Hydrogenated Grain Boundaries Control the Strength and Ductility of

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Hydrogenated Grain Boundaries Control the Strength and Ductility of Polycrystalline Graphene Nan-Nan Li, Zhendong Sha, Qing-Xiang Pei, and Yong-Wei Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp502084f • Publication Date (Web): 03 Jun 2014 Downloaded from http://pubs.acs.org on June 8, 2014

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The Journal of Physical Chemistry

Hydrogenated Grain Boundaries Control the Strength and Ductility of Polycrystalline Graphene †

†

Nan-Nan Li, Zhen-Dong Sha,‡ Qing-Xiang Pei,*, and Yong-Wei Zhang*, †

†

Institute of High Performance Computing, A*STAR, 1 Fusionopolis Way, Singapore 138632, Republic of Singapore ‡

International Center for Applied Mechanics, State Key Laboratory for Strength and

Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China

Abstract: In the growth of polycrystalline graphene via chemical vapor deposition, grain boundaries (GBs) were shown to be energetically favorable sites for hydrogenation. Thus it is of both scientific interest and technological significance to understand how hydrogenation on GBs affects the mechanical properties of polycrystalline graphene. Here we perform molecular dynamics

simulations to

investigate

the mechanical properties

of

hydrogenated

polycrystalline graphene. Our simulations reveal that the fracture strength of hydrogenated polycrystalline graphene is significantly reduced by the combined weakening effect of bond prestraining in highly defective GBs and sp3 hybridization of hydrogenated GB atoms. In addition, this reduction in fracture strength due to GB hydrogenation is observed in polycrystalline graphene samples of different grain sizes ranging from 2.5 to 10 nm. Our findings show that the loss of mechanical strength due to GB hydrogenation must be taken into account in the application of polycrystalline graphene for nanodevices.

Keywords: Graphene; Mechanical properties; Hydrogenation; Grain boundary; Molecular dynamics simulation

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1. INTRODUCTION Graphene, which exhibits exceptional electrical, thermal, optical and mechanical properties, has attracted great research attention in recent years. It promises a wide range of applications, including flexible electronics,1-2 optoelectronics devices

4-5

3

and nanoelectromechanical

. However, one significant obstacle to the practical use of graphene lies in the need

to manufacture macroscopically large samples. Several methods have been proposed so far, including evaporation of surface layer Si on SiC,6 graphite sonication in a proper liquid medium7 and chemical vapor deposition (CVD) on metals.8-9 However, polycrystallinity is often observed in graphene grown by the abovementioned methods on various substrates, such as SiC,10 Ir (111),11 Ni,12 and Cu.13 The grain boundaries (GBs) in polycrystalline graphene may affect its mechanical behavior. Therefore, considerable research effort has been dedicated to investigate the mechanical properties of polycrystalline graphene both experimentally and computationally. Mechanical tests using atomic force microscopy (AFM) showed that grain boundaries (GBs) severely weaken the mechanical strength of CVD graphene.13-14 Meanwhile, computational studies have also drawn various interesting conclusions regarding the effect of GBs in polycrystalline graphene. For example, a bi-grain model with an ordered GB was studied.15 This low-energy GB, which consists of regularly arranged dipoles of five and sevenfold carbon rings, was shown to have the compression stress on the pentagon side and tension on the heptagon side. If a series of such dipoles were placed head-to–tail, the arrangement can lead to the cancellation of tensile and compressive stress fields. As a result, an increase in mechanical strength can be achieved by increasing the dipole density through increasing the GB tilt angle.16 It was also suggested that the above relationship only holds if these pentagon-heptagon dipoles are evenly spaced, and even under such condition, the GB is still the weakest link because the bond shared by hexagon-heptagon rings was identified as the weakest bond.17 Other studies have pointed out, however, that the abovementioned studies focused exclusively on infinite GBs without any GB junctions. It is known that polycrystalline graphene in general contains junctions, where nonparallel GBs meet. Consequently, the stress cancellation arising from regularly spaced pentagon-heptagon dipoles may no longer be effective, and GB junctions may thus serve as an eminent stress amplifier and a favorable site for crack nucleation.18


