Modification of Defect Structures in Graphene by Electron Irradiation

Article pubs.acs.org/JPCC

Modification of Defect Structures in Graphene by Electron Irradiation: Ab Initio Molecular Dynamics Simulations Zhiguo Wang,*,†,‡ Y.G. Zhou,† Junhyeok Bang,§ M.P. Prange,‡ S.B. Zhang,§ and Fei Gao*,‡ †

Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu, 610054, Peopleʼs Republic of China ‡ Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, United States § Department of Physics, Applied Physics & Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, United States ABSTRACT: Defects play an important role on the unique properties of the sp2-bonded materials, such as graphene. The creation and evolution of monovacancy, divacancy, Stone-Wales (SW), and grain boundaries (GBs) under irradiation in graphene are investigated using density functional theory and time-dependent density functional theory molecular dynamics simulations. It is of great interest that the patterns of these defects can be controlled through electron irradiation. The SW defects can be created by electron irradiation with energy above the displacement threshold energy (Td, ∼19 eV) and can be healed with an energy (14−18 eV) lower than Td. The transformation between four types of divacanciesV2(5−8−5), V2(555−777), V2(5555−6−7777), and V2(55−77)can be realized through bond rotation induced by electron irradiation. The migrations of divancancies, SW defects, and GBs can also be controlled by electron irradiation. Thus, electron irradiation can serve as an important tool to modify morphology in a controllable manner and to tailor the physical properties of graphene.

1. INTRODUCTION Graphene has been attracting much attention because of its fascinating properties, such as extremely high mobility, high elasticity, quantum electronic transport, and electromechanical modulation. These properties demonstrate the potential application of graphene in future solid devices providing an alternative to traditional silicon semiconductors.1−3 Although perfect graphene has shown outstanding electronic phenomena such as ballistic electron propagation3 and the quantum Hall effect4 at room temperature, the absence of a band gap in the perfect graphene does not allow switching of graphene-based transistors with a high on−off ratio. Hence, tailoring the electronic properties by means of defects, adatoms, and geometrical confinement is crucial in order to realize graphene as a competitive material for future electronics. Molecular doping of NO2 and N2O2 induces p-type behavior in graphene.5 By carving graphene, one-dimensional graphene nanoribbons have been realized3 with nonzero band gaps. Defects, such as nonhexagonal rings in the carbon lattice, are more attractive than adatoms since such defects are more physically stable than gases absorbed on graphene.6 These structural defects can be deliberately introduced by irradiation or chemical treatments. Experimental results of ion-irradiated graphene suggest that the lattice defects can be considered as a potential source of intervalley scattering, which could in principle transform graphene from a metal into an insulator.7 Jafri et al.8 showed that the conductivity of graphene increases by more than 1 order © 2012 American Chemical Society

of magnitude by introducing defects using wet chemistry methods. Furthermore, a theoretical study by Wang and Pantelides9 showed that it may be possible to incorporate nitrogen into defected graphene at vacancy sites, which may be an efficient way of doping graphene. It was also theoretically shown that vacancies can induce two-dimensional magnetic order in grahpene,10 which was confirmed by the experimental observation of proton-bombarded graphite.11 There exist two types of intrinsic defects in graphene, that is, point defect (such as Stone-Wales defect,12 monovacancy, divancancy) and line defects (such as domain boundary13 and grain boundary (GB)14). The typical defect structures in graphene are shown in Figure 1. A monovacancy is created by simply removing one carbon atom, which leads to a V1(5−9) defect structure in which one dangling bond remains in the middle of the nine-membered carbon ring. After removing the undercoordinated atom of a monovacancy, a new bond is formed between the two new undercoordinated atoms, and a V2(5−8− 5) defect is created, which is conventionally considered as a divacancy. A divacancy can also be created by the coalescence of two monovacancies,15 where no dangling bond presents in a fully reconstructed V2(5−8−5) divacancy. The SW defect is one of the most common defects created by rotating a C−C bond by Received: April 23, 2012 Revised: July 1, 2012 Published: July 9, 2012 16070

