Duality of dislocation content of grain boundaries

The Frank-Bilby equation (FBE) can give many solutions for the dislocation content of a grain boundary (GB); most of them are considered to have little physical reality except in limited ranges of the angles which characterize low-angle GBs. We explore two such solutions, each of which is an accurate description for a different low-angle tilt GB with the same tilt axis. We develop a model that uses the two solutions to predict the coupling factor between normal motion and the shear strain produced by any (low- or high-angle) GB. Within this model, the two FBE solutions give rise to two possible modes of coupled GB motion which for the same GB under the same stress differ in direction of motion. Using molecular dynamics simulations we confirm our model. We find positive and/or negative coupled GB motion for all misorientation angles, and the model gives accurate predictions for the shear produced even by high-angle GBs where individual dislocations cannot be resolved. At low temperatures dual behaviour is observed for the same high-angle GB and applied stress: both coupling modes are found with a switch between them after some time. This switch signifies a change in the effective dislocation content. Dual behaviour indicates that both solutions for the dislocation content can be meaningful for the same GB. At higher temperatures only one mode is seen for each GB under the same shear stress, and the switch between the two modes seems to occur discontinuously at some high misorientation angle.