Size-dependent deformation behavior of nanocrystalline graphene sheets

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Size-dependent deformation behavior of nanocrystalline graphene sheets

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Zhi Yang a,∗ , Yuhong Huang b , Fei Ma a,c , Yunjin Sun e , Kewei Xu a,d , Paul K. Chu c a

State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China College of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, Shaanxi, China Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China d Department of Physics and Opt-electronic Engineering, Xi’an University of Arts and Science, Xi’an 710065, Shaanxi, China e Faculty of Food Science and Engineering, Beijing University of Agriculture, Beijing Key Laboratory of Agricultural Product Detection and Control of Spoilage Organisms and Pesticide Residue, Beijing Laboratory of Food Quality and Safety, Beijing 102206, China

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a r t i c l e

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i n f o

a b s t r a c t

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Article history: Received 7 November 2014 Received in revised form 19 March 2015 Accepted 31 March 2015 Available online xxx

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Keywords: Nanocrystalline graphene Deformation behavior Grain-size effect Molecular dynamics simulation

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1. Introduction

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Molecular dynamics (MD) simulation is conducted to study the deformation behavior of nanocrystalline graphene sheets. It is found that the graphene sheets have almost constant fracture stress and strain, but decreased elastic modulus with grain size. The results are different from the size-dependent strength observed in nanocrystalline metals. Structurally, the grain boundaries (GBs) become a principal component in two-dimensional materials with nano-grains and the bond length in GBs tends to be homogeneously distributed. This is almost the same for all the samples. Hence, the fracture stress and strain are almost size independent. As a low-elastic-modulus component, the GBs increase with reducing grain size and the elastic modulus decreases accordingly. A composite model is proposed to elucidate the deformation behavior. © 2015 Published by Elsevier B.V.

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Since the discovery of graphene, two-dimensional systems have rapidly become one of the research focuses in chemistry, physics and materials science due to their exciting and unique electronic [1], optoelectronic [2], as well as magnetic [3] properties. Particularly, the highest strength over 100 GPa [4,5], the excellent flexibility with an ultimate strain higher than 20% [1,6] and the exceptionally high electron mobility of 105 cm2 V−1 s−1 [7] of pristine graphene stimulate the interests in applying graphene in flexible devices. Stress is often exerted on graphene sheets to engineer the band structure and phonon spectrum as well as the device performances [8,9]. Hence, it is of great scientific and technological significance to study the deformation behavior and mechanical properties of graphene sheets. Chemical vapor deposition (CVD) on metals [10,11] is one of the common techniques to fabricate large-area and high-quality graphene sheets and they are usually polycrystalline [12–15] as a result of the uncontrollable nucleation processes [16]. Undoubtedly, the grain boundaries (GBs) are

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∗ Corresponding author. Tel.: +86 18302903653. E-mail addresses: [email protected] (Z. Yang), [email protected] (F. Ma), [email protected] (K. Xu), [email protected] (P.K. Chu).

considered a critical factor in determining the mechanical behavior of such a monolayer system [17–20]. Experimentally, nanoindentation based on atomic force microscopy (AFM) has been used to characterize the mechanical properties of graphene membranes [21–23]. But it is very difficult to observe the microstructure evolution in situ. Moreover, the stress field induced by AFM is inhomogeneous. This makes it difficult to study and fathom the intrinsic deformation mechanism. Recently, two-point and four-point bending approaches [24] are exploited to uniaxially stretch the graphene deposited on a flexible substrate or a tunable biaxial strain is exerted on the graphene deposited on a piezoelectric substrate due to piezoelectric effect [25]. For example, Garza et al. [26] demonstrated a reversible uniaxial strain >10% by pulling graphene sheets via a microelectromechanical system (MEMS). However, the applied strain is still smaller than the ultimate strain and it is difficult to elucidate the deformation mechanism experimentally. Molecular dynamics (MD) simulation enables researchers to examine the intrinsic mechanical behavior of graphene sheets [27]. It was found that the mechanical strength of graphene sheets depends on both grain misorientation and GB rotation [28]. Large-angle tilt boundaries are able to better accommodate the strained rings and are much stronger than low-angle boundaries having fewer defects [27]. Jhon et al. [29] further verified the effects of misorientation angle

http://dx.doi.org/10.1016/j.mseb.2015.03.019 0921-5107/© 2015 Published by Elsevier B.V.