dx.doi.org/10.1021/jp303905u | J. Phys. Chem. C 2012, 116, 16070−16079

The Journal of Physical Chemistry C

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tunneling microscope. Grantab et al.31 using atomistic simulation showed that graphene with large-angle-tilt GBs composed of an array of defects is as strong as pristine graphene and is much stronger than the ones with small-angle boundaries. Experimental results demonstrated that GBs can be seen as a potential source of intervalley scattering, which can reduce the electrical conductivity of graphene.32 The fascinating properties of graphene can be affected by these defects that are unavoidable formed during device fabrication. For example, graphene characterization and device fabrication often require an extensive use of scanning electron microscopy, transmission electron microscopy, and focused ion beam processing. Both electron and ion beams can be focused onto an area in several nanometers, which makes it possible to control the pattern of these defects.33,34 As the typical time between the particle impacts onto the same area is normally much longer than the typical time during which the extra energy is dissipated into other regions, one can neglect the temporal correlation between collision events and consider the initial damage from the impacts of energetic particles one by one.35 Thus, electron irradiation can be used as an effective method to modify the structure on graphene practically. In fact, the electron irradiation has been successfully used to modify the graphene properties36 and edge morphology in graphene layers37 experimentally. The possibility for selectively creating topological defects consisting of agglomerations of nonhexagonal rings could be more desirable in the context of carbon-based electronics.13,28 Recent improvement in transmission electron microscopy (TEM) techniques has shown the possibility of directly imaging the defective structures in graphene and of monitoring their evolution over time.21,38 In this paper, the creation and evolution of defects under electron irradiation were extensively studied using DFT and time-dependent DFT (TDDFT) molecular dynamics; we show how to control the pattern of defects in graphene by irradiation.

Figure 1. Atomistic configurations of monovacancy, divacancy, SW defects, and GBs in graphene.

90° resulting in the transformation of four hexagons into two pentagons and two heptagons around the two-bond-rotated atoms.12 Once a SW defect is formed, the pentagon/heptagons could move along the structure creating dislocation centers in the regions of positive (pentagons) and negative (heptagons) Gaussian curvature of the deformed graphene sheet. The curvature ultimately leads to the closing of nanostructure graphene.16,17 The study of vacancy-like defects in graphene suggested that single vacancy and divacancy have nearly the same formation energy18 indicating that a divacany is a more stable defect. These defects were studied in carbon nanotubes and graphene systems, where the changes in electron transport and electronic properties were discussed.19−21 SW defects have also been predicted to alter the electronic properties of graphene, to modify its chemical reactivity toward adsorbates, and to likely impact its unique transport properties.18,22,23 GBs also might change the material properties of graphene. Using chemical vapor deposition (CVD) growth technique, Lahiri et al.13 reported a graphene domain boundary between the facecentered domain and the hexagonal close packed domain on a Ni(111) surface and found that the domain boundary is metallic and can be engineered to form conducting molecular wires. Gao et al.24 reported the existence of graphene domain/grain boundaries after CVD growth on Cu(111), and they observed a decrease of the electron mobility which is caused by electron scattering at GBs. Kim et al.14 reported the direct mapping of high-angle grain boundaries composed of alternating pentagon− heptagon structures. Several attempts have been made to investigate the defects and grain boundaries in graphene using theoretical calculations. Density functional tight-binding calculations have been employed to study the structures, energies, and inflection angles of graphene grain boundaries.25 Liu and Yakobson26 used finite-temperature-annealing molecular dynamics simulations to compute graphene GBs structures and energies. Yzayev and Louie27 investigated the dislocations and GBs in graphene on the basis of dislocation theories and found that the GBs might be beneficially exploited via controlled GB engineering.28 The magnetic moments can exist at graphene GBs.29 Cockayne et al.30 using density functional theory (DFT) calculation investigated the GB loop in graphene and confirmed that the GB loop is observed as a flower pattern in scanning

2. COMPUTATIONAL METHOD All the calculations were performed using DFT within local density approximation (LDA)39 using the Ceperly-Alder parametrization as implemented in the SIESTA code,40 which adopts a linear combination of numerical localized atomic orbital basis sets for the description of valence electrons and norm-conserving nonlocal pseudopotentials for the atomic core.41 The charge density was projected on a real-space grid with a cutoff of 150 Ry to calculate the self-consistent Hamiltonian matrix elements. The pseudopotentials were constructed from four valence electrons for C atoms. Graphene contains 478 carbon atoms, but the test calculations for a larger supercell with 1342 atoms show that the 478 atom supercell is large enough to ensure localization of point defects within the unit cell. Sufficient vacuum space (3.0 nm) is assigned along the Z direction. Graphene with zigzag-oriented GBs and θ = 21.7° is investigated as shown in Figure 1. The simulation model of GBs in graphene consists of 868 carbon atoms with dimensions 5.12 × 4.67 nm.2 The initial direction of a primary recoil atom is represented by angles θ and ϕ as shown in Figure 2. After giving kinetic energy to an atom in graphene, the evolution of the system is involved using ab initio molecular dynamics (MD) method for all the atoms42 with a time step of 1.0 fs, and then, the system is further relaxed for 400 fs that is long enough for an escaping atom to return to its lattice site if no defect is created. All the simulations were initiated in the relaxed and undistorted graphene structure at 0 K. We start to search Td with recoil energy of 11 eV, and if there is no defect formation or 16071



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Similar calculation setups are used in the TDDFT simulations. Here, we have used a supercell that contains 72 atoms with 1 nm vacuum spacing along the Z direction, a time step of 24 attoseconds, and the Ehrenfest approximation. Details of the method can be found in ref 43. In Figure 2, TDDFT results have been compared with DFT results of the same supercell size.

