First principles calculations, employed to address the properties of polycrystalline graphene, indicate that the electronic structure of tilt grain boundaries in this system displays a rather complex evolution toward graphene bulk, as the tilt angle decreases, with the generation of a Dirac point, at the Fermi level, that lies not on the usual graphene Brillouin zone $\mathbf{K}$ point, and an anisotropic Dirac cone of low-energy excitations. Moreover, the usual $\mathbf{K}$-point Dirac cone falls below the Fermi level, and rises toward it as the tilt angle decreases. Further, our calculations indicate that the grain-boundary formation energy behaves nonmonotonically with the tilt angle, due to a change in the spatial distribution and relative contributions of the bond-stretching and bond-bending deformations associated with the formation of the defect.

• Received 17 November 2009

DOI:https://doi.org/10.1103/PhysRevB.81.073408