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^{1,a)}, Euijoon Yoon

^{1,2}, Nong-Moon Hwang

^{1}, Cai-Zhuang Wang

^{3}and Kai-Ming Ho

^{3}

### Abstract

The formation and development processes of dislocation in graphene are investigated by performing tight-binding molecular dynamics (TBMD) simulation and * ab initio * total energy calculation. It is found that the coalescence of pentagon-heptagon (5-7) pairs with vacancy defects induces the formation of dislocation due to the separation of two 5-7 pairs. In TBMD simulations, adatoms are ejected and evaporated from graphene surface so that the dislocation is developed. It is observed that diffusing carbon atoms nearby dangling bonds help non-hexagonal rings change into stable hexagonal rings. These results might give some ideas for the control of structural properties by inducing defect structures.

This work was supported by Basic Science Research Program (Nos. 2012-003007 and 2012-0000904), and by BK21 and WCU program (R31-2008-000-10075-0) through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology. The authors also acknowledge the support from KISTI under the Strategic Supercomputing Applications Support Program (KSC-2011-C2-02). Work at Ames Laboratory was supported by the US Department of Energy, Basic Energy Sciences, Division of Materials Science and Engineering, including a grant of computer time at the National Energy Research Supercomputing Centre (NERSC) in Berkeley, CA under Contract No. DE-AC02-07CH11358.

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## Figures

Snapshots from the TBMD simulation for development into dislocation from vacancy defects. (a) ∼3000 K (*t* = 2.0 ps), (b) ∼4400 K (*t* = 41.3 ps), (c) ∼4300 K (*t* = 52.7 ps), (d) ∼4500 K (*t* = 111.5 ps), (e) ∼4600 K (*t* = 115.7 ps), (f) ∼4500 K (*t* = 122.8 ps), (g) ∼4400 K (*t* = 149.5 ps), (h) ∼4500 K (*t* = 176.9 ps). The yellow and red colors indicate carbon atoms and bonds on hexagonal rings and non-hexagonal rings, respectively. The blue solid circles indicate carbon atoms with dangling bonds and the green solid circles and dotted circles in (e) and (g) indicate evaporated carbon atoms. In (h), the dashed lines are connecting atoms on zigzag structure and the abscission of solid lines at each 5-7 pair indicates the existence of dislocation with a missing zigzag line. Alphabets A and B indicate the first and second single vacancy approaching the V_{2} (5-7-7-5).

Snapshots from the TBMD simulation for development into dislocation from vacancy defects. (a) ∼3000 K (*t* = 2.0 ps), (b) ∼4400 K (*t* = 41.3 ps), (c) ∼4300 K (*t* = 52.7 ps), (d) ∼4500 K (*t* = 111.5 ps), (e) ∼4600 K (*t* = 115.7 ps), (f) ∼4500 K (*t* = 122.8 ps), (g) ∼4400 K (*t* = 149.5 ps), (h) ∼4500 K (*t* = 176.9 ps). The yellow and red colors indicate carbon atoms and bonds on hexagonal rings and non-hexagonal rings, respectively. The blue solid circles indicate carbon atoms with dangling bonds and the green solid circles and dotted circles in (e) and (g) indicate evaporated carbon atoms. In (h), the dashed lines are connecting atoms on zigzag structure and the abscission of solid lines at each 5-7 pair indicates the existence of dislocation with a missing zigzag line. Alphabets A and B indicate the first and second single vacancy approaching the V_{2} (5-7-7-5).

Snapshots from TBMD simulations for ejection and evaporation of an adatom during the development into dislocation. (a) ∼4500 K (Δ*t* = 0.0 ps) ((a) corresponds to Fig. 1(d) and Δ*t* is the elapsed time from (a)), (b) ∼4600 K (Δ*t* = 1.8 ps), (c)∼4400 K (Δ*t* = 2.2 ps), (d) ∼4500 K (Δ*t* = 3.7 ps). (e) ∼4600 K (Δ*t* = 3.9 ps), (f) ∼4600 K (Δ*t* = 4.2 ps). The yellow and red colors indicate carbon atoms and bonds on hexagonal rings and non-hexagonal rings, respectively. The blue colors indicate carbon atoms with dangling bonds and the green color and dotted circle in (f) indicate an evaporated carbon atom (see supplementary materials for Video S1). ^{ 29 }