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Fig. 1. (a) Typical model of nanocrystalline graphene sheets 18.5 nm × 18.5 nm in size under uniaxial tensile loading, (b) tensile stress-strain curves, (c) fracture stress and strain of the nanocrystalline graphene sheets as a function of grain size, and (d) elastic modulus. 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

and critical bond length on the tensile strength of polycrystalline graphene. However, based on an ideal GB model consisting of pentagon-heptagon pairs, Cao et al. [30] found that the mechanical strength deceases slightly with the misorientation angle and they ascribed the difference to the stress gradient around the crack tips. Hence, the mechanical strength of polycrystalline graphene can be either enhanced or weakened dependent on the detailed arrangement of the defects, but not just the defect density [31]. Although the deformation behavior and mechanical properties of graphene have been extensively studied, the single-crystal, bicrystal or hexagonal grain configurations as ideal models have usually been considered [27,32]. The influence of GBs on the deformation may be addressed to a certain degree, but it is different from the polycrystalline case with randomly distributed grain orientation and grain sizes. The mechanical deformation of nanocrystalline graphene sheets can be quite complicate depending on the grain size, morphology, orientation, and so on [33,18]. Particularly, when the grain size is reduced down to nanometer scale, the effects of the grain size and GBs may be appreciable. For example, Li et al. [34] found that the fracture strength are significantly reduced owing to the combined weakening effect of pre-straining in highly defective GBs and sp3 hybridization of hydrogenated carbons there, moreover, the smaller the grain size is, the larger the reduction in fracture strength is. In this work, MD simulation is performed to systematically investigate the deformation behavior and mechanical properties of nanocrystalline graphene in more realistic sense. Unexpectedly, they have almost the constant fracture strain and stress, nearly independent on the grain size, but the elastic modulus decreases sharply with the grain size. The results are completely different from the deformation behaviors exhibited in nanocrystalline

metals in which size-dependent strength is generally observed. A composite model with grain domains and GBs as two components is proposed to understand the size-dependent elastic modulus and size-independent fracture strength. 2. Models and simulation methods More realistic simulation models of nanocrystalline graphene with randomly distributed grain size and orientation are constructed by Voronoi tessellation [35]. A Voronoi tessellation represents a collection of convex polygons isolated by planar cell walls perpendicular to lines connecting neighboring points. Each cell is filled with randomly oriented graphene domains and the atomic layers adjacent to the planar cell walls are defined as GBs. The initial carbon–carbon bond length is set as 1.42 A˚ that is the same as the experimental value. If two atoms in GBs have too small ˚ from each other, one of them will be removed, separation (<1.41 A) while an atom will be added if there is a large void in GBs. Fig. 1a displays one of the typical atomic models 18.5 nm × 18.5 nm in size. The colors of the atoms are mapped according to the potential energy (PE), and GBs with higher PE are clearly evident. A set of Voronoi tessellations with N × N (N takes 2, 3,. . ., 10) grains are adopted to represent the nanocrystalline graphene sheets with average grain sizes of 9.25, 6.17, 4.63, 3.75, 3.08, 2.64, 2.31, 2.06, and 1.85 nm, respectively. The misorientation angles of the grain boundaries are randomly distributed in the range of 0–60◦ . For each average grain size, five models are built to avoid the accidental errors. The MD simulation is carried out using LAMMPS (Largescale Atomic/Molecular Massively Parallel Simulator) package. The 3D visualization software AtomEye is used for post-pocessing

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Fig. 2. (a) Residual stress and potential energy per atom of nanocrystalline graphene sheets at zero strain as a function of grain size and (b) Potential energy (PE) distribution in the nanocrystalline graphene sheets at zero strain.