3. RESULTS AND DISCUSSIONS 3.1. Effect of Explicit Electron Dynamics. Our results below report DFT molecular dynamics study without explicit electron dynamics. However, for fast ionic motion caused by collision with highly energetic electron beams, it is necessary to determine whether this ground-state Born−Oppenheimer dynamics is a valid approach as electrons cannot respond instantaneously to fast ionic dynamics. For this reason, we have performed molecular dynamics simulations, coupled with TDDFT, for the most prototypical systems. In particular, we study electronic energy dissipation at a kinetic energy either below or above the kinetic energy required for a primary recoil atom to permanently leave its equilibrium site and to not recover defined as displacement threshold energy Td. Our approach includes explicitly the electron dynamics. Figure 2 shows, for the case when the incident beam is normal to the graphene surface (θ = 0°), the kinetic energy evolutions for the DFT and TDDFT calculations. When a primary recoil atom is kicked off, as shown in Figure 2a for an initial energy of 24 eV, the primary recoil atom has higher kinetic energy in the TDDFT simulation than that in the DFT simulation by about 3 eV. This

Figure 2. Time evolution of the kinetic energy (K) for an initial K = (a) 24 and (b) 16 eV. Blue and black lines stand for primary recoil atom and the rest C atoms, respectively. Results by DFT are given in solid lines whereas those by TDDFT are given in dotted lines. The inset in a shows the difference of the primary recoil atom in time evolution between TDDFT and DFT at t = 60 fs with four different initial Kʼs. The arrows in b indicate phase delay due to explicit inclusion of the electron dynamics.

defect transformation occurring, the simulation will restart with higher recoil energies with an increment of 1.0 eV. For each defect transformation, Td is determined as a function of the recoil direction. This generally gives a total simulation number of 17− 25 for each case being studied and represents a greatly computational challenge beyond classical MD simulations.

Figure 3. Atomistic configuration of (a) a perfect graphene and (b) the one with SW defect. The inset shows the notations used in the computation. (c) Angular dependence of Td for perfect graphene. (d) The minimum healing energy as a function of θ and ϕ. The energy barrier as a function of rotation angle of the atom pair for the SW defect is also shown in the inset. 16072



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Figure 4. Healing process of a Stone-Wales defect upon knock-on displacement at θ = 45, ϕ = 60° with E0 = 14 eV. The top and bottom figures at each simulation time are viewed from Z and Y directions, respectively.

Figure 5. Migration of the SW defect under electron irradiation. The top and bottom figures at each simulation time are viewed from Z and Y directions, respectively.

remains inside the crystal, and the two sometimes can also recombine. In contrast, the energy transferred to graphene lattice (because of the initial impact) is small (1−2 eV for an initial energy = 24 eV) and the DFT error is also small ( 30 fs. In spite of the quantitative differences, however, qualitative trends in both simulations carry remarkable similarities. Therefore, our TDDFT simulation here justifies the use of DFT in the following discussion. 3.2. Creation of Monovacancy, Divacancy V2(5−8−5), and SW Defect. The formation energies, Ef, of defects were calculated using the equation,44 Ef = Edefect − Eperfect − nμ, where Edefect and Eperfect are the total energies of the defected and perfect supercells, respectively. μ is the chemical potential of carbon, which we took as the total energy of graphite. n is the number of carbon atoms that were added or removed. The calculated formation energies of monovacancy and SW defects are 7.78 and 4.75 eV, respectively, which agree with the reported values of 7.645 and 4.8 eV.46 The energy barrier as a function of the rotation angle of the atom pair for an SW defect is shown in the insert of Figure 3. The energy barrier is 10.2 eV above the perfect graphene or 5.4 eV above the SW defect level. We then investigated Td for graphene and the corresponding defect structures. Figure 3a and b shows the local atomic configuration of perfect and SW defects, respectively. The inset shows the notations used in the present study. The Z-axis is perpendicular to the layer of graphene, while the X- and Y-axes are along the (n, 0) and (n, n) directions, respectively. Figure 3c shows the angular dependence of Td, which is in the range of 19−23 eV. It is found that below Td, the primary recoil atom and its neighboring atoms undergo a strong vibration around their equilibrium sites and gradually come to rest. Two types of defects (monovacancy and SW defects) are found as the primary recoil atom energy, E0, equals or exceeds Td. For example, as the initial kinetic energy of the primary recoil atom is given along the Z axis, it is found that

