Anisotropic Shock Response of Stone–Wales Defects in Graphene

Shock response of a basic defect type in graphene, the Stone–Wales defect ...... J. C.; Ajayan , P. M. New Metallic Allotropes of Planar and Tubular...
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Anisotropic Shock Response of Stone−Wales Defects in Graphene X. J. Long,†,‡ F. P. Zhao,‡ H. K. Liu,‡,§ J. Y. Huang,‡,∥ Y. Lin,§ J. Zhu,*,† and S. N. Luo*,‡ †

College of Physical Science and Technology, Sichuan University, Chengdu, Sichuan 610064, PR China The Peac Institute of Multiscale Sciences, Chengdu, Sichuan 610207, PR China § State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China ∥ CAS Key Laboratory of Materials Behavior and Design, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230027, PR China ‡

ABSTRACT: Shock response of a basic defect type in graphene, the Stone−Wales defect (SWD), is investigated with molecular dynamics simulations. Shock compression is applied to embedded SWDs along the armchair and zigzag directions. Upon shock loading, C−C bonds tend to rotate to an orientation perpendicular to the shock direction. SWD’s shock response shows pronounced anisotropy because of the structural anisotropies in both graphene and SWD with respect to the loading direction, and overall SWD shows stronger resistance to deformation for the armchair-direction loading. For the zigzag-direction loading, slip nucleates in SWD via formation of two pentagons by compressing two meta- or other-position atoms together during a rotation of central C−C bond and grows by means of alternating formation of two pentagons and a twisted hexagon. For the armchair-direction loading, healing, generation, and pentagon−heptagon pair separation of SWD occur via a 90° rotation of C−C bond, whereas at high shock strengths, slip may nucleate via shuffle dislocations by collapsing two para-position atoms.

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magnetism.17,18 However, they can also degrade the mechanical performance and reliability of graphene-based materials.19−22 Previously, the mechanical properties of graphene with SWDs were investigated with density functional theory (DFT) calculations, and it is found that the formation energy of SWD depends on defect concentration as well as the direction of applied tension.23 For SWDs located near the edges of a graphene nanoribbon,24 its response to compression or tension is sensitive to the orientation of SWDs relative to the edge. Molecular dynamics (MD) simulations demonstrated that the SWDs in graphene nanoribbons under tension may annihilate via inverse rotation of C−C bonds, and the annihilation depends on strain rate and temperature.25 As shown by DFT calculations, the energy barrier to SWD annihilation can be reduced to 2.86 eV via absorbing W atoms and to 0.87 eV via absorbing C atoms.26,27 DFT calculations also showed that chemical functionalization of semiconducting graphene nanoribbons with SWDs can be achieved by carboxyl (COOH) groups.28 Shock response of the composites containing nanostructured carbon such as carbon nanotubes (CNTs) and graphene was investigated previously with MD simulations29−31 and experi-

INTRODUCTION As a typical 2D material, graphene has been of scientific and applied interests1 for such properties as extremely high mobility,2 high elasticity,3 quantum electronic transport,4,5 tunable band gap,6 and electromechanical modulation.7 It has potential applications in future solid devices, providing an alternative to the traditional silicon semiconductors.8,9 Similar to 3D materials, synthesis or unintended deformation inevitably introduces various kinds of defects, e.g., vacancies, adatoms, impurities, and topological defects.10,11 One of the most important defects in graphene is the Stone−Wales defect (SWD), with adjacent pairs of pentagonal and heptagonal rings (colored red and black in Figure 1; denoted as 5−7 pairs). This imperfection is created via rotation of a pair of C atoms.12 It was observed when positioning graphene under the tips of a scanning tunneling microscope and atomic force microscope because of the mechanical perturbation involved13,14 or under a high-resolution transmission electron microscope (HRTEM) because of electron radiation.15 Electron radiation under HRTEM may induce two kinds of damage in graphene: bond rotation and atom ejection. The first kind involves the formation of SWD, and the second kind involves the generation of V1 (5−9) defect (one atom ejected) and V2 (5−8−5) defect (two atoms ejected).10,15,16 Defects in graphene can be useful in some applications, including the promotion of reactivity and generation of © 2015 American Chemical Society

