Non-equilibrium grain boundaries with excess energy in graphene

Exploring an approach to grain boundary (GB) mesoscopic structure in 3D polycrystals, we develop a model description for equilibrium and non-equilibrium states of GBs in graphene. Non-equilibrium states of GBs in graphene are analyzed for the first time. On the base of this model, dependence of total energy for symmetric GBs on the misorientation angle, E(θ), in graphene was calculated. It was found that for the same average misorientation angle the energy in a non-equilibrium state of a GB in graphene can significantly exceed the energy in the equilibrium state. In graphene, the GB energy depends to a greater extent on the deviation from the equilibrium state than on the misorientation angle. It is proposed to account for the presence of non-equilibrium GBs in the explanations of unusual physical properties of graphene.