Theory of diffusion induced grain boundary migration: is mass transport along free surfaces important?

Abstract

A new approach is proposed for the description of diffusion-induced grain boundary migration (DIGM). The crucial difference between our approach and the previous investigations is that our analysis includes diffusion not only along the grain boundary but also along free surfaces which are in contact with the grain boundary. The well-posed mathematical problem is formulated by matching the diffusional fields at the triple junction. We take into account the elastic effects which arise due to the sharp concentration jump in front of the moving grain boundary. By means of several simplifications we derive the closed equation for the steady-state velocity of DIGM as a function of the supersaturation and the system parameters. We find that mass transport at the free surface plays a very important role in the DIGM phenomena. The solution shows asymmetry between the cases of alloying and dealloying. In the alloying case a solution exists even without elastic effects while in the case of dealloying the elastic effects are necessary for DIGM. We also discuss DIGM in the systems consisting of isotopes and show that DIGM does not exist in such systems.