Snapshots from TBMD simulations for ejection and evaporation of an adatom during the development into dislocation. (a) ∼4500 K (Δ*t* = 0.0 ps) ((a) corresponds to Fig. 1(d) and Δ*t* is the elapsed time from (a)), (b) ∼4600 K (Δ*t* = 1.8 ps), (c)∼4400 K (Δ*t* = 2.2 ps), (d) ∼4500 K (Δ*t* = 3.7 ps). (e) ∼4600 K (Δ*t* = 3.9 ps), (f) ∼4600 K (Δ*t* = 4.2 ps). The yellow and red colors indicate carbon atoms and bonds on hexagonal rings and non-hexagonal rings, respectively. The blue colors indicate carbon atoms with dangling bonds and the green color and dotted circle in (f) indicate an evaporated carbon atom (see supplementary materials for Video S1). ^{ 29 }

Atomic trajectories in “adatom-ejection” mechanism from *ab initio* calculation. ((a)-(c), left: top view, right: front view) and formation energies relative to pristine graphene by *ab initio* calculation for principal intermediated structures in our TBMD simulation (d). The yellow and red colors indicate atoms and bonds on hexagonal rings and non-hexagonal rings, respectively, and the blue colors indicate trajectories of adatom formed in “adatom-ejection” mechanism. A-C in (d) correspond to the configurations of four separated single vacancy defects (A), V_{2} (5-7-7-5) and two separated single vacancy defects (Fig. 1(a) ) (B), and V_{4} (5-7-7-5) (Fig. 1(d) ) (C), respectively. D-F in (d) correspond to structures in (a), (b), and (c) of this figure, respectively. G, H, and I in (d) correspond to the structures in Figs. 1(e) , 1(g) , and 1(h) , respectively. Inset in (d) shows the enlarged curve from D to F.

Atomic trajectories in “adatom-ejection” mechanism from *ab initio* calculation. ((a)-(c), left: top view, right: front view) and formation energies relative to pristine graphene by *ab initio* calculation for principal intermediated structures in our TBMD simulation (d). The yellow and red colors indicate atoms and bonds on hexagonal rings and non-hexagonal rings, respectively, and the blue colors indicate trajectories of adatom formed in “adatom-ejection” mechanism. A-C in (d) correspond to the configurations of four separated single vacancy defects (A), V_{2} (5-7-7-5) and two separated single vacancy defects (Fig. 1(a) ) (B), and V_{4} (5-7-7-5) (Fig. 1(d) ) (C), respectively. D-F in (d) correspond to structures in (a), (b), and (c) of this figure, respectively. G, H, and I in (d) correspond to the structures in Figs. 1(e) , 1(g) , and 1(h) , respectively. Inset in (d) shows the enlarged curve from D to F.

Snapshots from TBMD simulations for non-hexagonal to hexagonal ring transition by diffusion of carbon atoms near the dangling bonds. (a) ∼4600 K ((*t* = 145.9 ps, Δ*t* = 0.0 ps) (*t* is the total simulation time and Δ*t* is the elapsed time from (a)), (b) ∼4600 K (Δ*t* = 0.7 ps), (c) ∼4500 K (Δ*t* = 1.0 ps), (d) ∼4400 K (Δ*t* = 2.2 ps), (e) ∼4600 K (Δ*t* = 2.3 ps), (f) ∼4300 K (Δ*t* = 2.6 ps), (g) ∼ 4600 K (Δ*t* = 3.0 ps), (h) ∼4500 K (Δ*t* = 3.7 ps). The yellow and red colors indicate carbon atoms on hexagonal rings and non-hexagonal rings, respectively. The blue colors indicate atoms with dangling bonds and the green color and dotted circle in (h) indicate an evaporated carbon atom (see supplementary materials for Video S2). ^{ 29 }

Snapshots from TBMD simulations for non-hexagonal to hexagonal ring transition by diffusion of carbon atoms near the dangling bonds. (a) ∼4600 K ((*t* = 145.9 ps, Δ*t* = 0.0 ps) (*t* is the total simulation time and Δ*t* is the elapsed time from (a)), (b) ∼4600 K (Δ*t* = 0.7 ps), (c) ∼4500 K (Δ*t* = 1.0 ps), (d) ∼4400 K (Δ*t* = 2.2 ps), (e) ∼4600 K (Δ*t* = 2.3 ps), (f) ∼4300 K (Δ*t* = 2.6 ps), (g) ∼ 4600 K (Δ*t* = 3.0 ps), (h) ∼4500 K (Δ*t* = 3.7 ps). The yellow and red colors indicate carbon atoms on hexagonal rings and non-hexagonal rings, respectively. The blue colors indicate atoms with dangling bonds and the green color and dotted circle in (h) indicate an evaporated carbon atom (see supplementary materials for Video S2). ^{ 29 }

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