Grain boundary structure and migration in graphene via the displacement shift complete lattice

Abstract We describe grain boundary structure and migration in graphene using the concept of dislocations in the displacement shift complete lattice. The equivalence of displacement shift complete lattice dislocations and grain boundary kinks in graphene is shown both topologically and energetically. Topologically, a grain boundary kink and a displacement shift complete lattice dislocation both translate the coincident site lattice. The energetic equivalence is established through comparison of atomistic and continuum elasticity models of metastable states to show that DSC dislocations are well-described by elasticity theory. The continuum results are fitted to the atomistic results with one adjustable parameter, the DSC dislocation core radius. The atomistic results reveal that low sigma boundaries have large energy barriers to grain boundary motion, which match continuum results obtained for smaller core radii dislocations. The larger energy barriers for low sigma boundaries are consistent with experimental results reporting isolated, low sigma boundaries in grown graphene. The trends in the dislocation Burgers vector and fitted core radii across grain boundaries of different misorientation are expressed in a unified model. The analysis provides a framework for understanding grain boundary motion in graphene and can serve as a basis for engineering the atomic structure of graphene.