Out-of-plane path of the Stone-Wales transformation in graphene

Recently it has been realized that Stone-Wales (SW) defects in graphene are not simple two-dimensional objects but rather involve large vertical displacements of many atoms, resulting in a sinelike shape of the cross section [J. Ma et al., 2009 [11]]. Customarily, formation of sinelike SW defects is assumed to take place in two steps: 1) an in-plane 90° rotation of two carbon atoms with respect to the center of the C-C bond and 2) transverse shift of those atoms in the opposite direction. Here we show that there is another transformation path that does not go through a flat defect configuration. Following that path results in lower energy barriers for both formation and annealing of sinelike SW defects.