Atomistic-Scale Simulations of Defect Formation in Graphene under Noble Gas Ion Irradiation Kichul Yoon,† Ali Rahnamoun,† Jacob L. Swett,‡ Vighter Iberi,§,∥ David A. Cullen,⊥ Ivan V. Vlassiouk,# Alex Belianinov,∥,¶ Stephen Jesse,∥,¶ Xiahan Sang,∥ Olga S. Ovchinnikova,∥,¶ Adam J. Rondinone,∥ Raymond R. Unocic,∥ and Adri C.T. van Duin*,† †
Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ Advanced Technology Center, Lockheed Martin Space Systems Company, Palo Alto, California 94304, United States § Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States ∥ Center for Nanophase Materials Sciences, ⊥Materials Science and Technology Division, #Energy & Transportation Science Division, and ¶Institute for Functional Imaging of Materials, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States S Supporting Information *
ABSTRACT: Despite the frequent use of noble gas ion irradiation of graphene, the atomistic-scale details, including the effects of dose, energy, and ion bombardment species on defect formation, and the associated dynamic processes involved in the irradiations and subsequent relaxation have not yet been thoroughly studied. Here, we simulated the irradiation of graphene with noble gas ions and the subsequent effects of annealing. Lattice defects, including nanopores, were generated after the annealing of the irradiated graphene, which was the result of structural relaxation that allowed the vacancy-type defects to coalesce into a larger defect. Larger nanopores were generated by irradiation with a series of heavier noble gas ions, due to a larger collision cross section that led to more detrimental effects in the graphene, and by a higher ion dose that increased the chance of displacing the carbon atoms from graphene. Overall trends in the evolution of defects with respect to a dose, as well as the defect characteristics, were in good agreement with experimental results. Additionally, the statistics in the defect types generated by different irradiating ions suggested that the most frequently observed defect types were Stone-Thrower-Wales (STW) defects for He+ irradiation and monovacancy (MV) defects for all other ion irradiations. KEYWORDS: atomistic analysis of graphene, ion irradiation, ReaxFF, graphene defects, aberration-corrected STEM copy (HRTEM),31,32 scanning tunneling microscopy (STM),33 and Raman spectroscopy.28,34−36 Although these characterization tools can provide direct insight into the structural defects in graphene on the atomic scale, it has been very difficult to study the atomistic details regarding the time evolution of defects as well as the dynamic processes that occur during irradiation. Computationally, molecular dynamics (MD) or kinetic Monte Carlo (kMC) simulations have been employed to study the ion irradiation of graphene.37−40 In most cases, graphene was described either by the potentials of reactive
G
raphene is an ideal two-dimensional material that is composed of covalently bonded carbon atoms arranged in a hexagonal network1 and has been intensely studied due mostly to its remarkable mechanical, electronic, thermal, and chemical properties.1−12 Various types of defects, which can occur in graphene, are known to modify its properties.4,13−21 While there have been many efforts to avoid defects, due to their adverse effects on graphene properties, other studies aim to intentionally produce defects in graphene for a number of important applications.11,12,17,22−26 In many experiments, irradiation of electrons and ions has been used to introduce defects into graphene, and these defects have been characterized with various tools, including aberrationcorrected scanning transmission electron microscopy (STEM),27−30 high-resolution transmission electron micros© 2016 American Chemical Society
Received: May 7, 2016 Accepted: August 17, 2016 Published: August 17, 2016 8376
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Figure 1. Graphene irradiated with He+ ions at 25 kV: (a) ReaxFF-modeled graphene before the annealing; (b) ReaxFF-modeled graphene irradiated with the same doses used in the experiments, followed by annealing (top). The black arrow indicates a mobile monovacancy defect during the annealing without being reconstructed into a more stable form. Aberration-corrected STEM images of the graphene irradiated at 1015, 1016, and 1017 ions/cm2 (bottom).