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atomistic data obtained from MD simulation [36]. It can color encode any quantities defined by users. The interactions between carbon atoms are described by the adaptive intermolecular reactive empirical bond order (AIREBO) potential, which can accurately capture the interaction between carbon atoms as well as bond breaking and reforming [37]. The cutoff parameter describing the short-range C–C interaction is selected to be 2.0 A˚ in order to avoid spuriously high bond forces and nonphysical results at large defor´ mation [38]. The Nosee-Hoover thermostat is utilized to account for the thermal effect. Uniaxial tensile loading is applied along the x axis under deformation-control method, the atoms are allowed to move freely along y axis, and periodic boundary conditions are adopted along the two in-plane directions. The nominal strain εi and the nominal stress  i (i = x, y) are defined as [39]: li − li0 , li0

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εi =

142

where li0

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i =

1 ∂U , V 0 ∂εi

(1)

is the initial length along (i = x, y) directions, li is the length under stress, U is the strain energy, and V0 is the initial volume. ˚ is taken as the effective The interlayer separation of graphite, 3.4 A, thickness of the monolayer graphene. In atomic level, the stress is computed according to the virial theorem with the following form [40],

⎛

ij =

1 V

⎝1 2

 N

N

U





r ˛ˇ

˛=1 ˇ = / ˛



˛ˇ ˛ˇ xi xj r ˛ˇ

 N

−

⎞

m˛ x˙ i˛ x˙ j˛ ⎠ ,

(2)

˛=1

where V is the volume of the graphene sheets, N is the total number of atoms, x˙ i˛ is the ith component of the velocity of

atom ˛, m␣ is the mass of atom ˛, r˛ˇ is the distance between ˛,ˇ ˇ two atoms ˛ and ˇ, xj = xj˛ − xj , U is the potential energy

˛ˇ function, and r ˛ˇ = xj . Prior to uniaxial tensile loading, the

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nanocrystalline graphene are relaxed to an equilibrium state in the isothermal–isobaric ensembles with the temperature elevated from 300 to 1500 K gradually and then lowered down to 300 K. After the relaxation, the tensile loading is carried out at 300 K. The time step of 1 fs is adopted in the MD simulation, and a strain increment of 10−7 is applied for each step corresponding to a strain rate of 108 s−1 . A Poisson’s ratio of 0.165 is used [34].

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3. Results and discussion

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Fig. 1b depicts the stress–strain curves of the nanocrystalline graphene sheets under tensile loading. The results of single-crystal

graphene sheets loaded along the zigzag and armchair directions are also presented for comparison. The fracture strength and strain are 117 GPa and 25.74% for the graphene loaded along the zigzag direction and 93 GPa and 17.9% for that along armchair direction. The results are close to the measured tensile strength of 130 ± 10 GPa at an ultimate strain of 25% [4] as well as the previously calculated tensile strength of 121 ± 16 GPa at a failure strain of 22% ± 5% [41]. This validates the computation method and chosen parameters. Fig. 1c shows the fracture stress and strain estimated from Fig. 1b. The nanocrystalline graphene sheets display brittle fracture and have almost constant fracture strain and stress, nearly independent on the grain size after taking into account the error bars. It seems opposite to the case observed from nanocrystalline metals in which the size-dependent strength is often observed [42]. The average fracture stresses are close to that along the armchair direction but smaller than that along the zigzag direction. Hence, brittle fracture is preferred in the grains with the armchair orientation along the loading direction. The elastic modulus decreases sharply with reducing grain size, as shown in Fig. 1d. So the elastic deformation rather than the fracture strength is size dependent. As shown in Fig. 2a, both the residual stress and average potential energy per atom after optimization increase with reducing grain size because of the severely distorted lattice and increased dangling bonds in the GBs (Fig. 2b). The large potential energy gradients in the GBs may promote the formation of Stone–Wales (SW) defects, shearing bonds, and nano-voids, which can be thought as “lubricants” for strain transfer across the front grain domains with different orientations. It is more evident referencing to the evolution in bond length distribution in the GBs. Figs. 3–5 present the statistical bond length distribution in the GBs in three typical samples with grain sizes of 9.25, 3.75, and 2.31 nm, respectively. At zero strain, the GBs in all the samples have almost the same bond length distribution in the range of 1.35–1.55 A˚ with an average value of ˚ The average value is slightly elongated in the samples about 1.42 A. with smaller grains owing to the stronger interaction between the edges of neighboring grains [43]. As the strain is gradually exerted, the bond length distribution shifts toward the right indicating further elongated bond length, and it becomes more homogeneously distributed. At a tensile strain of 18% just before the brittle fracture, the bonds in the GBs are remarkably elongated and more than half ˚ The tendency is almost of the bond lengths are longer than 1.50 A. the same for the samples with different grain sizes. This leads to the size-independent fracture stress and strain. Fig. 6a and b shows the evolution of the atomic configuration. The colors are mapped according to the atomic potential energy and atomic stress, respectively. The atoms in GBs not only own the