23 eV is the minimum value to create a monovacancy, which agrees well with the value of 22.2 from other first-principle and analytical potential molecular dynamics calculations.47 However, it is slightly higher than the reported value. As the LDA functional is used in the present work for the exchange and correlation (XC) potential, we calculated the monovacancy formation energy using the generalized gradient approximations with the Perdew−Burke−Ernzerhof functional (PBE).48 The calculated value is 6.62 eV which is smaller than that obtained using LDA XC functional. This suggests that Td calculated using LDA XC functional may be slightly higher than that calculated using PBE XC functional. Fortunately, the electron threshold energy in graphene can be accurately measured, and an accurate estimation of the displacement cross section requires including the effects of lattice vibrations on the energy transferred from an electron to a target atom.49 However, the energy for the creation of an SW defect is relatively smaller and is about 19 eV, which agrees with the smaller formation energy of the SW defect. The mechanism for an SW defect formation is similar to that in SiC nanotubes.33 Further knocking on the two-coordinated C atoms of the monovacancy requires only 12 eV to create a V2(5−8−5) defect, which is roughly similar to the energy of 80 keV electron beam. Thus, monovacancy, divacancy, and SW defects can be created by electron irradiation. The creation of a single vacancy is a dominant process for the formation of a divacancy. 3.3. Healing and Migration of SW Defects. Initial kinetic energy E0 lower than the minimum Td value of 19 eV is tested in several directions to see whether the SW defects can be healed by low-energy irradiation. Simulation results show that the SW defect indeed can be healed. The minimum healing energy as a function of θ and ϕ is shown in Figure 3d. It is clearly shown that the healing energy is smaller than the Td, which suggests that the SW defects can be healed through irradiation without forming 16074



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initial recoil. The C2 atom further moves along the same direction, but the further relaxation results in the formation of the C1−C3 bond at 34 fs. This process heals the SW defect at 51 fs. However, it is clearly seen that a local curvature also appears, and the further structure relaxation recovers the local curvature after 400 fs resulting in a perfect graphene. To form an SW defect in graphene, an energy barrier should be overcome. As the energy of graphene with an SW defect is higher than that of perfect ones, a lower energy barrier is needed to overcome for the recovery of the SW defect, and the electron energy of healing the SW defect is generally smaller than that of the formation of the SW defect. The SW defect can also migrate under electron irradiation; however, the energy and initial direction of the knock-on atom should be well controlled. The SW defect can migrate at θ = 45 or 60°, ϕ = 30° with a recoil energy E0 = 19−20 eV (case I), but at θ = 45°, ϕ = 60° with a recoil energy E0 = 18 eV (case II). For case I, the healing energy (19 eV) is the same as Td (19 eV) along these directions, but for case II, the healing energy (18 eV) is smaller than Td (20 eV) along this direction. The migration process is similar for the two cases. Figure 5 shows the migration process at θ = 45°, ϕ = 60° with E0 = 18 eV. The recoil atom moves along the initial direction at the first stage, and the bond 2−3 breaks at 8 fs. At 30 fs, the recoil atom moves out of the graphene layer, a bond 1−3 forms, and the heptagon at the left transforms to the hexagon. With further relaxation, new pentagons/heptagons form at 75 fs, but the SW defect rotates 45° compared to the initial position. After relaxation for 400 fs, the atom 2 is knocked for the second time (at θ = 45°, ϕ = 120° with E0 = 18 eV), and the same process occurs, resulting in the SW defect rotation again. Compared with the structure at 0 fs, it is clearly shown that the SW defect can migrate under electron irradiation, and thus, it is expected that the position of SW defects can be precisely controlled though irradiation. 3.4. Relative Stability of V2 Defects. As shown in Figure 6, a V2(5−8−5) is not only a configuration to accommodate two missing atoms in graphene. In fact, the V2(5−8−5) is not even an energetically favored defect. The rotation of one bond (circled by a green ellipse or a red ellipse) in the octagon of the V2(5−8−5) defect leads to the arrangement of three pentagons and three heptagons forming a V2(555−777) or two pentagons and two heptagons forming a V2(55−77), respectively. One step further would transform the V2(555−777) into a V2(5555−6−7777) defect by rotating the bond circled by the blue ellipse. However, the barrier for bond rotation from the V2(5−8−5) to the V2(555−777) is previously estimated to be at least 4−10 eV,50 and thus, temperatures higher than 3000 K would be needed to initiate the transformation. In the case of graphene, an ab initio study of defects indicated that a V2(555−777) is more stable than a V2(5−8−5) by a value of 0.9 eV,51 whereas the V2(5−8−5) is more stable than the V2(555−777) in carbon nanotube that is due to the tube curvature.19 Our calculations show that the stability of these four types of divacancy defects follows the order of V2(555−777) > V2(5555−6−7777) > V2(5−8−5) > V2(55− 77). 3.5. Transformation of V2(5−8−5) Defect under Irradiation. As the V2(5−8−5) defect is not the most energetically favored defect, it may transform into other divacancy structures especially under electron irradiation. However, the energy barrier for bond rotation from the V2(5− 8−5) to the V2(555−777) is estimated to be at least 4−10 eV,50 and thus, it excludes thermally activated transformation at room temperature but can be activated by irradiation. Indeed, it has been observed that the defect structures of divacancies can