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While the abovementioned computational studies deal with ordered GBs in the form of pentagon-heptagon, one can also expect disordered GBs in samples obtained by coalescence of independently growing nuclei during typical CVD growth.19 Indeed, it was shown from both experiments nine-fold rings

20

and simulations

21

that eightfold rings as well as four- and

also exist on GBs of polycrystalline graphene, though with a lower

possibility. In addition, dangling bonds were also observed.19 Therefore, with the presence of H atoms during the CVD growth, there is always a certain degree of hydrogenation on the chemically active GB atoms of polycrystalline graphene, which has been supported by both experimental and computational results. For example, experimentally, extrinsic impurities (e.g., oxygen, hydroxyl, hydrogen, etc.) were observed on grain boundaries of CVD graphene.13,

22

Computationally, density-functional tight-binding calculations showed that

hydrogen adsorption on carbon atoms at irregular polygons on GBs is energetically more favorable than that at regular hexagons,21 and hydrogenation on the carbon atoms with dangling bonds was also shown to be energetically favorable.19 Therefore, it is reasonable to expect a certain degree of GB hydrogenation in the process of CVD growth. Moreover, hydrogenation is often deliberately introduced on the grown graphene to modify the electronic and magnetic properties.23-28 For example, hydrogenation on the GB of polycrystalline graphene could be used to control the magnetism in graphene.29 Thus, it is of both scientific interest and technological significance to understand the effects of GB hydrogenation on the mechanical properties of polycrystalline graphene. In this work, we perform molecular dynamics simulations to study the mechanical properties of hydrogenated polycrystalline graphene with the focus on the effect of GB hydrogenation. We find that GB hydrogenation plays a dominant role in determining the mechanical strength of polycrystalline graphene.

2. SIMULATION METHOD The simulation models of polycrystalline graphene as shown in Figure 1a were generated using the Voronoi tessellation method,30-32 with the dimensions of 30 × 30 nm. The average grain sizes ranging from 2.5 to 10 nm were obtained for different samples. It was also made sure that the grain positions were randomly distributed within the simulation sheet. The polycrystalline structure was then annealed at a high temperature of 3000 K for 50 ps, followed by a 10 ps quenching to room temperature (300 K), in order to eliminate unusually



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low or high density regions at the GBs. Due to lattice distortion, the stress levels of the GB atoms significantly deviate from the stress levels of grain interior atoms, which provides an easy and clear method to identify GB atoms in polycrystalline graphene. Specifically, the polycrystalline graphene samples were subjected to a uniaxial tensile load with a strain rate of 0.0001 ps-1 for 2 ps, and those atoms which experience a large deviation from the average atomic stress were identified as GB atoms. This selection method is found to produce approximately the same result with a different method using atomic potential energy as the criterion. First-principles studies

33-35

on the energetics of hydrogen chemisorption have shown

that the most stable configuration is for the H atom to bond on top of a carbon atom, forming sp3 hybridization, preferably on the defect sites. It was also shown that a complete one-side hydrogenation on graphene is unfavorable.35 Therefore, in this study, H atoms were added alternatively on both sides of the graphene sheet (see Figure 1b). In this way, the generated configuration is found to have the lowest energy and thus is the most stable. Addition of H atoms on GB was random with H coverage ranging from 0% to 100% with the upper limit corresponding to the complete hydrogenation of all GB atoms of the polycrystalline graphene. To study the mechanical properties of the obtained structures, MD simulations were performed using the software of Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).36 Periodic boundary conditions were imposed in the in-plane directions, and the adaptive intermolecular reactive bond order (AIREBO) potential was employed to describe the interatomic force,37 with a cutoff distance of 2.0 Å.38-39 The simulation time step was set at 0.0001 ps. The temperature was maintained at 300 K using the Nose-Hoover thermostat. In addition, the Virial theorem was adopted to calculate the atomic stresses in the samples. To examine the fracture behavior, a tension deformation with the strain rate of 0.0001 ps-1 was imposed along the horizontal direction. Before applying the tension deformation, the samples underwent energy minimization to ensure that the systems were in equilibrium. From the simulated stress-strain curves, Young’s modulus, fracture strength and strain were obtained. Young’s modulus was calculated from the slope of the linear region, and fracture strength and strain were determined from the point where the maximum stress was reached.


