Stability and Dynamics of the Tetravacancy in GrapheneAlex W. Robertson,† Gun-Do Lee,*,‡ Kuang He,† Euijoon Yoon,‡ Angus I. Kirkland,†

and Jamie H. Warner*,†

†Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom‡Department of Materials Science and Engineering, Seoul National University, Seoul 151-742, Korea

*S Supporting Information

ABSTRACT: The relative prevalence of various configurations of thetetravacancy defect in monolayer graphene has been examined using aberrationcorrected transmission electron microscopy (TEM). It was found that the twomost common structures are extended linear defect structures, with the 3-foldsymmetric Y-tetravacancy seldom imaged, in spite of this being a low energy state.Using density functional theory and tight-binding molecular dynamicscalculations, we have determined that our TEM observations support a dynamicmodel of the tetravacancy under electron irradiation, with Stone−Wales bondrotations providing a mechanism for defect relaxation into lowest energyconfigurations. The most prevalent tetravacancy structures, while not necessarilyhaving the lowest formation energy, are found to have a local energy minimum inthe overall energy landscape for tetravacancies, explaining their relatively highoccurrence.

KEYWORDS: Graphene, ACTEM, HRTEM, electron microscopy, defects, TEM, DFT

The transport properties of graphene have been extensivelyinvestigated and show promise for future device

technologies due to its monatomic thickness and high carriermobility.1 More specifically, the development of spintronicdevices requires materials whose magnetic properties can becontrolled, so as to maximize the relative resistance change.Graphene has been investigated as a candidate material for suchdevices, with zigzag edges,2 dopants,3−5 and vacancystructures6−9 proposed as exhibiting ferromagnetism. However,understanding the distribution and stability of these defectsneeds to be confirmed through experiment.The theoretical and modeling literature on vacancies in

graphene is extensive;10−14 however, it is important to be ableto validate these calculations with experimental data. Exper-imental techniques such as scanning tunneling microscopy15

are invaluable in this regard, and recent work using aberrationcorrected transmission electron microscopy (ACTEM)16 hasalso enabled the study of graphene at the atomic level,17,18 withaccelerating voltages of 80 kV or less greatly reducingsputtering damage.19 ACTEM has the additional advantage ofbeing able to controllably generate defects in situ by electronbeam induced radiation damage. This can be achieved byincreasing the accelerating voltage above the knock-onthreshold of ∼80 kV,20 or by significantly increasing thecurrent density,21 before resetting the beam to conditions thatno longer cause damage to the material. This latter approach tothe generation of defects permits their characterization in largequantities, providing increased statistical confidence in thestability and prevalence of defect structures studied. Previously,these approaches have been used for the characterization of

both the mono- and divacancy defect.17,22−24 However, morecomplex vacancies that can exhibit many configurations, such asthe tetravacancy, have received little experimental attention todate. The tetravacancy is of particular interest due to itpotentially exhibiting magnetism when in certain configura-tions,25,26 but experimental confirmation is required regardingwhether the tetravacancy actually stabilizes in the form of thesemagnetic structures or instead exhibits another stableconfiguration.There are multiple different permutations of the tetravacancy

defect, with the simplest ones illustrated in Figure 1, togetherwith the naming scheme for each. The extended armchairdefect (Figure 1a) is denoted as an extended defect after ref 27,which refers to its ability to form an infinitely long chain from arepeating unit along an appropriate axis, specifically thearmchair axis for the defect shown in Figure 1a. The defectin Figure 1b is formed by removing two adjacent carbon dimersfrom different armchair axes and is known as a U-vacancy.Alternatively, removing two dimers from parallel armchair axesyields the parallel armchair tetravacancy shown in Figure 1c.The tetravacancy in Figure 1d can be interpreted as an edgedislocation, with the two dislocation cores occupying adjacentlattice planes.28,29 Finally, Figure 1e shows a 3-fold symmetricY-vacancy, which together with the dislocation pair has beenthe subject of extensive theoretical studies.25,26,30−41 However,

