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 theta(1) and theta(2), respectively. Here we present a systematic theoretical study on the structure and stability of GBs in graphene as a function of the misorientation angle, Phi = (theta(1) - theta(2)) and the GB orientation in multi-crystalline graphene, which is denoted by Theta = (theta(1) + theta(2)). It is surprising that although the number of disorders of the GB, i.e., the pentagon-heptagon pairs (5 vertical bar 7s), reaches the maximum at Phi similar to 30 degrees, the GB formation energy versus the Phi curve reaches a local minimum. The subsequent M-shape of the E-f vs. the Phi curve is due to the strong cancellation of the local strains around 5 vertical bar 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 similar to 30 degrees. Besides, this study also showed that the formation energy of GBs is less sensitive to Theta, although the twin boundaries are slightly more stable than others.