What are grain boundary structures in graphene?

We have developed a new global optimization method for the determination of the interface structure based on the differential evolution algorithm. Here, we applied this method to search for the ground state atomic structures of the grain boundary (GB) between armchair and zigzag oriented graphene. We find two new grain boundary structures with a considerably lower formation energy of about 1 eV nm(-1) than those of the previously widely used structural models. We also systematically investigate the symmetric GBs with the GB angle ranging from 0° to 60°, and find some new GB structures. Surprisingly, for an intermediate GB angle, the formation energy does not depend monotonically on the defect concentration. We also discovered an interesting linear relationship between the GB density and the GB angle. Our new method provides an important novel route for the determination of GB structures and other interface structures, and our comprehensive study on GB structures could provide new structural information and guidelines to this area.