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Several experiments have revealed the presence of grain boundaries in graphene that may change its electronic and elastic properties. Here, we present a general theory for the structure of [0001] tilt grain boundaries in graphene based on the coincidence site lattice (CSL) theory. We show that the CSL theory uniquely classifies the grain boundaries in terms of the misorientation angle θ and periodicity d using two grain-boundary indices (m,n), similar to the nanotube indices. The structure and formation energy of a large set of grain boundaries generated by the CSL theory for 0 ◦ 32.2 ◦ ,o ther nonhexagonal rings are also possible. We discuss the importance of these findings for the interpretation of recent experimental results.

Theory and hierarchical calculations of the structure and energetics of [0001] tilt grain boundaries in graphene