empirical bond order (REBO)41,42 or by reactive force field (ReaxFF).43,44 Energetic ions were considered to damage graphene via nuclear collisions only, while the electronic contribution was ignored due to graphene’s excellent electronic and thermal properties.37,38 In this sense, the incoming “atoms” were commonly referred to as “ions” in the analogy for experiments. Lehtinen et al.37 reported the effects of ion energy on defect type and concentration under the impact of various noble gas ions with free-standing graphene. Although the study presented a significant amount of data regarding the impacts, they were limited to single ion impact events. Lehtinen et al.,38 in the following year, reported morphological changes in graphene under multiple ion impacts by using kMC methods. However, the defect formation in the method was described based on the statistical data obtained from the single ion impact. Therefore, the accuracy appears to be reduced at high dose irradiation. In addition, the analyses of atomistic-scale details, such as defect features and dynamic processes that occur during irradiation, were lacking. In this study, we use the fully dynamic ReaxFF method45 to understand the nature and evolution of defects in graphene that were created by ion beam irradiation and subsequent annealing and support these results with experimental evidence. In addition, the dynamic processes were described, including reconstruction of Frenkel defects (adatom−vacancy pair) into Stone-Thrower-Wales (STW) defects and healing of Frenkel defects during annealing. The simulation results were compared with experimental results generated using helium ion microscopy and aberration-corrected STEM imaging.
RESULTS AND DISCUSSION STEM images of graphene irradiated under an accelerating voltage of 25 kV at 1015, 1016, and 1017 He+ ions/cm2 and 26.7 kV at 1.5 × 1014, 6.22 × 1014, and 2.55 × 1015 Ne+ ions/cm2 are presented in the second rows of Figures 1b and 2b. The graphene models in the first rows of the Figures 1b and 2b were taken from the ReaxFF simulations after ion irradiation, followed by the annealing processes described in the Methods section. He+ irradiation at a dose of 1015 ions/cm2 did not generate any observable defects, both in the experiment and the simulation, due to the low probability of generating defects via the impact of graphene by He+ irradiation, possible covering of the defects by the contamination, and due to healing and reknitting occurring as a result of defect interaction with hydrocarbon surface contamination. At a higher dose, STWtype defects and small nanopores were generated in the experiment, while only STW defects were generated in the ReaxFF simulation. Larger nanopores, as well as amorphized regions, were observed at the highest dose in the experiment, and a smaller nanopore and similar amorphizations were observed in the ReaxFF simulations. In both the experiments and simulations, the accumulation of a significant amount of defects, due to a high dose, and the subsequent reconstruction of the defects resulted in amorphization of almost the entire impacted region. Similarly, with Ne+ irradiation, as the dose increased, the defect density and size of the nanopores increased, as shown in Figure 2b. Note that the energy and doses used in the Ne+ irradiation experiments are not exactly the same as the ones used in the ReaxFF simulations. An 8377
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Figure 2. Graphene irradiated with Ne+ ions at 26.7 kV (experiments) and 25 keV (simulations): (a) ReaxFF-modeled graphene before the annealing; (b) ReaxFF-modeled graphene irradiated at 1014, 1015, and 2 × 1015 ions/cm2, followed by annealing (top). The black arrows indicate mobile monovacancy defects during the annealing without being reconstructed into more stable forms. Aberration-corrected STEM images of the graphene irradiated at 1.50 × 1014, 6.22 × 1014, and 2.55 × 1015 ions/cm2 (bottom).
known reconstructed form of a divacancy defect. Indeed, the two monovacancy defects initially coalesced into a divacancy defect, followed by reconstruction to the 5555−6−7777 defect. In graphene irradiated at 1015 Ne+ ions/cm2, some monovacancy defects were still mobile (indicated by black arrows) without being reconstructed into a more stable structure, even after extended high-temperature annealing. A higher density of defects was generated at 2 × 1015 Ne+ ions/cm2, and the defects were composed mostly of mono- and divacancy defects. After the annealing, most of the vacancy-type defects were reconstructed, forming a small nanopore, as well as an amorphization region around the nanopore. The ratios of five-, six-, and seven-membered rings within the impacted area were obtained as 12.4, 77.1, and 8.6%, respectively. The irradiation of heavier ions, such as Ar+ and Kr+ ions, on graphene also were simulated to investigate the generation of higher defect density and larger nanopores. As indicated in Figure 3b,d, the nanopore and the amorphized area generated by the irradiation of the highest-dose Kr+ was the largest among the ones generated by all other conditions. Long-ordered edge structures were not observed in all cases because of the edge strain effect that forced the formation of circular-shaped nanopores, lowering the structural energies. The graphene structures before annealing are presented in Figure 3a,c. Some characteristic defects were observed, including 555−777 defects in the Ar+-irradiated (1014 and 1015 ions/cm2) graphene, which are also well-known reconstructed forms of a divacancy defect, and 555555−66−777777 defect in Kr+-irradiated (1014 ions/ cm2) graphene, which is a reconstructed form of a tetravacancy defect.