Received: January 4, 2015 Revised: March 11, 2015 Published: March 11, 2015 7453

DOI: 10.1021/acs.jpcc.5b00081 J. Phys. Chem. C 2015, 119, 7453−7460

Article

The Journal of Physical Chemistry C

potential,34 which can accurately describe interactions between C atoms including bond breaking and forming.35 The cutoff distance for short-range interactions is 2 Å in order to avoid spuriously high bond forces and nonphysical results at large deformation stages.36,37 Before shock loading, all the graphene sheets are thermalized to an equilibrium state with the isothermal−isobaric (NPT) ensemble. The time step for integrating the equation of motion is 1 fs. Periodic boundary conditions are applied in two in-plane directions. In engineering applications including graphene-based electronic devices, graphene is usually confined between two hard substrates (e.g., SiO2).38 Thus, we constrain the out-of-plane movements of graphene in our simulations to mimic such embedded graphene systems. The supercell is constrained along the out-of-plane direction, via setting the velocities and forces to zero in this direction. The initial temperature is 200 K in the 2D case in the present study (equivalent to 300 K in 3D), and the NPT run durations are more than 300 ps. Upon shock loading, the microcanonical NVE ensemble is applied.39,40 Several layers of atoms (30 Å in width) on the left edge are used as a piston, which is accelerated within 0.1 ps to a terminal particle velocity, up, and drives a shock to propagate into the graphene sample along the x axis. Periodic boundary conditions are applied only along the y axis, and the motion along the z axis is constrained. The time step for integrating the equation of motion is 0.1 fs for shock simulations. When the leading shock front reaches the free surface on the right-hand side, it is reflected as a release fan propagating backward (toward the original SWD). Because the nominal length is 600 nm for a round trip between the SWD and the free surface, the corresponding duration is sufficiently long (>20 ps) to allow complete structural evolution of the shocked SWD. The atomic-level deformation can be characterized with the slip vector in terms of the maximum relative displacement30,41

Figure 1. Initial atomic configurations of SWDs with four different loading geometries: A30, A90, Z0 and Z60. A and Z refer to the armchair and zigzag directions, respectively, and 0, 30, 60, and 90 refer to the angles between the central C−C bond (colored black) in SWD and the shock direction.

ments,32 including a-SiC and polymer matrices reinforced by CNTs29,30,32 and graphene/Cu laminates.31 In contrast to the composites with randomly mixed CNTs,32 the composites with well-aligned CNTs show pronounced anisotropy in shock response.29,30 CNTs have positive or negative effects on their mechanical properties. The graphene/Cu laminates display improved penetration resistance against projectile impact.31 Although these studies addressed shock response of CNTs and graphene in their composites, the response of preexisting defects was not examined. Defects in 3D solids may be a source, sink, and barriers to dislocation formation and twinning, and a natural question is whether these mechanisms are present in shocked 2D graphene with SWDs. Investigations on shock responses of defects in graphene are absent, in contrast to copious studies on nonshock conditions. In this work, we present the first MD simulations of shock response of SWDs in graphene. Shock compression is imposed along two representative crystal orientations, the armchair and zigzag directions. Shock-induced generation and annihilation of SWDs, pentagon−heptagon pair separation of SWD, and slip nucleation from SWD or perfect hexagon sites are observed. Deformation depends on both SWD orientations and shock strength.

si = x ij − X ij : |x ij − X ij|max

(1)

Here, xij and Xij are the vector difference in the positions of atom i and its nearest atom j in current and reference configurations, respectively. The reference configurations are the initial structures at zero strain. The total scalar slip follows as si = |si|.