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3. RESULTS AND DISCUSSION We first analyze the energetics of hydrogenation on the GB atoms of polycrystalline graphene. Our energy minimization simulation shows that for the sample with an average grain size of 10 nm, hydrogenation on GB atoms leads to a reduction in the system potential energy of 2.68 eV/H-atom. This calculation supports that hydrogenation on GB atoms is energetically favorable during the CVD growth. The result is also relevant to the discussion of graphene as a potential hydrogen carrier.40-41 Figure 1 shows a typical hydrogenated polycrystalline graphene with 60% H-coverage on GBs after equilibration. Here, the H-coverage on GBs is defined as the ratio of the number of H atoms over the number of GB atoms. Unlike single crystalline graphene, a certain degree of buckling is clearly visible (Figure 1c). These buckled features help minimize the energy of the system and thermally stabilize the polycrystalline structure.15, 42-43 As shown in Figure 1d, the tensile deformation behavior of polycrystalline graphene consists of an initial regime where the slope of the stress-strain curve increases. This entropic elastic behavior can be attributed to the wrinkling of the sample. As the applied strain increases, the sample gradually flattens and its resistance to stretching increases. The sample subsequently enters a linear elastic regime, where the C-C bonds are directly stretched. The Young’s modulus is calculated by fitting the data in this regime to a linear model. The sample eventually undergoes a sudden catastrophic failure. For the sample with 60% H-coverage, little plastic deformation is observed, and crack propagation is normal to the loading direction, which indicates a brittle fracture. Next, we proceed to study the effect of H-coverage on the mechanical strength of polycrystalline graphene. With increasing H atoms adsorbed on the GB atoms, we find that Young’s modulus, fracture strength and fracture strain follow a decreasing trend as shown in Figures 2b-d, indicating that hydrogenation has a weakening effect on the mechanical properties. It is seen that for H-coverage from 0 to 100%, all the three quantities decrease approximately linearly with H-coverage (Figures 2b-d). With an increasing H-coverage, the graphene sample gradually becomes softer, weaker and more ductile (Figures 2a-f). We find that when H-coverage is zero or low, fracture of polycrystalline graphene is triggered mostly by a single crack site (Figure 2e), and propagation of this crack leads to a brittle failure (Figure 2a). At a higher H-coverage, however, the sample cracks at multiple sites simultaneously (Figure 2f). The growth and linkup of these cracks lead to a certain degree of 5 ACS Paragon Plus Environment


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ductility (Figure 2a). The above results clearly indicate that these hydrogenated GB sites are the weakest links and are most prone to cracking. It is also seen that fracture strength and strain are much more sensitive to hydrogenation than Young’s modulus, as they drop by almost 60% and 30%, respectively, compared to a 20% reduction in Young’s modulus. This difference in response to hydrogenation can be attributed to the fact that Young’s modulus reflects the elastic behavior of the whole sample, while the fracture strength and strain are related to the breaking of local weakest bonds. The above results show that the reduction in mechanical strength of polycrystalline graphene is closely related to the H-coverage on GB. In the following discussion, we examine the details of the fracture process in order to understand the exact role of GB hydrogenation. Figures 3 and 4 depict sequences of snapshots that capture the crack initiation and propagation of polycrystalline graphene without and with GB hydrogenation, respectively. For pure polycrystalline graphene without GB hydrogenation (Figure 3), cracks initiate at GBs, usually at highly defected segments or triple junctions, where a high concentration of irregular polygons exists. This observation can be explained by the high prestrain experienced by the C-C bonds in irregular polygons along GBs. These bonds are thus broken first, highlighting that GBs are the weakest link in polycrystalline graphene. This result is consistent with previous simulations on pure polycrystalline graphene.18 In the case of polycrystalline graphene with GB hydrogenation, where the local carbon bonding is converted from sp2 to sp3 hybridization,44-45 a similar failure mechanism is observed. As shown in Figure 4, cracks also initiate at grain boundaries, usually at highly defected segments or triple junctions, where there is usually a high concentration of irregular polygons as well. However, the fracture strength and strain for the case with GB hydrogenation are much lower than that without GB hydrogenation.