increase in both the defect density and nanopore size with an increase in the dose was in qualitative agreement between the experiments and simulations, although the ReaxFF simulations seemed to generate smaller nanopores compared to the experiments. The discrepancy may arise from the fact that impurity atoms (such as Si, Cu, and Fe) are inherently present within or on the graphene lattice and within the contamination layer, the presence of which may have potentially catalyzed the nanopore enlargement process during He+ and Ne+ irradiation and subsequent STEM imaging. Metal-catalyzed etching of graphene, also called chiseling, has been previously reported.27,46 Indeed, as indicated in the STEM images of He+and Ne+-irradiated graphene, the high-contrast metal atoms (likely Fe or Cu) and medium-contrast Si atoms were observed at the edges of the large nanopores, suggesting the possibility of metal-catalyzed etching of graphene. We also note that the possibility of intrinsic underestimation of the simulation models cannot be ruled out as the cause of the discrepancy. The structural evolution of He+- and Ne+-irradiated graphene after annealing is demonstrated in Figures 1 and 2 (before annealing (a), and images in the first rows of (b) after annealing). STW defects were stable even at the hightemperature annealing, and no structural changes were observed in the graphene irradiated at 1016 He+ ions/cm2. However, the defects in graphene irradiated at 1017 He+ ions/ cm2 were significantly reconstructed, mainly forming five-, six-, and seven-membered rings, and their ratios within the impacted region were 25.0, 53.2, and 16.9%, respectively. The two monovacancy defects generated by 1014 Ne+ ions/cm2 were reconstructed into a 5555−6−7777 defect, which is a well8378
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Figure 3. ReaxFF-modeled graphene irradiated with 25 keV Ar+ and Kr+ ions at 1014, 1015, and 2 × 1015 ions/cm2. (a,b) Ar+-irradiated graphene before and after annealing, respectively. The black arrow indicates a mobile monovacancy defect during the annealing without being reconstructed into a more stable form. (c,d) Kr+-irradiated graphene before and after annealing, respectively.
The sputtering yields by He+, Ne+, Ar+, and Kr+ irradiation at 25 keV were obtained as around ∼0.03, ∼13, ∼30, and ∼50%, respectively. These values are in reasonable agreement with the values reported by Lehtinen et al., that is, ∼0.05, ∼16, ∼35, and ∼64% for He+, Ne+, Ar+, and Kr+ impact, respectively. However, the values from the current study were consistently lower, and the difference increased as the size of the irradiating ion increased. This can be explained by considering the fact that our data were obtained from the multiple ion impacts, while the data by Lehtinen et al.37 were obtained from a multiple number of independent single ion impacts and average of the numbers of sputtered atoms in each impact. In our multi-ion impacts, some ions passed through open areas in graphene, which were generated as the result of previous impacts with ions, and they did not contribute to any defect generation. Therefore, the sputtering yields from this study were lower than the previously reported values. Linear carbon chain (LCC) structures were generated in both Ar+- and Kr+-irradiated graphene as the result of collision cascades that were initiated by the impact of the heavy ions with graphene. The average bond order between neighboring carbon atoms in the LCC structures was obtained as ∼1.6,
