It was recalled that the Frank-Bilby equation could give many solutions for the dislocation content of a grain boundary. Most of them were considered to have little physical reality except within limited ranges of the angles which characterized low-angle grain boundaries. Two such solutions were explored here. Each of them was an accurate description of a different low-angle tilt grain boundary; having the same tilt axis. A model was developed that used the 2 solutions to predict the coupling factor between normal motion and the shear strain produced by a low- or high-angle grain boundary. Within this model, the 2 Frank-Bilby equation solutions gave rise to 2 possible modes of coupled grain boundary motion which, for a given grain boundary under the same stress, differed in direction of motion. The model was confirmed using molecular dynamics simulations. Positive and/or negative coupled grain boundary motion was found for all misorientation angles, and the model furnished accurate predictions of the shear produced even by high-angle grain boundaries; where individual dislocations could not be resolved. At low temperatures, a dual behavior was observed for the same high-angle grain boundary and applied stress. Both coupling modes were found, with a switch between them after some delay. This switch indicated a change in the effective dislocation content. The dual behavior indicated that both solutions for the dislocation content could be meaningful for the same grain boundary. At higher temperatures, only one mode was observed for each grain boundary under a given shear stress, and the switch between the 2 modes appeared to occur discontinuously at some high misorientation angle.

Duality of Dislocation Content of Grain Boundaries. J.W.Cahn, Y.Mishin, A.Suzuki: Philosophical Magazine, 2006, 86[25-26], 3965-80