PHYSICAL REVIEW B 84, 075445 (2011) Dynamics and stability of divacancy defects in graphene Youngkuk Kim, 1 Jisoon Ihm, 1 Euijoon Yoon, 2,3,4,5 and Gun-Do Lee 2,* 1 Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Republic of Korea 2 Department of Materials Science and Engineering, Seoul National University, Seoul 151-742, Republic of Korea 3 Department of Nano Science and Technology, Graduate School of Convergence Science and Technology, Seoul National University, Suwon 433-270, Republic of Korea 4 Department of Materials Science and Engineering, WCU Hybrid Materials Program, Seoul National University, Seoul 151-742, Republic of Korea 5 Energy Semiconductor Research Center, Advanced Institutes of Convergence Technology, Seoul National University, Suwon 443-270, Korea (Received 4 May 2011; published 10 August 2011) A divacancy (DV) is one of the most abundant and most important defects in irradiated graphene, which modifies electronic and chemical properties of graphene. In this paper, we present ab initio calculations to study the dynamics and stability of DVs in graphene. Divacancies in graphene have various reconstructed structures, such as triple pentagon-triple heptagon (555-777) and pentagon-octagon-pentagon (5-8-5) patterns. A direct observation of the structural transformations between these reconstructions was recorded in transmission electron microscope images reported by Girit et al. in Science 323, 1705 (2009). We clarify the atomic structures of DVs observed in the experiment and investigate the atomic processes and energetics for the observed dynamical motions in great detail. It is found that a series of Stone–Wales-type transformations are responsible for the migration and structural transformations of DVs and that a pentagon-heptagon-heptagon-pentagon (5-7-7-5) defect appearing as an intermediate structure during the dynamical process plays an important role in the transformations of DVs. DOI: 10.1103/PhysRevB.84.075445 PACS number(s): 61.48.Gh, 31.15.A−, 61.72.jd I. INTRODUCTION Since the first realization of graphene, 1–3 tremendous efforts have been made to explore its physical properties as well as the potential applications in industries. Unique properties of graphene, such as ultrahigh electron mobility, 2,4,5 high thermal conductivity, 6 and extreme mechanical properties, 7 have been examined, and it is now widely accepted that graphene is one of the most promising materials for future electronic devices. Another exciting aspect of graphene-based materials is that their exotic properties can be enriched by atomic-scale defects engineering. 8–12 Defects engineering of graphene can enor- mously extend the scope of applications, making graphene- based industry more plausible and promising. Indeed, chem- ical modifications, for example, by molecular doping 13–15 or functionalization, 16,17 are popularly suggested, and producing atomic vacancies by ionic irradiations 18,19 is also a promising way to modify properties of graphene. In particular, recently developed high-resolution transmission electron microscopy (TEM) is very useful to prove carbon-based materials. Since electron irradiation is a highly effective method to introduce various types of structural defects in graphene, many TEM studies are reported on defective graphene systems. 20,21 For example, a recent TEM study by Cretu et al. 22 has shown that the graphene properties can be tailored by reconstructed point defects. They have pointed out the importance of divacancies (DVs) due to their abundance at room temperature. The existence of DVs has also been predicted by other theoretical calculations showing the formation energy is lower than that of two isolated monovacancies (MVs), 23,24 and the MVs have a tendency to coalesce to a DV. 24,25 Recently, Girit et al. has reported the real-time dynamics of carbon atoms in defected graphene using the aberration- corrected TEM technique. 26 The subatomic resolution of the TEM images allows the direct observation of carbon atoms in graphene and provides clear images depicting the edge structure of graphene. Furthermore, the TEM images from the supplementary movie S1 (“the TEM images” from now on) in the report happen to show various structural forms of DVs and their dynamics. These contain crucial clues to understanding the structural change of DVs. Since the dynamics of DVs and their possible control are critical issues for graphene applications, we perform first-principles calculations in this paper to provide plausible explanations for the stability and dynamics of the DV. We first inspect the movie S1 and choose eight consecutive frames in which we presume that important information for the dynamics of DVs is recorded. Then we analyze those frames manifesting their atomic structures. Using ab initio computational methods, we investigate energetically favorable diffusion pathways corresponding to the dynamics observed in the frames and provide associated energy barriers. The microscopic mechanism is also provided for various types of migrations of triple pentagon-triple heptagon (555-777) and pentagon-octagon-pentagon (5-8-5) defects. Our results show 555-777 and 5-8-5 defects can migrate and rotate in the graphene plane through a sequence of Stone–Wales (SW)-type transformations. Since a specific motion of DVs has its own mechanism with distinct energy barriers, there exists a possibility to control the types of DVs produced depending on the energy of incident electrons in a TEM experiment. 27 II. COMPUTATIONAL METHOD The ab initio total energy calculations are performed with the plane-wave-basis-set VASP code 28 using a rectangular periodic supercell containing 126 carbon atoms with a single DV. The plane-wave basis is used with a kinetic energy cutoff of 400 eV. We use projector augmented wave (PAW) 075445-1 1098-0121/2011/84(7)/075445(5) ©2011 American Physical Society