indicating that the carbon atoms are coordinatively unsaturated and thus reactive. All of the unsaturated carbon atoms in the irradiated graphene are colored blue in Figures S3−S6 in the Supporting Information section 4, allowing them to be easily identified. Indeed, the LCC structures were reconstructed into more stable forms during the annealing process, as shown in Figure 3 and Figure S4. Still, the nanopore edges were composed of coordinatively unsaturated atoms, suggesting that they could be the reaction sites for functionalization of graphene. Functionalization of nanopore edges was briefly explored by performing the hybrid grand canonical Monte Carlo/molecular dynamics (GC-MC/MD) method described by Senftle et al.47 The system initially consisted of the relaxed graphene in vacuum that was taken after Kr+ 2 × 1015 ions/cm2 irradiation, followed by high-temperature annealing. OH radicals were inserted into the system, following the acceptance criterion that was described in ref 47, and water molecules that formed during MD minimization were eliminated. The pore edges were functionalized either by hydroxyl groups or atomic oxygen, forming an epoxide-like arrangement, as shown in Figure S11, turning into hydrophilic edges. This kind of functionalized 8379
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percentage of displaced carbon atoms appear to exponentially increase in the logarithmic x-scale plot, but it is actually closer to linear or converging, as indicated in the linear x-scale plot (inset of Figure 4a). On an experimental time scale (∼seconds), defects generated by ion impact are expected to experience relaxation between individual impacts, but this is not the case on the MD time scale. However, the relaxation before additional ion impacts does not seem to be significantly affecting the defect density, as observed from the results of several test simulations in Figure S10. In order to statistically investigate the correlation between the type of defects and the type of irradiating ions, we performed 100 simulations for each ion irradiation, with doses of 1016, 2 × 1014, 1014, and 6.6 × 1013 ions/cm2 for He+, Ne+, Ar+, and Kr+, respectively. The doses were chosen so that a similar defect density could be generated. The defect yields (%), defined as the total number of defects generated divided by the total number of impacts and multiplied by 100, were obtained as ∼0.4, ∼18, ∼34, and ∼48%, respectively, for the impacts by He+, Ne+, Ar+, and Kr+. Figure 5 summarizes the
nanopore edges will be beneficial in various applications, including membranes for aqueous proton transfer and water desalination. In order to quantitatively compare the defects generated in the simulations, we obtained the atomic ratio of the displaced carbon atoms from graphene (related to the size of the nanopore, defined as a single aperture defect greater than a tetravacancy) and its crystallinity (related to the area of the amorphized region). We note that once the number of defects has reached a high enough density, such that they are likely to aggregate when annealed, the fraction of carbon atoms displaced is related to the size of the nanopores. We present in Figure 4a the ratio of the number of displaced carbon atoms
Figure 4. Quantitative measures of the defect density in the irradiated graphene. Data were obtained by averaging three independent results. (a) Change in the displaced carbon atoms (%), defined as the number of displaced carbon atoms over the number of total carbon atoms in pristine graphene within the impacted region, with respect to dose. Linear x-scale plot with the same data (inset). He refers to the bottom x-axis, while Ne, Ar, and Kr refer to the top x-axis. (b) Change in the crystallinity (%), defined as the number of six-membered rings over the total number of rings in the impacted region, with respect to a dose.
Figure 5. Statistics from 100 simulations in each He+ (1016 ions/ cm2), Ne+ (1.6 × 1014 ions/cm2), Ar+ (1014 ions/cm2), and Kr+ (6.6 × 1013 ions/cm2) irradiation: (a) types of defects generated by different ions; (b) types of reconstructed structures of Frenkel defects; (c) adatom distribution from their original lattice position.