Received: January 10, 2014Revised: February 14, 2014Published: March 3, 2014

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there is no experimental evidence to suggest that these defectsare the more prevalent forms.By selective creation of defects using high beam current

density irradiation at 80 kV in the ACTEM, we have been ableto create many tetravacancy defects for study,21 yieldinghundreds of images of isolated tetravacancies. Graphene wassynthesized by chemical vapor deposition (CVD) on a liquidcopper catalyst42 and transferred to a holey silicon nitride TEMgrid by a PMMA scaffold. This was characterized by a JEOL2200MCO TEM fitted with CEOS third-order probe andimage aberration correctors operated at 80 kV. Raw ACTEMimages were typically subjected to one of two processingmethods, as noted in the respective figure captions. Smoothedimages were processed using a nearest-neighbor smoothing (3× 3) operator, and maximized filtered images replaced a pixel

value with the largest intensity value of the neighboring pixels.29

We also performed density functional theory (DFT)calculations and tight-binding molecular dynamics (TBMD)simulations10,34,43−45 (see Supporting Information) to studythe stability and formation processes, respectively, of thetetravacancy in graphene.

■ RESULTS AND DISCUSSION

Examination of all of the various configurations of the graphenetetravacancy imaged indicates that the defects shown in Figure2 were more prevalent than other structures. Figure 2a shows asmoothed ACTEM image of a reconstructed extendedtetravacancy, denoted as such so as to maintain consistencywith the nomenclature used to describe reconstructed zigzag

Figure 1. Atomic models of basic tetravacancy structures: (a) extended armchair vacancy; (b) U-vacancy; (c) parallel armchair vacancy; (d)dislocation core pair; (e) symmetric Y-tetravacancy. Armchair axes are highlighted in green and zigzag axes in light blue. Atoms removed to formeach vacancy are circled in blue.

Figure 2. The two most frequently observed tetravacancy defects. (a) Smoothed ACTEM image of a reconstructed extended vacancy. (b)Maximized filtered image calculated from (a). (c) Atomic model corresponding to the defect in (a). (d) Smoothed ACTEM image of an extendedarmchair vacancy, with a corresponding maximized filtered image and atomic models in (e) and (f), respectively. Scale bar is 0.5 nm in all cases. Thecolor scheme in (c) and (f) represents the number of carbons in each ring, with 4 = green, 5 = yellow, 6 = red, 7 = blue, and 8 = purple.

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edges.46 This was the most frequently observed tetravacancytype, seen for ∼20% of the recorded tetravacancies, and is

composed of a reconstructed repeating unit along the zigzagaxis. In Figure 2b, the image is subjected to a maximizing filter,

Figure 3. (a) Smoothed ACTEM image of a Y-tetravacancy defect along with (b) maximized filtered image and (c) atomic model. Scale bar in allcases is 0.5 nm.

Figure 4.Maximized filtered ACTEM images and accompanying atomic models of observed tetravacancy structures. The color scheme in the atomicmodels represent the number of carbons in each ring, with 4 = green, 5 = yellow, 6 = red, 7 = blue, and 8 = purple. Scale bars are 0.5 nm in all cases.

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and a color-coded atomic model of the defect is shown inFigure 2c. Figure 2d shows a representative ACTEM image ofthe second most common tetravacancy, the extended armchair,as in Figure 1a. Figure 2e,f shows the maximized filter andatomic model of Figure 2d, respectively.Our ACTEM analysis shows evidence for only two of the

postulated tetravacancy structures in Figure 1; the extendedarmchair vacancy (shown in Figure 2d) and limited occurrenceof the Y-tetravacancy (Figure 3). Figure 3a shows a smoothedACTEM image of an isolated Y-tetravacancy structure,alongside a maximized filtered image and atomic model (Figure3b,c). We have not found any instances of an isolated parallelarmchair vacancy, dislocation dipole or the U-vacancy.Figure 4 shows a montage of other observed tetravacancy

structures, for which we have calculated formation energiesusing DFT. The remaining rare tetravacancy structures thatwere occasionally observed were not analyzed further but arepresented in the Supporting Information for reference. The

infrequent observation of notionally stable tetravacancystructures, such as the Y-vacancy or the dislocation dipole,provides insight into the formation mechanisms for tetrava-cancies. We find that some of the observed tetravacancystructures comprise alternating 5- and 7-membered rings thatform a closed loop that surrounds rotationally misalignedcentral 6-membered rings (e.g., Figure 4a), which is a moreenergetically favorable defect configuration;39 however, severalalso have gaps in the loop (e.g., Figure 4h,j). The mostfrequently observed structures resemble pairs of overlappingdivacancies, as illustrated in Figure 5. For this specificconfiguration, there are three stable divacancy types: the 585(Figure 5a), the 555-777 (Figure 5b), and the 5555-6-7777divacancy (Figure 5c), which transform between one anothervia Stone−Wales (SW) rotations.24 The majority of theobserved tetravacancies can be assembled from composites ofthese structures that overlap across a single carbon ring (Figure5d−g). This is in contrast to structures that are formed by the