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RESULTS AND DISCUSSION Shocks along the Armchair Direction: A30 and A90. For A30 SWD impacted at up ≥ 3.5 km/s, SWD heals through a 90° rotation of its central C−C bond, whereas SWD remains intact for lower impact velocities. The healing process and the corresponding potential energy (PE) evolution are illustrated in Figure 2. Here, PE represents the potential energy averaged over the six central atoms of SWD (atoms 1−6, Figure 2). When the shock reaches the SWD at t ≈ 3.6 ps, PE increases sharply from −7.3 eV to a higher level of −6.45 eV. The shockcompressed SWD retains its structural integrity for about 3.6 ps, with PE fluctuating around its baseline (−6.45 eV) within this period. Between 7.3−7.5 ps (instants I−IV), a thermal fluctuation leads the structure to cross the energy barrier (the peak is at −5.90 eV), and then PE drops to a lower, stable value of −7.08 eV. Consistently, the SWD heals with its two pentagons and two heptagons evolving into hexagons, via a gradual, clockwise, 90°, bond rotation of the central C−C bond (I−IV). Upon transforming from its initial structure (I) to a transient one (II), the C−C bond undergoes a rotation of

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METHODOLOGY We construct an ∼400 × 20 nm2 (x × y dimensions), singlecrystal graphene layer. A SWD is embedded in the otherwise perfect graphene at 100 nm away from the left edge where shock loading is exerted along the x-axis direction. Varying the relative orientation between the central C−C bond of SWD and the shock direction, we obtain four representative configurations and loading geometries of structurally identical SWDs, A30, A90, Z0, and Z60, for shock simulations (Figure 1). Here “A” and “Z” denote the armchair and zigzag shock directions, respectively, and the numbers following them indicate the angles between the central SWD C−C bond (black atoms) and the shock direction. We use the large-scale atomic/molecular massively parallel simulator (LAMMPS)33 for MD simulations. The force field is described by the reactive empirical bond order (REBO) 7454

DOI: 10.1021/acs.jpcc.5b00081 J. Phys. Chem. C 2015, 119, 7453−7460

Article

The Journal of Physical Chemistry C

Figure 3. Slip in graphene with A30 SWD impacted at up = 7.2 km/s, accompanied by its quick healing. The Burgers vector is obtained from the Burgers circuit (red arrows). Color-coding of atoms is based on the total slip.

shock direction (−1, 1), the probabilities are equal for the slips with b = (−1, 0) or (0, 1). In unshocked graphene, vectors (1, 0) and (0, 1) are at 30° with the shock direction (−1, 1); upon shock compression, the angle between the slip direction and the shock direction becomes ∼45° because of lattice distortion, approximately following the maximum shear stress direction. We examine further the nucleation process of shock-induced slip in Figure 4. It is worth noting that healed SWDs may not

Figure 2. Healing of A30 SWD for up = 3.5 km/s. The top figure shows the evolution of PE averaged over atoms 1−6; I−IV denote the key instants of the healing process (inset), and the corresponding configurations are shown at the bottom. The red lines represent the baselines of PE.

about 30°, giving rise to an increase in PE and a less stable configuration with two decagons. With further rotation (II− III−IV), the two decagons transform into four stable hexagons. The shock loading raises the average PE, and thermal fluctuations supply the boost for crossing the energy barrier to finally annihilate the SWD. This annihilation mechanism is different from other two mechanisms proposed previously: via absorbing metal atoms26 and adding a C atom.27 The absorbed metal atoms lower the energy barrier for central C−C bond rotation by changing the frontier orbital in transition state,26 whereas the added C atom is bonded with the constituent atoms of SWD and then all related carbon atoms are rearranged to form a hexagonal network with a movable atom. With increasing impact velocity to up ≥ 7.2 km/s, the quick healing of SWD is followed by nucleation and growth of slip in the shocked graphene (Figure 3). However, the slip nucleation site is random and independent of the healed SWD, indicating that the SWD has been fully healed upon compression. In Figure 3, the Burgers circuit is applied to obtain the Burgers vector b, which represents the direction and magnitude of slip or lattice distortion. With the primitive cell lattice vectors denoted as i and j, the shock direction can be written as (−i, j) or simply (−1, 1). By summing the four vectors in the Burgers circuit, we obtain the Burgers vector b = (0, 1), which is parallel to the zigzag direction of the graphene. Additionally, slips with b = (−1, 0) are observed at other nucleation sites and for runs with different random number seeds during velocity assignment. Because (−1, 0) and (0, 1) are axisymmetric about the

Figure 4. Slip development along the zigzag direction in graphene with A30 SWD, via shuffle dislocations (up = 7.2 km/s). (a, b, c, and d) Configurations at 1.60, 1.68, 1.70, and 1.72 ps, respectively. The colorcoding is based on total slip. The schematics on the bottom panels illustrate the key deformation features marked by dashed lines in the atomic configurations on the top panels. The blue lines describe the deformation of the initial hexagon, and the black lines depict the formation and movement of shuffle dislocations.