to the total number of carbon atoms in the pristine graphene (within the impacted region) and in Figure 4b the crystallinity of the defected graphene, defined as the number of sixmembered rings over the total number of rings in the impacted graphene. It is clear that as the dose increased and the type of irradiating ions became heavier, more carbon atoms were displaced from the graphene, generating larger nanopores. Also, the crystallinity of the graphene surrounding the nanopores decreased, indicating that more severe amorphization occurred under irradiation with a higher dose and heavier ions. Note that the x-axes in Figure 4a,b are logarithmic in scale. The
statistical analysis results. In the He+ irradiation, STW defects (65.1%) were the most frequently generated defect type, followed by Frenkel defects (23.4%). Under the 1016 He+ ions/ cm2 irradiation, the probability of generating monovacancy defects was negligible. In Ne+, Ar+, and Kr+ irradiations, however, the monovacancy defect (∼73%) was most frequently observed. The ratios of all the defects generated in Ne+, Ar+, and Kr+ irradiations were very similar. The reason for having more vacancy-type defects in Ne+, Ar+, and Kr+ irradiations was the larger amount of energy transfer between ions and graphene after impact, which was caused by larger collision 8380
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ACS Nano cross sections. On the contrary, energy transfer via the impact of He+ with graphene, in most cases, was not enough to overcome complete carbon displacement from the graphene. Instead, formation of STW and Frenkel defects, which required a lower amount of energy, were most frequently observed. The number of sputtered atoms per ion impact for Ne+, Ar+, and Kr+ were measured as 0.19, 0.27, and 0.56, respectively, in the 400 simulations. Frenkel defects were the second most frequently observed defect type in each irradiation condition. We collected the defect structures immediately after the irradiations and obtained the distribution of adatoms from their original site (center of vacancy). The results are summarized in Figure 5c. With He+ irradiation, all the adatoms were distributed within 5 Å, while in the irradiations of all other ions, some adatoms were displaced further than 10 Å (indicated as the infinity symbol, ∞). The adatoms were distributed further away as a result of grazing collisions by heavy ions that transferred higher energies to the adatoms, which resulted in the displacement of carbon atoms along the graphene’s plane direction and finally the adatoms being trapped by interactions with other carbon atoms in the graphene. The peaks were observed at approximately 3 Å in all cases. Figure 5b presents the reconstruction of Frenkel defects. In this process, the irradiated graphene structures were annealed at 2000 K for 100 ps, and the reconstruction processes during annealing were monitored. Note again that we used 2000 K for the annealing to accelerate the diffusion of adatoms and their subsequent reconstruction, both of which are known to be observed near room temperature.32,48,49 The annealing time and temperature were chosen to allow most of the adatoms to be reconstructed into a more stable form, while monovacancy and STW defects remained at their original positions. After annealing, most of the Frenkel defects either reconstructed into STW or healed, forming six-membered rings. In the graphene irradiated with a series of heavier ions, an increased number of adatoms were displaced further away from the vacancy site, and some of these adatoms were not able to encounter a vacancy site, even after their long migration paths during annealing, leaving them as Frenkel defects. Also, in some other cases, the adatoms that were distributed further away were merged into the pre-existing complex defects, forming even more complex defects. The dynamic processes that described the reconstruction of Frenkel defects into STW defects and perfect six-membered rings are presented in Figure 6a,b, respectively. In both cases, an adatom was first brought near the vacancy site. When the bond between the adatom and a neighboring atom (1−2 bond,
in Figure 6a) rotated approximately 90°, followed by all the atoms in the defect site becoming saturated through bond formation with their neighbors, the STW defect was generated. However, when the adatom (1, in Figure 6b) moved toward the center of the vacancy without any bond rotation, the Frenkel defect was healed, forming perfect six-membered rings. The reconstruction of Frenkel defects in CNT was previously reported by Kotakoski et al.,32 and the results from the current study are consistent with their results. The types of defects observed more than three times are summarized in Figure 7a (He+-irradiated graphene) and Figure
Figure 7. Types of defects that were observed more than three times in 100 simulations of each He+ (1016 ions/cm2), Ne+ (1.6 × 1014 ions/cm2), Ar+ (1014 ions/cm2), and Kr+ (6.6 × 1013 ions/cm2) irradiation: (a) types of defects observed from He+-irradiated graphene ((a-3) and (a-4) were reproduced with permission from ref 28; copyright 2014 Nature Publishing Group); (b) types of defects observed from Ne+-, Ar+-, and Kr+-irradiated graphene.
