Dynamics and stability of divacancy defects in graphene

Youngkuk Kim, Jisoon Ihm, Euijoon Yoon, and Gun-Do Lee

Phys. Rev. B 84, 075445 – Published 10 August 2011

Abstract

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.

Received 4 May 2011

DOI:https://doi.org/10.1103/PhysRevB.84.075445

Authors & Affiliations

Youngkuk Kim¹, Jisoon Ihm¹, Euijoon Yoon^2,3,4,5, and Gun-Do Lee^2,*

¹Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Republic of Korea
²Department of Materials Science and Engineering, Seoul National University, Seoul 151-742, Republic of Korea
³Department of Nano Science and Technology, Graduate School of Convergence Science and Technology, Seoul National University, Suwon 433-270, Republic of Korea
⁴Department of Materials Science and Engineering, WCU Hybrid Materials Program, Seoul National University, Seoul 151-742, Republic of Korea
⁵Energy Semiconductor Research Center, Advanced Institutes of Convergence Technology, Seoul National University, Suwon 443-270, Korea

^*Corresponding author: gdlee@snu.ac.kr

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Vol. 84, Iss. 7 — 15 August 2011

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Images

Figure 1
Aberration-corrected TEM images of DVs in a single-layer graphene reported in supplementary movie S1 of Ref. 26. (a) The fifth frame of the movie S1. The rectangular (red) region contains a single DV and shows various DV reconstructions. The magnified images in this region for eight consecutive frames are drawn in (b)–(i). (b) The rectangular region in the fifth frame. This frame contains a triple pentagon and triple heptagon (555-777) defect. (c) The same rectangular region of the sixth frame. (d) The seventh frame in which the 555-777 defect structure is restored. (e) The eighth frame, which captures an intermediate stage between two 555-777 defects in (d) and (f). (f) A 555-777 defect rotated by 60° with respect to the 555-777 defect in (d). (g)–(i) The 10th–12th frames. Theses frames contain a record of a single pentagon-octagon-pentagon defect (5-8-5) migration. Dashed circles in (g)–(i) are shifted one hexagon unit to the left compared to solid circles in (b)–(f) to highlight the migration of the 5-8-5 defect. Printed with the kind permission of the authors of Ref. 26.Reuse & Permissions
Figure 2
Atomic structures of DV reconstructions (a)–(d), printed with the kind permission of the authors of Ref. 26 (bars and dots are added by us for visual help), and the corresponding simulated total charge density plots (e)–(h). (a) 555-777 defect corresponding to Fig. 1b. (b) 5-8-5 defect corresponding to Fig. 1i. (c) 5-8-5 defect with dangling bonds corresponding to Fig. 1g. (d) 555-777 defect with the tilted carbon dimer [corresponding to Fig. 1c] indicated by the two (red) arrows compared to (a). Solid (blue) bars and dots indicate their structural models. (e)–(h) Simulated total charge density plots from ab initio calculations for structural models of (a)–(d), respectively.Reuse & Permissions
Figure 3
Microscopic atomic process for the rotational motion of a 555-777 defect. (a) 555-777 defect. (b) 5-8-5 defect. (c) 5-7-7-5 defect. (d) 5-8-5 defect. (e) 555-777 defect. (f) The charge density plot obtained by averaging the three intermediate structures, (b)–(d). (g) Energy barriers for this process and formation energies relative to the 555-777 defect. Atomic structures shown in (b)–(e) can be obtained by a SW transformation of the dark (red) dimer shown in (a)–(d), respectively.Reuse & Permissions
Figure 4
Microscopic atomic process for the migration of a 5-8-5 defect. (a) 5-8-5 defect corresponding to the TEM image in Fig. 1g. (b) 5-7-7-5 defect. (c) 5-7-7-5 defect. (d) 5-8-5 defect. The atomic structure in (d) corresponds to the atomic assignment of Fig 1i. Dark (red) dimer in each figure is the part which undergoes an SW-type transformation. (e) Superposition of the atomic structures, (a)–(d). (f) The simulated total charge density plot obtained by averaging the four structures, (a)–(d). (g) Schematic diagram representing energy barriers for the 5-8-5 migration from (a) to (d) and formation energies relative to the 555-777 defect.Reuse & Permissions

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