A careful examination reveals that

cracking always occurs at highly defected, hydrogenated GB segments or junctions. This observation can be explained by the combined effect of two factors: (i) the irregular polygons at GBs or GB junctions which act as an effective stress amplifier and (ii) the sp2 to sp3 transition of these atomic bonds through hydrogenation which weakens the strength of these bonds. The weakening effect arising from sp2 to sp3 transition was explored by previous studies,46-47 which attributed the weakening effect of hydrogenation to the weaker and unsupported sp3 bonds in a 2D system. Different from the sp3 bonds in a 3D system, such as diamond, where the sp3 bonds form a 3D network, the out-of-plane sp3 bonds in a 2D system impose less restriction to the bond rotation toward in-plane, and thus are much easier to break 6 ACS Paragon Plus Environment

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than sp2 bonds during tensile defomation.46-47 In the current study, the weakening effects arising from both highly defected GBs and hydrogenation work together to further weaken the hydrogenated polycrystalline graphene, making hydorgenated GB atoms the weakest link that dictates the failure of the polycrystalline graphene. Finally, we examine the effect of the grain size on the failure behavior of polycrystalline graphene with GB hydrogenation. To do so, we constructed polycrystalline graphene samples with different average grain sizes of 2.5, 5, 7.5 and 10 nm. The samples were generated through Voronoi construction with randomly distributed grain sizes, shapes and crystallographic orientations that are consistent with experimental observations.14, 48 All the samples have the same dimensions of 30 nm x 30 nm, so that the possible sample size effect can be eliminated from the simulations. For each average grain size, four samples are generated and the fracture strength is taken as the average of the four samples. The samples undergo full GB hydrogenation, i.e. all GB atoms are hydrogenated. The simulated fracture strength versus the grain size is shown in Figure 5a. It can be seen that the smaller the grain size, the larger the fracture strength reduction. This can be understood by the fact that the density or percentage of GB atoms increases as the average grain size decreases as seen in Figure 5b. Those hydrogenated GB atoms act as weak links in the polycrystalline graphene structure and reduce the fracture strength. This finding is consistent with the weakest-link model,49 which states that the failure strength of a structure reduces with increasing number of weak links in the structure. Based on the weakest-link model, we find that the simulation data in Figure 5a can be fitted by a power law relation: = 14.64 . , where is the facture strength in GPa and d is the average grain size in nm. It is also noted that the grain size in most experimental graphene samples is in micrometer range,50 much larger than the nanometer grain size in the present simulations. For polycrystalline graphene with micrometer grain size, we can extrapolate the data in Figure 5a based on the obtained formula of = 14.64 . . The extrapolated fracture strength for the fully GB hydrogenated polycrystalline graphene with grain size of 1 and 10 µm is 39.9 and 55.7 GPa, respectively, which are much lower than the fracture strength of pristine polycrystalline graphene (80 to 83 GPa).51 This shows that GB hydrogenation can also have a significant effect on the strength of polycrystalline graphene with micrometer grain size.



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4. CONCLUSION In summary, we have performed MD simulations to explore the effect of GB hydrogenation on the mechanical properties and fracture behavior of polycrystalline graphene. The following conclusions are drawn from this study: 1) The fracture strength, fracture strain and elastic modulus decrease with increasing H coverage on GB atoms. The fracture strength and strain show a more pronounced reduction than the Young’ modulus. 2) Two weakening factors, i.e., bond prestrain in highly irregular polygons at GBs or junctions, and sp2 to sp3 bonding transition due to hydrogenation, work together to further weaken polycrystalline graphene. 3) The fracture strength of fully GB hydrogenated polycrystalline graphene decreases with decreasing its average grain size, following a power-law relation. The present work shows that hydrogenated grain boundaries control the strength and ductility of polycrystalline graphene. Hence, for the application of polycrystalline graphene in nanodevices, it is necessary to account for the loss of mechanical strength due to GB hydrogenation.

AUTHOR INFORMATION Corresponding Author *Q.X.: Telephone: +65 64191225. E-mail: [email protected]. Y.W.: Telephone: +65 64191478. E-mail: [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS The authors gratefully acknowledge the use of computing resources at the A*STAR Computational Resource Centre, Singapore.