7b (Ne+-, Ar+-, and Kr+-irradiated graphene). In Figure 7a, the STW-type defects in (a-3) and complex defects in (a-4) were experimentally observed after He+ irradiation.28 Surprisingly, similar defect types were observed in our simulations, as shown in (a-1) and (a-2). Other types of complex defects also were observed, including an inverse STW defect adjoining a 5−8−5 defect (a-5) and 5555−77−8 (a-6). In Figure 7b, the frequently observed defects in Ne+-, Ar+-, and Kr+-irradiated graphene were as follows: monovacancy (b-1); STW (b-2); Frenkel defect that was not completely reconstructed (b-3); divacancy (b-4); 5−8−5 (b-5); and 555−777 (b-6), both of which were reconstructed from divacancy; 555−6−777, which was observed also from He+-irradiated graphene (b-7); divacancy with an adatom (b-8); incomplete combination of a STW and 5−9 reconstructed monovacancy (b-9); 5−77−8−5 that was reconstructed from a monovacancy adjoining a STW defect.
CONCLUSIONS We investigated the atomistic-scale details of graphene under irradiation by noble gas ions and the subsequent annealing to monitor the evolution of defects as a result of irradiating ion type and dose. The annealing allowed the defects generated in graphene to reconstruct into more stable structures, forming nanopores or amorphized regions. Irradiation by a series of heavier ions (with larger collision cross section) and at higher
Figure 6. Dynamic processes of the representative reconstruction of Frenkel defects: (a) STW defect reconstructed from the Frenkel defect; (b) perfect six-membered rings reconstructed from the Frenkel defect. 8381
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the structures before and after the annealing processes are discussed below. In all other irradiation simulations (Ne+, Ar+, and Kr+), the irradiated graphene structures were collected after the impacts from fewer doses (1014, 1015, 2 × 1015 ions/cm2) since they were much more destructive compared to the He+ ions, due to larger collision cross sections. The graphene structures were initially annealed at 1500 K for 25 ps, in the same manner as the He irradiation simulations, but a subsequent longer annealing was performed at a higher temperature (3000 K) to accelerate relaxation of the graphene structures with higher densities of vacancy-type defects. Note that monovacancy defects are known to be mobile, even at slightly above room temperature.52,53 However, the time scales for the diffusion of monovacancy defects at near room temperatures are not achievable in atomistic simulations. Therefore, a high temperature (3000 K) was used in the annealing. Experimental Methods and Details. He+ and Ne+ irradiation experiments were performed using a Zeiss ORION NanoFab scanning helium ion microscope, which is equipped with a gas field ion source and operated at 25−27 kV, 0.1−1 pA beam current, and a 0° angle of incidence. To achieve the desired dose, the beam was scanned over the suspended chemical vapor deposition graphene (graphene grown via chemical vapor deposition) with a 500 nm field of view divided into 512 × 512 pixels, which optimizes beam overlap for uniform dosing. For each dose, the appropriate dwell time and number of frames was chosen to achieve the correct dose given the beam current. Aberration-corrected STEM imaging was performed using a Nion UltraSTEM operated at 60 kV accelerating voltage, which is below the knock-on radiation damage threshold for pristine graphene. The graphene defects were also observed to be stable under these imaging conditions (60 pA probe current, 32 μs dwell time, 7.8 pm pixel size). However, imaging by the electron beam may have a minor effect on modifying the graphene defects produced via ion beam irradiation.54 Medium-angle annular dark-field (MAADF) images were acquired with a convergence semiangle of 30 mrad and a 54−200 mrad collection semiangle. Prior to STEM imaging, the samples were baked for approximately 8 h under high vacuum at 160 °C in order to reduce surface contamination. To quantitatively analyze graphene defects, the atomically resolved MAADF STEM images were processed by first masking off regions that contain only the atomically resolved areas and then processed using a PCA-based sliding filter.55,56 Atomic columns were identified using an atom finding algorithm;57 highlighted in the atomically identified images are sets of defects that are common to this dosing of He+ and Ne+.
doses (causing a higher probability of displacing carbon atoms from graphene) resulted in larger nanopores, as well as a wider amorphized region around the nanopores. We found highly encouraging agreement on the trend in the evolution of defects between the simulations and experiments. The types of defects generated by different irradiating ions were statistically analyzed. The He+-irradiated graphene most frequently exhibited STW defects (65.1%), while the Ne+-, Ar+-, and Kr+-irradiated graphenes most frequently exhibited monovacancy defects (∼73%). This study provides insight into generating well-defined porosity in graphene and as a preliminary step in designing well-characterized functionalized carbon materials.
