Structures and electronic properties of symmetric and nonsymmetric graphene grain boundaries

The graphene grain boundaries with periodic length up to 18 Å have been studied using density functional theory. Atomic structures, thermodynamic stabilities and electronic properties of 40 grain boundaries with symmetric and nonsymmetric structures were investigated. According to the arrangements of pentagons and heptagons on the boundary, grain boundaries were cataloged into four classes. Some nonsymmetric grain boundaries constructed here have identical misorientation angles to the experimentally observed ones. The formation energies of grain boundaries can be correlated with the misorientation angle and inflection angle. Nonsymmetric grain boundaries possess comparable formation energies to their symmetric counterparts when the periodic length along the defect line is larger than 1 nm. Analysis of electronic density of states shows that the existence of a grain boundary usually increases the density of states near the Fermi level, whereas some symmetric grain boundaries can open a small band gap due to local sp2-to-sp3 rehybridization.