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List of Figure Captions Figure 1. Simulation sample of a polycrystalline graphene with H coverage of 60% on grain boundary atoms. (a) The top view of the 30 × 30 nm polycrystalline graphene sheet with an average grain size 10 nm. Atoms are colored according to their coordination numbers, with H atoms in red. (b) Local zoom view, which shows the highly defective and disordered GBs and triple junction of the simulation sample with the presence of 4, 5, 7, 8- membered rings. (c) The side view of the hydrogenated polycrystalline graphene after equilibration at 300 K, in which buckling can be observed. The atoms are colored according to their out-of-plane displacement. (d) The stress-strain curve obtained from MD simulation under uniaxial tension. Figure 2. The correlation between H coverage on GB atoms and mechanical properties. (a) The tensile stress-strain curves of polycrystalline graphene with different degrees of hydrogenation on grain boundaries only. (b-d) The variation of the Young’s modulus, fracture strain and strength with H coverage, respectively. (e-f) The fracture process of the polycrystalline graphene with H coverages of 10% and 100%, respectively. Atoms are colored according to their atomic stress. Figure 3. The fracture process of polycrystalline graphene without hydrogenation. (a) Crack initiation preferentially starts at highly defective segments of GBs or triple junction, as indicated by the red dotted circle. (b-c) Intergranular crack propagation perpendicular to the loading direction. (d) Transgranular crack propagation indicated by the red arrow. Atoms are colored according to their atomic stress. Figure 4. Crack formation and propagation in polycrystalline graphene with 60% hydrogenation on grain boundary atoms. (a-d) Crack initiation and propagation. Atoms are colored according to atomic stress in the top row and coordination numbers in the bottom row. In coordination number coloring, hydrogen atoms are highlighted in red. Figure 5. The correlations among the average grain size, the density of GB atoms, and the fracture strength of polycrystalline graphene. (a) The trend of the fracture strength of polycrystalline graphene with full GB hydrogenation as a function of the grain size. (b) The density of GB atoms as a function of the grain size.



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Figure 1. Simulation sample of a polycrystalline graphene with H coverage of 60% on grain boundary atoms. (a) The top view of the 30 × 30 nm polycrystalline graphene sheet with an average grain size 10 nm. Atoms are colored according to their coordination numbers, with H atoms in red. (b) Local zoom view, which shows the highly defective and disordered GBs and triple junction of the simulation sample with the presence of 4, 5, 7, 8- membered rings. (c) The side view of the hydrogenated polycrystalline graphene after equilibration at 300 K, in which buckling can be observed. The atoms are colored according to their out-of-plane displacement. (d) The stress-strain curve obtained from MD simulation under uniaxial tension.


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Figure 2. The correlation between H coverage on GB atoms and mechanical properties. (a) The tensile stress-strain curves of polycrystalline graphene with different degrees of hydrogenation on grain boundaries only. (b-d) The variation of the Young’s modulus, fracture strain and strength with H coverage, respectively. (e-f) The fracture process of the polycrystalline graphene with H coverages of 10% and 100%, respectively. Atoms are colored according to their atomic stress.



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Figure 3. The fracture process of polycrystalline graphene without hydrogenation. (a) Crack initiation preferentially starts at highly defective segments of GBs or triple junction, as indicated by the red dotted circle. (b-c) Intergranular crack propagation perpendicular to the loading direction. (d) Transgranular crack propagation indicated by the red arrow. Atoms are colored according to their atomic stress.


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Figure 4. Crack formation and propagation in polycrystalline graphene with 60% hydrogenation on grain boundary atoms. (a-d) Crack initiation and propagation. Atoms are colored according to atomic stress in the top row and coordination numbers in the bottom row. In coordination number coloring, hydrogen atoms are highlighted in red.



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Figure 5. The correlations among the average grain size, the density of GB atoms, and the fracture strength of polycrystalline graphene. (a) The trend of the fracture strength of polycrystalline graphene with full GB hydrogenation as a function of the grain size. (b) The density of GB atoms as a function of the grain size.


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ACS Paragon Plus Environment

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Hydrogenated Grain Boundaries Control the Strength and Ductility of

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