Figure 7. (a) Threshold displacement energy and (b) the corresponding divacancy structures. Typical transformations of V2(5−8−5) to V2(555−777) and V2(5−8−5) to V2(55−77) and V2(5−8−5) migration under irradiation, where the primary recoil atom is denoted by a white circle.

new defects. All the Td and healing energy are evaluated for the SW defect in perfect graphene but may have lower values at a location near a defect. This agrees with that fact that the Td for the carbon atoms at GBs is smaller than that in perfect graphene (see discussion in section 3.9). The healing energy exhibits anisotropic behavior depending on the direction of the initial momentum of the atom, which ranges from 13 to 19 eV. The smallest value is about 13 eV at ϕ = 60°. The healing energy increases with the increasing ϕ from 60 to 120°. From Figure 3b, we can see that ϕ = 60° is the direct orientation for the rotated C−C bond to recover its perfect position. The healing process of an SW defect is an inverse process of its formation during irradiation, which involves the bond breaking and rotation of the C−C bond. Figure 4 shows a typical healing process with θ = 45, ϕ = 60°, and E0 = 14 eV. Starting from an SW defect, the C2 atom moves along the orientation of the initial momentum leading to C2−C3 bond breakage at 3 fs after the 16075



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Figure 8. Threshold displacement energy for a V2(555−777) defect and the corresponding defect structure. As energy transfers to the atom circled by the white circle, no structure transformation is observed for energy lower than 22.0 eV, and as energy transfers to the atom circled by the green circle, the transformation of V2(555−777) → V2(5555−6−7777) occurs. As energy transfers to the atom circled by the red circle, the transformation of V2(555− 777) →V2(5−8−5) occurs or a vacancy is formed depending on the energy and initial orientation.

Figure 9. Threshold displacement energy for a typical transformation of V2(5555−6−7777)→V2(555−777), where the primary recoil atom is denoted by a white circle.

divacancy structures are shown in Figure 7b. Three types of evolutions of the V2(5−8−5) defect are observed under electron irradiation, that is, transformation from a V2(5−8−5) to a V2(555−777), a V2(5−8−5) to a V2(55−77), and the V2(5−8− 5) migration, and the corresponding Td is in the range between 16.0 and 22.0 eV. It can be seen from Figure 7b that the transformation probability from a V2(5−8−5) to a V2(555−777) is the highest. The smallest Td is 16 eV at θ = 60, ϕ = 90°, which is smaller than that for creating a new defect. As examples, the

convert between different configurations via bond rotation under 80 keV irradiation.21 To understand the mechanisms behind transformation, we have carried out extensive simulations of defect transformation as a function of the recoil angles searching all possible transformation paths. The maximum energy transferring to a carbon atom is set to be 22.0 eV, which is lower than that of creating a V1(5−9) defect, and thus, there is no new monovacancy being generated. Figure 7a shows the angular dependences of Td for transformation, and the corresponding 16076



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Figure 10. Threshold displacement energy for V2(55−77) defect, a vacancy of V2(55−77) defect, and transformation of V2(55−77) to V2(5−8−5).

Figure 11. Atomistic configuration of GBs after irradiation with Td for a primary recoil atom shown in Figure 1.

structure of a divacancy. As irradiation is a nonequilibrium process, the V2(555−777) defect can also be transferred into other structures under irradiation. Figure 8 shows the evolution of a V2(555−777) defect under irradiation. As the atomic arrangement of the middle atom (white circle) is the same as that of the pristine graphene, we did not find any structure transformation with θ varying from 0 to 60° and ϕ from −30 to 0° for a primary recoil atom energy less than 22.0 eV. As electron energy transfers to the carbon atom indicated by the green circle, the transformation from a V2(555−777) to a V2(5555−6−7777) occurs. The smallest energy is found to be

atomic evolutions of typical transformations from a V2(5−8−5) to a V2(555−777), a V2(5−8−5) to a V2(55−77), and the V2(5− 8−5) migration under electron irradiation are also shown in Figure 7. The primary recoil atom generally moves along the initial momentum direction, which leads to bond breaking and rebonding. The transformations from a V2(5−8−5) to a V2(555−777) and from a V2(5−8−5) to a V2(55−77) occur through bond rotation, but the V2(5−8−5) migration occurs through the bond breaking and rebonding. 3.6. Transformation of a V2(555−777) Defect under Irradiation. The V2(555−777) defect is the most stable 16077



