General theory of interdiffusion growth in diffusion couples

This paper shows that it is possible to treat solid-phase growth thoroughly with methods of fluid mechanics. Based on the concept ‘flow point’ borrowed from fluid mechanics, the general equations are derived to describe atomic interdiffusion in diffusion couples. Two types of phase growth, i.e. volume and interface growths, are mathematically defined as the growing expansion of flow points within interdiffusion field and the creation of flow points at interphase interface, respectively. Mathematical discussions on the thickness–time dependence also indicate that phase growth in diffusion couples can be really interface-controlled when the interface coefficient is much smaller than the characteristic diffusion coefficient. It is also shown that with certain conditions Darkenʹs equations can be strictly deduced from the general equations and Darkenʹs equations should be only applicable for the binary interdiffusion system, in which system no new phase should be created. Furthermore, the Kirkendall velocity expressed by one of the Darkenʹs equations should be defined as the velocity of flow point within that system.