Nature of localized phonon modes of tilt grain boundaries in graphene

Pattern of atomic displacements for localized phonon modes in polycrystalline graphene. Left: geometries of (a) translational grain boundaries GB(2,0)|(2,0); tilt grain boundaries: (b) GB(2,1)|(1,2); (c) (3,2)|(2,3); GB(4,3)|(3,4). Right: pattern of atomic displacements for high-frequency localized phonon modes, showing strong localization in the grain boundary core (positioned at the origin), in the tilt grain boundaries.419