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only 14.0 eV at θ = 60 and ϕ = 150°. As electron energy transfers to the carbon atom indicated by the red circle, the transformation from a V2(555−777) to a V2(5−8−5) occurs but with a high energy and a small probability as seen in Figure 8a and b. The relative stability of these three types of divacancies has been discussed above and is in the order of V2(555−777) > V2(5555− 6−7777) > V2(5−8−5). However, the energy difference between the V2(555−777) and the V2(5555−6−7777) is very small (∼0.08 eV), and thus, the transformation from the V2(555−777) to the V2(5555−6−7777) is much easier. On the other hand, the energy difference between the V2(555−777) and the V2(5−8−5) is relatively larger (∼0.25 eV), so that a higher energy is needed for the transformation. 3.7. Transformation of a V2(5555−6−7777) Defect under Irradiation. As discussed previously, high-resolution TEM images show that the divacancy structures can transform into each other under electron irradiation and also that these transformations can lead to the divacancy migration.38 Similar to the transformation from a V2(555−777) to a V2(5555−6− 7777), a V2(5555−6−7777) can also transform to a V2(555− 777) under electron irradiation. The evolutions of a V2(5555− 6−7777) under irradiation are shown in Figure 9. The most likely transformation is from a V2(5555−6−7777) to a V2(555−777) with the primary recoil atom energies ranging between 17.0 and 22.0 eV. There is no other structure transformation occurring even with a recoil energy of 22.0 eV, which confirms that this divacancy structure is relatively irradiation resistant. Kotakoski el al.38 have shown that the displacement threshold energy for atoms in the central part of the reconstructed defects is higher than that for perfect graphene, which explains why defect structures tend to grow into larger amorphous patches instead of collapsing into holes under continuous electron irradiation at low voltages.21 A typical transformation process at θ = 45, ϕ = 60° with E0 = 17 eV is also shown in Figure 9, and the corresponding transformation occurs with a single bond rotation. The present results strongly support the observations by Kotakoski el al.38 3.8. Transformation of a V2(55−77) Defect under Irradiation. The V2(55−77) defect is the most unstable structure of a divacancy. Figure 10 shows the displacement energy as a function of the recoil directions. A V2(55−77) defect can easily transform to a V2(5−8−5) defect with a small knock on energy for θ smaller than 10°. As θ is increased beyond 10°, a vacancy will be created. The vacancy also occurs for the V2(55− 77) defect under irradiation as shown in Figure 10, which will cause the hole formation under electron irradiation as observed by Kotakoski et al.21 3.9. Patterns of GBs in Graphene under Irradiation. There are two typical types of GBs in graphene, that is, a zigzagoriented GB consisting of pentagon/heptagons (5−7) pairs and an armchair-oriented GB composed of two diagonally opposed pentagon/heptagons (5−7−5−7) pairs.31,52 The 5−7 and 5−7− 5−7 pairs are separated by several hexagons, and the misorientation angle θ is determined by the numbers of hexagons. Sufficient vacuum space (3.0 nm) remains in the direction perpendicular to the planar of graphene. We focus on the carbon atoms near the GBs, and the inset of Figure 1 shows the six carbon atoms that are considered. The initial momentum of primary recoil atom is perpendicular to graphene. Figure 11 shows the Td and the corresponding defect pattern for the six carbon atoms in the GBs. Different defect patterns can be formed after irradiation. For examples, the C atom is ejected from the GBs and a 7−4−9 ring cluster is formed for the atom 1. For the atom 2, a 5−7−5−7−5−7 ring line can be formed after

irradiation. The 5−7 ring moves to the left though bond rotation about one lattice parameter away from the atom 4 forming a kink structure, which is very similar to the movement of the GBs in bulk materials under irradiation.53,54 The mechanism of the GBs motion through sequential bond rations in graphene has been confirmed by the aberration-corrected high-resolution transmission electron microscopy.55

