Ternary diffusion path in terms of eigenvalues and eigenvectors

Abstract

Based on the transfer matrix methodology, a new analysis is presented for the description of slopes of the ternary diffusion path for a solid–solid diffusion couple. Concentration profiles and diffusion paths for isothermal, ternary diffusion couples are examined in the context of eigenvalues and eigenvectors obtained from the diagonalisation of the ternary interdiffusion coefficients employed for their representation. New relations are derived relating the decoupled interdiffusion fluxes to combinations of concentration gradients through the major and minor eigenvalues, and the diffusion path becomes parallel to the major eigenvector at each path end. General expressions for the slope of the ternary diffusion path at any section of the couple are also derived in terms of eigenvalue and eigenvector parameters. Expressions for the path slope at the Matano plane involve only concentrations, major and minor eigenvalues and eigenvector parameters. New constraints relating the eigenvalues and the concentration gradients of the individual components are also presented at selected sections, where the diffusion path is parallel to the straight line joining the terminal composition points on an isotherm. Applications of the various relations are illustrated with the aid of a hypothetical couple and an experimental Cu–Ni–Zn diffusion couple.