The favourable large misorientation angle grain boundaries in graphene

A grain boundary (GB) in graphene is a linear defect between two specifically oriented graphene edges, whose title angles are denoted as θ1 and θ2, respectively. Here we present a systematic theoretical study on the structure and stability of GBs in graphene as a function of the misorientation angle, Φ = (θ1 - θ2) and the GB orientation in multi-crystalline graphene, which is denoted by Θ = (θ1 + θ2). It is surprising that although the number of disorders of the GB, i.e., the pentagon-heptagon pairs (5-7s), reaches the maximum at Φ ∼ 30°, the GB formation energy versus the Φ curve reaches a local minimum. The subsequent M-shape of the Efvs. the Φ curve is due to the strong cancellation of the local strains around 5-7 pairs by the "head-to-tail" formation. This study successfully explains many previously observed experimental puzzles, such as the multimodal distribution of GBs and the abundance of GB misorientation angles of ∼30°. Besides, this study also showed that the formation energy of GBs is less sensitive to Θ, although the twin boundaries are slightly more stable than others.