necessarily be the slip nucleation sites, and slip nucleation for shocks along the armchair direction can be regarded as homogeneous. Upon shock, two opposing atoms, numbered 1 and 2, are squeezed close to each other (Figures 4a,b), forming a horizontal bond, which is then rotated as a result of stress relaxation. Meanwhile, the C−C bonds between atoms 2 and 3 and atoms 1 and 8 break, yielding a pair of centrosymmetrical shuffle dislocations42,43 (Figure 4c). In the shuffle dislocation centered at atom 3, the breaking of the bond between atoms 4 and 7 is accompanied by rebonding of atoms 3 and 4; as a result, this shuffle dislocation center moves by one unit j vector from atom 3 to atom 7 (Figure 4d). Similarly, the shuffle dislocation centered at atom 8 is now centered at atom 7455

DOI: 10.1021/acs.jpcc.5b00081 J. Phys. Chem. C 2015, 119, 7453−7460

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The Journal of Physical Chemistry C

As mentioned above, high impact velocity may yield A90 SWDs in graphene. Nevertheless, it does not necessarily mean that A90 SWDs always remain intact under shock loading. The shock-induced deformation process of an A90 SWD (Figure 6)

9. In this way, the two shuffle dislocations move apart along the zigzag direction and grow via repeating such processes along the same direction (Figure 3). It is interesting to note that for an impact velocity of 6.5 ≤ up < 7.2 km/s random nucleation of A90 SWDs takes place along with annihilation of A30 SWDs without slip. The nucleation process of A90 SWD and the evolution of PE are shown in Figure 5. At ∼5.5 ps, the shock wave arrival induces a rapid

Figure 6. Separation of pentagon-heptagon pairs (5−7 pairs) of A90 SWD induced by bond rotation at up ≥ 7 km/s. The top figure shows the evolution of PE averaged over atoms 2−7; I−IV denote the key instants of the separation process, and the corresponding configurations are shown at the bottom. Atoms labeled with 1 and 2 are the central atoms of A90 SWD. The C−C bond connecting atoms 3 and 4 is rotated here.

Figure 5. Creation of A90 SWD in graphene with A30 SWD shocked at 6.5 ≤ up < 7.2 km/s. The top figure shows the evolution of PE averaged over atoms 1−6; I−IV denote the key instants of the healing process (inset), and the corresponding configurations are shown at the bottom. The red lines represent the baselines of PE.

is observed at up ≥ 7.0 km/s. Initially (instant I), SWD consists of two adjacent 5−7 pairs, one with shared atoms 2 and 3 and the other with shared atoms 1 and 8. At instant IV, the former moves by one unit i vector (defined in Figure 3) to share atoms 6 and 4. The two 5−7 pairs of A90 SWD are separated by two hexagons during the transformation (I−IV) through a 90° rotation of the C−C bond connecting atoms 3 and 4. The evolution of PE and key configurations around 4.7 ps (I−IV) are presented in Figure 6. Similar to the bond rotation during the annihilation of A30 SWD and creation of A90 SWD, the 90° bond rotation in the separation of 5−7 pairs also involves crossing an energy barrier (II). However, since the energy peak is rather high (at −3.84 eV), this separation of 5−7 pairs occurs only in a small portion of A90 SWDs (including preset and created ones), e.g., only 2 out of 30 for up = 7 km/s, and it is extremely rare for two 5−7 pairs to be separated by four hexagons. The bond-rotation-induced separation of 5−7 pairs is similar to the Stone−Wales wave;44 the diffusing distance of 5−7 pairs is short because the energy barrier for bond rotation is rather high in our shock simulations.