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Fig. 3. Bond length distribution in the GBs of nanocrystalline graphene sheets with a grain size of 9.25 nm at strains of 0%, 6%, 12% and 18%.

Fig. 5. Bond length distribution in the GBs of nanocrystalline graphene sheets with a grain size of 2.31 nm at strains of 0%, 6%, 12% and 18%.

highest potential energy, but also are highly stressed compared to the inner parts of the grain domains. Under tensile loading, structure transformation usually occurs at GBs to release the extra potential energy and the stress. Nano-cracks nucleate randomly from the intersection of three GBs, then propagate along the

weakest GBs or experience transgranular fracture along zigzag/armchair direction, dependent on the stress distribution. This is similar to the observation in HR-TEM [44]. As shown in Fig. 6b, the crack tips develop along grain boundaries perpendicular to the loading direction, resulting in destructive fracture. Specifically, brittle fracture often initiates from heptagons and ends at pentagons because of the ridge or funnel centering on the pentagon induced by local buckles. The stress oscillates at small strains as a result of lattice distortion [45] and it is governed by the competition between bond breaking and rotation at a crack tip [46]. A kinetically favorable fracture path features an alternating sequence of bond rotation and breaking, which is related to the thermal or stress fluctuation induced nano-cracks [47]. As reported previously, the GBs exhibit good accommodation to the bond rotation and reforming [48]. This will result in the complete stress relaxation in GBs and promote the formation of pentagon-heptagon pairs because of the low formation energy [49–51]. A series of such structure transformation might guarantee nearly the same atomic configuration in GBs of nanocrystalline graphene, and thus nearly a constant fracture stress no matter the grain size. As shown in Fig. 1d, the elastic modulus of the nanocrystalline graphene sheets decreases from 850 to 740 GPa when the grain size is reduced from 9.25 to 2.06 nm. Since the bonds in GBs are usually longer than those in grains, the elastic modulus of the former should be lower than that of the later taking into account the inharmonic effects. In this two-dimensional system with nano-grains, the contribution of the GBs to the elastic modulus cannot be ignored. Fig. 7 presents the model with high-elastic-modulus grain domains isolated by low-elastic-modulus GBs. The strain is mainly shared by GBs along the x direction rather than the y direction, so the model can be simplified into a composite structure with grain domains and GBs as the two component phases. The elastic modulus can be evaluated roughly by referencing to that of composite materials, i.e., the reciprocal relationship of elastic modulus. Given the elastic modulus E0 and EGBs of the grain domains and GBs, the elastic

Fig. 4. Bond length distribution in the GBs of nanocrystalline graphene sheets with a grain size of 3.75 nm at strains of 0%, 6%, 12% and 18%.

