Grain rotation by dislocation climb in a finite-size grain boundary

We investigate the kinetics of grain rotation in a bicrystal with a tilt grain boundary by studying the relaxation of an edge dislocation wall in a discrete-dislocation approach. The boundary is infinitely extended in one direction and of finite size in the orthogonal one. The relaxation process is simulated numerically by solving the equations of motion of the dislocations, assuming climb by diffusive transport in the boundary plane. Surprisingly, we find that boundaries never rotate all the way into coincidence. Instead, the final state is a metastable array with 18 dislocations and, hence, with a finite misorientation that depends on the boundary length and the Burgers vector. All boundaries with fewer than 18 dislocations are also metastable. The relaxation time to reach the metastable configuration is found to be proportional to the logarithm of the number of dislocations and to the cube of the length of the boundary. We give a critical discussion of image force arguments that underlie earlier work on grain rotation, and verify that the present analysis of image forces does satisfy the boundary conditions at the free surfaces. The results have implications for the kinetics of rotation of nanoparticles on a substrate and for the stability of grain and subgrain boundaries in thin metal films.