increase in PE, and an A90 SWD is generated at ∼7.7 ps, leading to a slight PE increase because SWD represents a “trapped,” local minimum state with higher energy than the perfect hexagon (by approximately 0.3 eV). The atomic configurations at four key instants I−IV show that the creation of A90 SWD is achieved by a successive rotation of the central C−C bond, and the total rotation is 90°. Particularly, when the PE reaches the peak (II), the central C−C bond rotates by about 27°. The mechanism for random formation of A90 SWDs differs from slip in shocked graphene; the former involves local deformation with a 90° rotation of the central C−C bond between two adjacent hexagons and the energy barrier is lower. On the other hand, slip grows from a pair of shuffle dislocations via compressing two opposing atoms in a single hexagon to form a bond that then rotates. Thus, a higher stress amplitude is required for slip formation. 7456

DOI: 10.1021/acs.jpcc.5b00081 J. Phys. Chem. C 2015, 119, 7453−7460

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The Journal of Physical Chemistry C Radiation-induced bond rotations in V2 (5−8−5) can transform it into V2 (555−777) or V2 (5555−6−7777), which contain 5−7 pairs similar to SWD.10,45 Although V1 (5−9) and V2 (5−8−5) defects are common in graphene and share certain similarity with SWD, they are not observed in our shock simulations. A group of 5−7 pairs are also called glide dislocations and are usually regarded as edge dislocations in graphene together with shuffle dislocations.42,43,46,47 Small probability and short separation of glide dislocations indicate a high energy barrier. Contrarily, the shuffle dislocations shown in Figure 4 move apart much more easily (they move rapidly and immediately after their formation). This discrepancy is caused by their different migration mechanisms: shuffle dislocation moves by breaking one bond and forming another, glide dislocation moves mainly through a 90° bond rotation except for bond breakage (between atoms 5 and 4 and atoms 3 and 7) and formation (between atoms 5 and 3 and atoms 4 and 7). This result is consistent with previous works.42,46,47 Because shuffle dislocation generated at a hexagon site moves and promotes the growth of slip much more easily than glide dislocations involved in SWD, slip prefers to nucleate at a hexagon site and grow via shuffle dislocation. Shocks along the Zigzag Direction: Z0 and Z60. When Z0 SWD is shocked at up ≥ 3.9 km/s, its central C−C bond is initially rotated by 90° (Figures 7a,b,c,d), and then slip

Figure 8. Slip in graphene initially with Z0 SWD after its central C−C bond rotates by 90°. The Burgers vector is obtained from the Burgers circuit (red lines with arrows). Color-coding is based on the total slip. up = 3.9 km/s.

Figure 9. Initial stages of slip along the armchair direction in graphene with a Z0 SWD after its central C−C bond rotates by 90° (see Figure 7); up = 3.9 km/s. (a, b, and c) Configurations at 5.00, 5.02, and 5.07 ps, respectively. In the schematics in the bottom panels, the dotted arrows denote the moving directions of atoms or ring. The carmine lines depict the dragged atoms and reference atoms; the central hexagon containing the carmine lines is the twisted hexagon 2−4−10− 9−8−7 (b).

two pentagons, 1−11−12−13−7 and 2−3−5−6−4, labeled as I and II in the corresponding diagrams at the bottom, respectively. Pentagon I moves along the arrow direction relative to pentagon II and drags atoms 8 and 9 to move along the same direction relative to atoms 2, 4, and 10 (Figure 9a), resulting in a twisted hexagon 2−4−10−9−8−7 (Figure 9b). Then, atom 14 moves close to atom 10, and atom 18 moves close to atom 9, yielding the next pair of pentagons 9−8−20− 19−18 (III) and 10−17−16−15−14 (IV), as shown in Figure 9c. Subsequent relative movement between pentagons III and IV leads to the formation of another twisted hexagon. Such processes repeat, and slip grows along the armchair direction (Figure 8). For Z60 SWD, slip occurs at an impact velocity of up ≥ 3.9 km/s. Two parallel slips originate from the heptagons of the Z60 SWD during rotation of its central C−C bond perpendicular to the shock direction (Figure 10). Heptagon 1−2−3−4−5−6−7 deforms first, as shown in Figures 10a,b: Atom 5 moves toward atom 3, and drags atoms 8 and 9 to move relative to atoms 4, 10 and 11, resulting in a twisted hexagon 4−5−8−9−10−11. Then, atom 14 moves toward atom 9, and atom 15 toward atom 10, leading to a pair of pentagons 9−8−12−13−14 (III) and 10−15−16−17−18 (IV) (Figure 10c). The subsequent relative movement between these two pentagons creates another twisted hexagon. Such

