A transfer matrix method was presented for the development of solutions for multi-component diffusion couples containing any number of components. Expressions were derived for the transfer matrix and its integral so that interdiffusion fluxes and concentrations of all components could be determined at any section in the diffusion zone from the initial values of either interdiffusion fluxes or concentration gradients available at some other section. The method utilizes interdiffusion coefficients evaluated as average values over various regions of the diffusion zone by the method of moments developed by Dayananda. An integration of interdiffusion fluxes at a selected section over time or of the interdiffusion fluxes over a region in the diffusion zone could be determined by using the transfer matrix method. Concentration profiles determined by the transfer matrix method for a ternary Cu–Ni–Zn diffusion couple were shown to be identical to those generated from the Fujita–Gosting method.

A Transfer Matrix Method for the Calculation of Concentrations and Fluxes in Multicomponent Diffusion Couples. L.R.Ram-Mohan, M.A.Dayananda: Acta Materialia, 2006, 54[9], 2325-34