METHODS Computational Methods and Details. ReaxFF is a reactive molecular dynamics method that can describe connectivity changes smoothly, allowing for an accurate description of the chemical reactions entailed in bond formation and dissociation.45 The changes in the connectivity of particles are determined at every iteration step by bond orders that are calculated based on interatomic distances. Accordingly, valence and torsion angles, as well as chemical bonds, are treated properly, ensuring that their energy contributions disappear upon bond dissociation. In addition, nonbonded interactions such as van der Waals and Coulomb interactions are considered between particles, irrespective of connectivity. A detailed description of ReaxFF can be found elsewhere.43,45 Molecular dynamics simulations were performed using ReaxFF, implemented in the large-scale atomic/molecular massively parallel simulator (LAMMPS) package.50 In the irradiation simulations of He+, Ne+, Ar+, and Kr+ ions, graphene was described by the carbon parameters,4 which were developed from the ReaxFF C-2013 carbon parameters,44 and the repulsive interactions between graphene and ions were described by parameters that were optimized against a set of data obtained from density functional theory (DFT) calculations and Ziegler-Biersack-Littmark universal repulsive potential.51 The parametrization results (Figure S1), DFT settings, and force field parameters are provided in the Supporting Information. The periodic graphene sheet was constructed with approximate dimension of 52 × 40 Å2 and was fully equilibrated at 300 K by using a Nosé-Hoover thermostat. Ions with the impact energy of 25 keV were irradiated within the center area (30 × 20 Å2) of graphene, and the periodic edges were kept at 300 K, playing the role of heat sink during MD simulations in a microcanonical ensemble (Figure S2). We note that the overall defects were generated within the irradiated region, and it was extremely rare to see collision of irradiation-induced carbon adatoms with the edge region where the temperature is controlled, indicating that the artifacts that might have originated from the simulation boundary conditions seemed to produce negligible effects on defect density. Extremely small time steps (0.005, 0.01, 0.015, and 0.02 fs for He+, Ne+, Ar+, and Kr+ irradiations, respectively) were used to ensure the conservation of energy during the high-energy impacts. Note that the dose rates in the simulations could not be matched to the ones in the experiments, due to computational limits. Therefore, in order to avoid any artifacts that may arise in the simulations due to the use of different dose rates, we carefully chose the dose rates of 1027, 5 × 1025, 3.5 × 1025, and 2.4 × 1025 ions/cm2·s for He+, Ne+, Ar+, and Kr+ irradiations, respectively, which allowed a long enough time for the termination of cascade collisions between the impacts of each ion. In He+ irradiation simulations, the graphene structures were extracted after impacts of 1015, 1016, and 1017 ions/cm2. Each irradiated graphene structure was first annealed at 1500 K for a short time (25 ps) and cooled to 300 K to eliminate any unrealistic configurations. In order to allow more complete reconstruction of the defects, which may occur near room temperature in experiments but not during molecular dynamics time scale, a subsequent annealing was performed at 2000 K for a longer period (1.25 ns). A comparison of
ASSOCIATED CONTENT S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b03036. ReaxFF parametrization results, simulation setup, configuration of the irradiated graphene with coordinatively unsaturated atoms colored blue, quantitative image analysis of graphene defects from STEM images, effects of relaxation before additional ion impacts on defect density, and brief exploration of functionalization of nanopore edges (PDF)
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS Research was supported as part of the Fluid Interface Reactions, Structures and Transport (FIRST) Center, an Energy Frontier 8382
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Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (K.Y., X.S., R.R.U., A.C.T.vD.). Ion irradiation and scanning transmission electron microscopy was conducted as part of a user proposal at Oak Ridge National Laboratory’s Center for Nanophase Materials Sciences (CNMS), U.S. Department of Energy Office of Science User Facility (J.S., V.I., D.A.C., I.V., O.S.O.), and by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Batelle, LLC, for the Department of Energy (A.B., S.J.). A.R.’s contributiondevelopment of the Kr/C ReaxFF parameterswas supported by the U.S. Air Force Office of Scientific Research (AFOSR), Grant No. FA9550-11-1-0158.
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