Figure 7. Snapshots of the 90° rotation of the central C−C bond in Z0 SWD shocked at up = 3.9 km/s, followed by slip as shown in Figure 8. (a, b, c, and d) Configurations at 4.32, 4.37, 4.38, and 5.00 ps, respectively.

develops along the armchair direction (Figure 8). Given the primitive lattice vectors i and j defined in Figure 8, the shock direction can be written as (0, 1), and the Burgers vector is b = (1, 2), which is parallel to the armchair direction. For different MD runs at the same impact velocity, we also find another Burgers vector b = (−1, 1). Both (−1, 1) and (1, 2) are equivalent and axisymmetric about the shock direction (0, 1). In unshocked graphene, directions (−1, 1) and (1, 2) are at an angle of 30° to the shock direction (0, 1), and this angle changes to ∼45° because of lattice distortion accompanying slip along the maximum shear stress direction. We present in Figure 9 the details of the slip evolution in the shocked Z0 SWD after a 90° bond rotation (Figure 7). This rotation of the central C−C bond gives rise to the formation of 7457

DOI: 10.1021/acs.jpcc.5b00081 J. Phys. Chem. C 2015, 119, 7453−7460

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The Journal of Physical Chemistry C

During the annihilation of A30 SWD, the central C−C bond also reorients itself closer to an orientation perpendicular to the shock direction. Bond rotation plays a key role in the deformation of SWD. When its central C−C bond is oriented perpendicular to the shock direction, the effective torque relevant to this bond is the lowest possible and thus most stable. Previously, an SWD with the central C−C bond nonparallel to the tensile direction was observed to heal by bond rotation under nonshock loading, but one with the central C−C bond parallel to tension is difficult to annihilate.25 Such deformation is also caused by the relative ease of bond rotation, consistent with shock-induced deformation. Our results demonstrate that the shock response of SWDs is anisotropic: for loading along the armchair direction, shock compression induces healing, generation, and 5−7 pair separation of SWD, whereas for loading along the zigzag direction, shock-induced slip nucleates at the defects (Z0 and Z60 SWDs) while their central C−C bond is rotated perpendicular to the shock direction. Slip in shocked graphene is an important mechanism of anisotropic deformation in shocked graphene with SWDs. In defective graphene, slip nucleates at healed SWDs or perfect hexagons for the armchair-direction loading, but nucleates at SWDs for the zigzag-direction loading. For comparison, we shock pristine graphene along the zigzag direction to examine slip nucleation in pristine graphene. Slip is observed at up ≥ 4.5 km/s (Figure 12). Initially, the meta-position atoms 1 and 3 in

Figure 10. Deformation process of a Z60 SWD shocked at up = 3.9 km/s. (a, b, and c) Configurations at 5.00, 5.32, and 5.46 ps, respectively. Coloring of the atoms belonging to the original SWD is fixed, whereas the other atoms are color-coded by the total slip. In the schematics in the bottom panels, the dotted arrows denote the moving directions of atoms. In a, the two dotted lines are arranged along the armchair direction and pass through the centroids of hexagons 4′−5′− 8′−9′−10′−11′ and 4−5−8−9−10−11, respectively; d = |i|.

processes repeat, and slips grow along the armchair direction (Figure 11), similar to the Z0 SWD (Figures 8 and 9).

Figure 11. Two parallel slips originating from Z60 SWD after deformation, as shown in Figure 10, with an offset of 1.5d. Coloring of the atoms in the original SWD is fixed, whereas the other atoms are color-coded by the total slip. up = 3.9 km/s.

Figure 12. Slip nucleation in pristine graphene shocked along the zigzag direction. (a, b, c, and d) Configurations at 2.00, 2.58, 2.62, and 2.81 ps, respectively. The atoms are color-coded by the total slip. up = 4.5 km/s.

