Effect of impurities on the stability of a moving grain boundary

Abstract

A two-dimensional model for impurity-controlled grain boundary migration, which accounts for both forward and lateral diffusion of bound impurities, has been developed and analyzed as a function of grain boundary shape, applied driving force, impurity concentration and temperature. Local boundary shape and concomitant variation of impurity concentration are interrelated through appropriate force and flux balances for all finite macroscopic grain boundary velocities v 0. When v 0 is less than a critical value v 1, the boundary remains planar, whereas when v 0 exceeds a critical value v 2, breakaway of the boundary from impurities occurs. In either case distribution of impurities is not affected. When v 1 < v 0 < 2, however, boundary shape and concentration profile are inherently unstable. In this case boundary shape may fluctuate greatly with only slight redistribution of impurities or the impurity profile may fluctuate greatly with only slight variation of boundary shape. Likelihood of these processes depends on the relative degree of impurity diffusion parallel and perpendicular to the moving boundary. Therefore, the present model indicates that clustering of impurities in the boundary and subsequent breakaway of the boundary from these clusters are natural consequences of grain boundary migration.