusion couple assembly, the input data needed for the calculations are the concentration gradients, interdiffusion fluxes and composition developed at the Matano plane at a given time. The diffusion parameters determined by the new analysis help ensure that the calculated concentration profiles, interdiffusion fluxes and concentration gradients of the components are continuous everywhere including the Matano plane. The application of the analysis is illustrated and discussed with selected experimental diffusion couples investigated in the Cu-Ni-Zn ternary system.