The other heptagon of Z60 SWD deforms later and goes through a similar process to develop into slip. However, the centroids of the headstream hexagons 4′−5′−8′−9′−10′−11′ and 4−5−8−9−10−11 are not arranged in the same armchair row, as depicted by the dashed line in Figure 10a but rather with an offset of one lattice spacing, d = |i|. During their growing process, the two slips broaden their width by 0.5d, and the resultant two parallel slips are separated by 1.5d (Figure 11). The central C−C bonds of the four SWD configurations prefer to rotate to an orientation perpendicular to the shock direction under shock loading. For example, the central C−C bonds of Z60 and Z0 SWDs rotate from 60° to 90° (Figure 11) and from 0° to 90° (Figure 7), respectively. The central C−C bond of A90 SWD remains perpendicular to the shock direction despite the fact that its two 5−7 pairs are separated.

the hexagon 1−2−3−4−5−6 are compressed close to each other (Figures 12a,b), and then atoms 2 and 7 in the hexagon 2−3−7−8−9−10 are squeezed together (Figures 12b,c,d), leading to the formation of two pentagons, 1−3−4−5−6 and 2−7−8−9−10. The resulting configuration in Figure 12d is analogous to that in Figure 9b for Z0 SWD, the sequential evolvement is similar to Figure 9c, and the final slip resembles that shown in Figure 8. Comparing the slip nucleation processes for loading along the armchair (Figure 4) and zigzag directions (Figure 12), we find that the initial step for both slip nucleation processes involves compressing two atoms in a hexagon to form a bond: two para-position atoms for the armchair direction and two 7458

DOI: 10.1021/acs.jpcc.5b00081 J. Phys. Chem. C 2015, 119, 7453−7460

Article

The Journal of Physical Chemistry C

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meta-position atoms for the zigzag direction. Compressing the para-position atoms together is much more difficult, so a much higher shock velocity (7.2 km/s) is needed for slip nucleation. This explains why bond rotation of A30 and A90 SWDs is accompanied not by slip nucleation but rather by healing, generation, or 5−7 pair separation. On the contrary, it is easier to squeeze two meta- or other-position atoms together during a rotation of the central C−C bond because of a shorter distance involved for Z0 and Z60 SWDs: atoms 1 and 7 and atoms 2 and 3 in Figure 7 for Z0 SWD and atoms 3 and 5 and atoms 3′ and 5′ in Figure 10 for Z60 SWD. Slip nucleates and grows after compressing two atoms, and neither healing nor the 5−7 pair separation of SWD is observed. Shock response of SWD is strongly influenced by the orientations of graphene and SWD with respect to shock direction. Similarly, placing SWDs of different orientations near the edge of graphene nanoribbons may lead to warped or planar ribbons because of anisotropic stress related to SWD.24 Such anisotropic behaviors are due to the structural anisotropies in both graphene and SWD, which are coupled in response to directional loading.

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CONCLUSIONS We have investigated deformation of the SWD in graphene under shock loading along the armchair and zigzag directions, and the central C−C bond of SWD is oriented at different angles (0−90°) with the shock direction. C−C bonds tend to rotate to an orientation with the least torque, perpendicular to the shock direction. Deformation also involves slip, and the slip direction is at an angle of about 45° with the shock direction, following the maximum shear stress direction. However, the shock response of SWD exhibits strong anisotropy because of the structural anisotropies in both graphene and SWD, and overall SWD shows stronger resistance to deformation for the armchair-direction loading. For shocks along the zigzag direction, slip may nucleate at SWDs or from pristine hexagons via formation of two pentagons by compressing two meta- or other-position atoms together and grows by means of alternating the formation of pentagons and a twisted hexagon. Shocks along the armchair direction may lead to annihilation or generation of SWDs or to separation of pentagon−heptagon pairs (glide dislocations) via a 90° rotation of the C−C bond. At high shock strengths, shuffle dislocations can be created homogeneously in pristine graphene or on annihilated SWD sites by collapsing two paraposition atoms, and slips grow via moving the formed shuffle dislocations apart rather than by glide dislocations.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone:+86 28 85418566. Fax: +86 28 85412322. *E-mail: [email protected]. Phone: +86 28 85993168. Notes

The authors declare no competing financial interest.

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DOI: 10.1021/acs.jpcc.5b00081 J. Phys. Chem. C 2015, 119, 7453−7460

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DOI: 10.1021/acs.jpcc.5b00081 J. Phys. Chem. C 2015, 119, 7453−7460