Thermal stability of graphene edge structure and graphene nanoflakes

One of the most exciting recent developments in nanoscience was the discovery of graphene (single sheets of carbon atoms, a two-dimensional "(2D) crystal") and the subsequent discovery of the fascinating properties of this new material, e.g., electrons behaving as massless relativistic particles and an anomalous quantum Hall effect [A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 (2007)]. It is also surprising that large sheets of graphene exist as it was widely believed that 2D crystals are unstable. Furthermore, because of the stability of folded graphene sheets, i.e., carbon nanotubes (CNTs), a fascinating question is why does not graphene spontaneously transform into CNTs? In this paper, we explore the thermal stability of small pieces of graphene, i.e., graphene nanoflakes by ab initio quantum mechanical techniques. We find that indeed nanoflakes are stable to being heated and do not under any conditions used here transform to CNTs. They do not, however, remain strictly 2D as at finite temperatures, they undergo extensive vibrational motion and remain buckled if annealed and then quenched to room temperature.