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Q6 Fig. 6. (a) Structure evolution under uniaxial loading and (b) the stress distribution diagrams. The colors on atoms are mapped by a software AtomEye [36]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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modulus of nanocrystalline graphene sheets, E, can be calculated as: 1 1 − fGBs fGBs = + , E E0 EGBs



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fGBs =

Nzig + Narm 2

(3)



−N ×

2 × 100%, Nzig + Narm

(4)

in which E0 = 2Ezig Earm /(Ezig + Earm ) is an average value of perfect graphene sheets along the zigzag and armchair directions, fGBs is the area ratio of GBs, and Nzig , Narm and N are the numbers of atoms in zigzag-oriented, armchair-oriented single-crystal and nanocrystalline graphene sheets, respectively. EGBs is fitted from the result of the sample with an average grain size of 3.7 nm and it is about 220 GPa. Although the value is smaller than that of ideal boundaries in nanocrystalline graphene [52], the results are still reasonable if the detailed atomic configuration in the GBs is taken into account. The pentagon–heptagon pairs in ideal GBs are usually disrupted

by larger rings with more than seven atoms (so-called nano-voids). Accordingly, the elastic modulus of the ideal GBs of graphene sheets can be calculated as [53]: EGBs =

0 EGBs

×e

−bf

,

b = 8/(2 [(0.5 − )(0.5 + ) × a/c + 0.1]),

(5)

a/c ≈ 1.1 for roundwhere shaped nano-voids, f is the area ratio of the nano-voids relative to GBs phase, and  ≈ 0.165 is the Poisson’s ratio of nanocrys0 talline graphene. The elastic modulus EGBs is calculated to be about 720 GPa which is in good agreement with the reported values [27,51]. As shown in Fig. 8a, the predicated elastic modulus fits well with the MD simulations. The size dependence is related to the area ratio of boundary phase (Fig. 8b). Apparently, GBs are crucial to mechanical deformation of nanocrystalline graphene. On the one hand, GBs at which the fracture usually initiates can better accommodate bond rotation and reforming. This is almost the same for the nanocrystalline graphene sheets in this grain size range because of uniformly distributed

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Fig. 7. Schematic composite model with grain domains and GBs as two components, in which red squares denote the grain domains and yellow parts indicate the GBs. The blue springs embedded in the GBs paned by solid lines are subjected to larger stress along the x direction than that paned by dashed blue line under tensile loading. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. (a) Elastic moduli of nanocrystalline graphene sheets obtained by MD simulation and those fitted according to composite models and (b) area ratio of nano-voids and the boundary domains (red) (unit: %). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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defective zones. As a result, they exhibit almost constant fracture stress and strain. However, in nanocrystalline metals, the plastic deformation is mainly dominated by dislocation movement, i.e., slipping of crystalline planes, and it is easier for dislocations to slip off the nano-grains with a smaller size. Consequently, it is difficult for plastic deformation to take place and the mechanical strength is considerably enhanced. On the other hand, GBs as a low-elasticmodulus component cannot be ignored in this atomic-layer-thick system and become more significant as the grain size is reduced. This leads to the gradually decreased elastic modulus, as observed in nanocrystalline metals [54,55]. The results are also instructive to exploration of composite materials with graphene sheets as an ideal reinforcing component.

4. Conclusion MD simulation is conducted to investigate the effects of grain size on the mechanical deformation of nanocrystalline graphene. The results show that the fracture stress and strain change slightly but the elastic modulus decreases as the grain size diminishes. Statistical analysis of the atomic configuration suggests that the GBs at which brittle fracture usually initiates might experience structure reconstruction under tensile loading. The bond length approaches a similar quasi-homogenous distribution at a strain just before frac-

ture, independent on the grain size. This leads to almost constant fracture strain and stress. Moreover, the GBs as a low-elasticmodulus component become dominant and the effects are more pronounced as the grain size drops. As a result, the elastic modulus decreases gradually with reducing grain size. A composite model with grain domains and GBs as two components is postulated to understand the grain-size-dependent elastic modulus. Specifically, the ratio of these two components determines the elastic modulus of nanocrystalline graphene, as illustrated in nanocrystalline metals.