4. CONCLUSION The creations and evolution of monovacancy, divacancy, StoneWales (SW), and grain boundaries (GBs) under electron irradiation are studied using ab initio molecular dynamics simulations. The SW defects can be easily healed through irradiation without creating a new defect. Four types of divacanciesV2(5−8−5), V2(555−777), V2(5555−6−7777), and V2(55−77)can transform into each other, and the threshold energies for these transformations are determined as a function of recoil directions. These defects can migrate by bond rotation under electron irradiation representing an important pathway of altering graphene morphology, which will change the hexagonal structure into a network of pentagons, hexagons, and heptagons. This provides a pathway to drastically vary the local atomic structure with the remaining sp2 bonding and thus the flat or almost flat carbon membrane. Irradiation can serve as a useful tool to modify morphology in a controllable manner and to tailor the physical properties of graphene.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Z.W.); [email protected] (F.G.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Z. Wang was financially supported by the Young Scientists Foundation of Sichuan (09ZQ026-029). F. Gao was supported by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy (DOE) under Contract DE-AC05-76RL01830. A portion of this research was performed using the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the U.S. Department of Energy’s Office of Biological and Environmental Research, located at Pacific Northwest National Laboratory and operated for DOE by Battelle.

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REFERENCES

(1) Geim, A. K. Science 2009, 324, 1530. (2) Han, M. Y.; Ozyilmaz, B.; Zhang, Y. B.; Kim, P. Phys. Rev. Lett. 2007, 98, 206805. (3) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306, 666. (4) Novoselov, K. S.; Jiang, Z.; Zhang, Y.; Morozov, S. V.; Stormer, H. L.; Zeitler, U.; Maan, J. C.; Boebinger, G. S.; Kim, P.; Geim, A. K. Science 2007, 315, 1379. (5) Wehling, T. O.; Novoselov, K. S.; Morozov, S. V.; Vdovin, E. E.; Katsnelson, M. I.; Geim, A. K.; Lichtenstein, A. I. Nano Lett. 2008, 8, 173. (6) Nair, R. R.; Sepioni, M.; Tsai, I. L.; Lehtinen, O.; Keinonen, J.; Krasheninnikov, A. V.; Thomson, T.; Geim, A. K.; Grigorieva, I. V. Nat. Phys. 2012, 8, 199. (7) Chen, J. H.; Cullen, W. G.; Jang, C.; Fuhrer, M. S.; Williams, E. D. Phys. Rev. Lett. 2009, 102, 236805. 16078