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Acknowledgments

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This work was jointly supported by National Natural Sci- Q4 ence Foundation of China (Grant Nos. 51271139, 51471130, 51171145, 51302162), the Natural Science Foundation of Shanghai (2013JM6002), Fundamental Research Funds for the Central Universities, and Guangdong-Hong Kong Technology Cooperation Funding Scheme (TCFS) GHP/015/12SZ. References [1] A.C. Neto, F. Guinea, N. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81 (2009) 109. [2] F. Bonaccorso, Z. Sun, T. Hasan, A. Ferrari, Nat. Photonics 4 (2010) 611.

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[3] [4] [5] [6]

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[7]

331 332 333 334 335 336 337 338

[8] [9] [10] [11] [12] [13] [14]

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[15] [16] [17]

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[18]

345 346

[19]

347 348

[20]

349 350

[21]

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[22]

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[23] [24]

356 357 358

[25] [26]

359 360

[27] [28]

D. Xiao, W. Yao, Q. Niu, Phys. Rev. Lett. 99 (2007) 236809. C. Lee, X. Wei, J.W. Kysar, J. Hone, Science 321 (2008) 385. J. Van den Brink, Nat. Nanotechnol. 2 (2007) 199. S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, et al., Nat. Nanotechnol. 5 (2010) 574. K.I. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, et al., Solid State Commun. 146 (2008) 351. T. Mueller, F. Xia, P. Avouris, Nat. Photonics 4 (2010) 297. F. Xia, D.B. Farmer, Y.-M. Lin, P. Avouris, Nano Lett. 10 (2010) 715. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, et al., Science 324 (2009) 1312. M. Andersen, L. Hornekær, B. Hammer, Phys. Rev. B 86 (2012) 085405. D.W. Kim, Y.H. Kim, H.S. Jeong, H.-T. Jung, Nat. Nanotechnol. 7 (2011) 29. B.I. Yakobson, F. Ding, ACS Nano 5 (2011) 1569. K. Kim, Z. Lee, W. Regan, C. Kisielowski, M. Crommie, A. Zettl, ACS Nano 5 (2011) 2142. L.P. Biró, P. Lambin, New J. Phys. 15 (2013) 035024. A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, et al., Nano Lett. 9 (2008) 30. A.W. Tsen, L. Brown, M.P. Levendorf, F. Ghahari, P.Y. Huang, R.W. Havener, et al., Science 336 (2012) 1143. C.S. Ruiz-Vargas, H.L. Zhuang, P.Y. Huang, A.M. van der Zande, S. Garg, P.L. McEuen, et al., Nano Lett. 11 (2011) 2259. P.Y. Huang, C.S. Ruiz-Vargas, A.M. van der Zande, W.S. Whitney, M.P. Levendorf, J.W. Kevek, et al., Nature 469 (2011) 389. G.-H. Lee, R.C. Cooper, S.J. An, S. Lee, A. van der Zande, N. Petrone, et al., Science 340 (2013) 1073. M.C. Wang, C. Yan, D. Galpaya, Z.B. Lai, L. Ma, N. Hu, et al., J. Nano Res. 23 (2013) 43. J.H. Warner, E.R. Margine, M. Mukai, A.W. Robertson, F. Giustino, A.I. Kirkland, Science 337 (2012) 209. M. Wang, C. Yan, L. Ma, N. Hu, M. Chen, Comput. Mater. Sci. 54 (2012) 236. O. Frank, G. Tsoukleri, J. Parthenios, K. Papagelis, I. Riaz, R. Jalil, et al., ACS Nano 4 (2010) 3131. J. Lu, Y. Bao, C.L. Su, K.P. Loh, ACS Nano 7 (2013) 8350. H.H. Pérez Garza, E.W. Kievit, G.F. Schneider, U. Staufer, Nano Lett. 14 (2014) 4107. R. Grantab, V.B. Shenoy, R.S. Ruoff, Science 330 (2010) 946. J. Wu, Y. Wei, J. Mech. Phys. Solids 61 (2013) 1421.

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[29] Y.I. Jhon, P.S. Chung, R. Smith, K.S. Min, G.Y. Yeom, M.S. Jhon, RSC Adv. 3 (2013) 9897. [30] A. Cao, Y. Yuan, Appl. Phys. Lett. 100 (2012) 211912. [31] Y. Wei, J. Wu, H. Yin, X. Shi, R. Yang, M. Dresselhaus, Nat. Mater. 11 (2012) 759. [32] L. Yi, Z. Yin, Y. Zhang, T. Chang, Carbon 51 (2012) 373. [33] Z. Song, V.I. Artyukhov, B.I. Yakobson, Z. Xu, Nano Lett. 13 (2013) 1829. [34] N.-N. Li, Z.-D. Sha, Q.-X. Pei, Y.-W. Zhang, J. Phys. Chem. C 118 (2014) 13769. [35] J. Schiøtz, F.D. Di Tolla, K.W. Jacobsen, Nature 391 (1998) 561. [36] J. Li, Model Simul. Mater. Sci. 11 (2003) 173. [37] D.W. Brenner, O.A. Shenderova, J.A. Harrison, S.J. Stuart, B. Ni, S.B. Sinnott, J. Phys.: Condens. Matter 14 (2002) 783. [38] O.A. Shenderova, D.W. Brenner, A. Omeltchenko, X. Su, L.H. Yang, Phys. Rev. B 61 (2000) 3877. [39] J. Schiøtz, F.D. Di Tolla, K.W. Jacobsen, System 214 (1977) 300. [40] A. Hadizadeh Kheirkhah, E. Saeivar Iranizad, M. Raeisi, A. Rajabpour, Solid State Commun. 177 (2014) 98. [41] Q.X. Pei, Y.W. Zhang, V.B. Shenoy, Carbon 48 (2010) 898. [42] N. Wang, Z. Wang, K. Aust, U. Erb, Acta Metallur. Mater. 43 (1995) 519. [43] Q. Lu, R. Huang, Phys. Rev. B 81 (2010) 155410. [44] K. Kim, V.I. Artyukhov, W. Regan, Y. Liu, M. Crommie, B.I. Yakobson, et al., Nano Lett. 12 (2011) 293. [45] F. Hao, D. Fang, Phys. Lett. A 376 (2012) 1942. [46] S.S. Terdalkar, S. Huang, H. Yuan, J.J. Rencis, T. Zhu, S. Zhang, Chem. Phys. Lett. 494 (2010) 218. [47] I. Ovid’ko, A. Sheinerman, J. Phys. D: Appl. Phys. 46 (2013) 345305. [48] H.I. Rasool, C. Ophus, W.S. Klug, A. Zettl, J.K. Gimzewski, Nat. Commun. (2013) 4. [49] O.V. Yazyev, Solid State Commun. 152 (2012) 1431. [50] S. Malola, H. Häkkinen, P. Koskinen, Phys. Rev. B 81 (2010) 165447. [51] Z. Shan, E. Stach, J. Wiezorek, J. Knapp, D. Follstaedt, S. Mao, Science 305 (2004) 654. [52] H. Zhang, Z. Duan, X. Zhang, C. Liu, J. Zhang, J. Zhao, Phys. Chem. Chem. Phys. 15 (2013) 11794. [53] K. Phani, S. Niyogi, J. Mater. Sci. 22 (1987) 257. [54] A. Latapie, D. Farkas, Scr. Mater. 48 (2003) 611. [55] S.-J. Zhao, K. Albe, H. Hahn, Scr. Mater. 55 (2006) 473.

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