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(8) Jafri, S. H. M.; Carva, K.; Widenkvist, E.; Blom, T.; Sanyal, B.; Fransson, J.; Eriksson, O.; Jansson, U.; Grennberg, H.; Karis, O.; Quinlan, R. A.; Holloway, B. C.; Leifer, K. J. Phys. D: Appl. Phys. 2010, 43, 045404. (9) Wang, B.; Pantelides, S. T. Phys. Rev. B 2011, 83, 245403. (10) Palacios, J. J.; Fernandez-Rossier, J.; Brey, L. Phys. Rev. B 2008, 77, 195428. (11) Barzola-Quiquia, J.; Esquinazi, P.; Rothermel, M.; Spemann, D.; Butz, T.; Garcia, N. Phys. Rev. B 2007, 76, 161403. (12) Stone, A. J.; Wales, D. J. Chem. Phys. Lett. 1986, 128, 501. (13) Lahiri, J.; Lin, Y.; Bozkurt, P.; Oleynik, I. I.; Batzill, M. Nat. Nanotechnol. 2010, 5, 326. (14) Kim, K.; Lee, Z.; Regan, W.; Kisielowski, C.; Crommie, M. F.; Zettl, A. ACS Nano 2011, 5, 2142. (15) Lee, G. D.; Wang, C. Z.; Yoon, E.; Hwang, N. M.; Ho, K. M. Phys. Rev. B 2006, 74, 245411. (16) Miyamoto, Y.; Rubio, A.; Berber, S.; Yoon, M.; Tomanek, D. Phys. Rev. B 2004, 69, 121413. (17) Bhowmick, S.; Waghmare, U. V. Phys. Rev. B 2010, 81, 155416. (18) Carlsson, J. M.; Scheffler, M. Phys. Rev. Lett. 2006, 96, 046806. (19) Amorim, R. G.; Fazzio, A.; Antonelli, A.; Novaes, F. D.; da Silva, A. J. R. Nano Lett. 2007, 7, 2459. (20) Oeiras, R. Y.; Araujo-Moreira, F. M.; da Silva, E. Z. Phys. Rev. B 2009, 80, 073405. (21) Kotakoski, J.; Krasheninnikov, A. V.; Kaiser, U.; Meyer, J. C. Phys. Rev. Lett. 2011, 106, 105505. (22) Kang, J.; Bang, J.; Ryu, B.; Chang, K. J. Phys. Rev. B 2008, 77, 115453. (23) Boukhvalov, D. W.; Katsnelson, M. I. Nano Lett. 2008, 8, 4373. (24) Gao, L.; Guest, J. R.; Guisinger, N. P. Nano Lett. 2010, 10, 3512. (25) Malola, S.; Hakkinen, H.; Koskinen, P. Phys. Rev. B 2010, 81, 165447. (26) Liu, Y. Y.; Yakobson, B. I. Nano Lett. 2010, 10, 2178. (27) Yazyev, O. V.; Louie, S. G. Phys. Rev. B 2010, 81, 195420. (28) Yazyev, O. V.; Louie, S. G. Nat. Mater. 2010, 9, 806. (29) Cervenka, J.; Katsnelson, M. I.; Flipse, C. F. J. Nat. Phys. 2009, 5, 840. (30) Cockayne, E.; Rutter, G. M.; Guisinger, N. P.; Crain, J. N.; First, P. N.; Stroscio, J. A. Phys. Rev. B 2011, 83, 195425. (31) Grantab, R.; Shenoy, V. B.; Ruoff, R. S. Science 2010, 330, 946. (32) Jauregui, L. A.; Cao, H. L.; Wu, W.; Yu, Q. K.; Chen, Y. P. Solid State Commun. 2011, 151, 1100. (33) Wang, Z. G.; Gao, F.; Li, J. B.; Zu, X. T.; Weber, W. J. Nanotechnology 2009, 20, 075708. (34) Wang, Z. G.; Gao, F.; Li, J. B.; Zu, X. T.; Weber, W. J. J. Appl. Phys. 2009, 106, 084305. (35) Krasheninnikov, A. V.; Nordlund, K. J. Appl. Phys. 2010, 107, 071301. (36) Teweldebrhan, D.; Balandin, A. A. Appl. Phys. Lett. 2009, 94, 013101. (37) Cruz-Silva, E.; Botello-Méndez, A. R.; Barnett, Z. M.; Jia, X.; Dresselhaus, M. S.; Terrones, H.; Terrones, M.; Sumpter, B. G.; Meunier, V. Phys. Rev. Lett. 2010, 105, 045501. (38) Kotakoski, J.; Meyer, J. C.; Kurasch, S.; Santos-Cottin, D.; Kaiser, U.; Krasheninnikov, A. V. Phys. Rev. B 2011, 83, 245420. (39) Ceperley, D. M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 566. (40) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745. (41) Troullier, N.; Martins, J. L. Phys. Rev. B 1991, 43, 1993. (42) Gao, F.; Xiao, H. Y.; Zu, X. T.; Posselt, M.; Weber, W. J. Phys. Rev. Lett. 2009, 103, 027405. (43) Meng, S.; Kaxiras, E. J. Chem. Phys. 2008, 129, 054110. (44) Van de Walle, C. G.; Neugebauer, J. J. Appl. Phys. 2004, 95, 3851. (45) Kaxiras, E.; Pandey, K. C. Phys. Rev. Lett. 1988, 61, 2693. (46) Li, L.; Reich, S.; Robertson, J. Phys. Rev. B 2005, 72, 184109. (47) Lehtinen, O.; Kotakoski, J.; Krasheninnikov, A. V.; Tolvanen, A.; Nordlund, K.; Keinonen, J. Phys. Rev. B 2010, 81, 153401. (48) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865.

(49) Meyer, J. C.; Eder, F.; Kurasch, S.; Skakalova, V.; Kotakoski, J.; Park, H. J.; Roth, S.; Chuvilin, A.; Eyhusen, S.; Benner, G.; Krasheninnikov, A. V.; Kaiser, U. Phys. Rev. Lett. 2012, 108, 196102. (50) Ewels, C. P.; Heggie, M. I.; Briddon, P. R. Chem. Phys. Lett. 2002, 351, 178. (51) Lee, G. D.; Wang, C. Z.; Yoon, E.; Hwang, N. M.; Kim, D. Y.; Ho, K. M. Phys. Rev. Lett. 2005, 95, 205501. (52) Wang, Z. G.; Zhou, Y. G.; Zhang, Y. W.; Gao, F. J. Phys. Chem. C 2012, 116, 2271. (53) Campana, C.; Boyle, K. P.; Miller, R. E. Phys. Rev. B 2008, 78, 134114. (54) Sakaguchi, N.; Shibayama, T.; Kinoshita, H.; Takahashi, H. J. Nucl. Mater. 2002, 307, 1003. (55) Kurasch, S.; Kotakoski, J.; Lehtinen, O.; Skákalová, V.; Smet, J.; Krill, C. E.; Krasheninnikov, A. V.; Kaiser, U. Nano Lett. 2012, 12, 3168.

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