Figure 5. (a−c) The three divacancy types; the 585, 555-777 and 5555-6-7777, respectively. (d) An extended armchair tetravacancy can beassembled by two 585 divacancies, sharing a carbon ring. The overlapping 5-membered rings in the center yield the 4-membered ring in the middleof the extended armchair defect. (e) Two 555-777 defects both overlapping over their 5-membered rings yields the defect imaged by TEM in Figure4k. (f) An extended reconstructed tetravacancy can be formed by a 555-777 merged with a 5555-6-7777. Overlapping the 5-membered ring with a 7-membered ring produces a 6-membered ring. (g) The defect in Figure 4g is a 5555-6-7777 defect and a 5-8-5 defect overlapping between a 7- and a5-membered ring, creating a 6-membered ring in the resultant defect. The color scheme in the atomic models represent the number of carbons ineach ring, with 4 = green, 5 = yellow, 6 = red, 7 = blue, and 8 = purple.

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ejection of four adjacent carbons, as shown in Figure 1,explaining our failure to observe configurations such as thedislocation core pair and the rare occurrences of the Y-vacancy.We propose that tetravacancies form by the migration andsubsequent coalescence of a pair of divacancies, rather than bysequential sputtering of an additional two carbons adjacent toan existing divacancy. Although divacancies can be readilyformed from monovacancies due to sequential carbon ejection,this is due to the significantly decreased knock-on threshold ofan undercoordinated carbon atom in the monovacancy.However, due to the reconstruction that a divacancy undergoesafter formation, there is no similarly large reduction in knock-on threshold for the neighboring carbons. Therefore, theejection of a further two neighboring carbon atoms is notsignificantly more likely to occur next to an existing divacancyrather than in a pristine graphene region. However, we notethat it is feasible that ion bombardment may formtetravacancies such as Y-vacancy by the ejection of adjacentcarbon atoms, as the larger mass incident particles will sputtermultiple carbon atoms in a single collision.3

In order to better understand the relationship betweenpredicted stability, as calculated from DFT, and the frequencyof our experimental observations, we present Figure 6a, whichshows the calculated formation energy as a function of totalabundance. The defect energy is plotted relative to the lowestenergy configuration, defined as zero. This shows anapproximately linear relationship between the four mostprevalent tetravacancy structures and their formation energy.However, the remaining 13 structures show no discernible

correlation. This could be a statistical consequence of their lowobservation count, as they were only imaged in fewer than 20instances. However, it is also necessary to consider that alldefects are continually irradiated by the electron beam, which at80 kV provides sufficient energy to provoke continued defectevolution through SW bond rotations.47 The defect state is thusdynamic, which can lead to oscillations between two or morelow-energy configurations through bond rotations, potentiallyreducing the number of times an individual structure isobserved. An example model of this is shown in Figure 6b,where a single SW rotation from the common reconstructedextended vacancy yields an alternative low-energy structure thatwas only observed on a few occasions. Example TEM images ofa similar such oscillation are presented in the SupportingInformation. Continued irradiation also explains why highenergy defect structures are ever observed, as more complexdefects may form through the evolution of an existing defect bymultiple SW rotations (Figure 6c). The SW rotation requiressignificant energy to unwind, inhibiting thermal annealing,47

and thus a defect can evolve in stages to a high energy state.This is illustrated in Figure 6d for the three defectscorresponding to the data points circled in red in Figure 6a.The lowest energy configuration can undergo a single SWrotation, increasing its energy by approximately 0.6 eV, and thisnew structure can also evolve via another SW rotation, alsoraising the energy by 0.6 eV. However, at each of theseevolution stages it is more probable that an electron collisionwill transfer sufficient energy only to unwind the SW rotationbackward but insufficient to push it to a higher energy state, as

Figure 6. (a) Scatter plot of the DFT calculated formation energy against observation frequency of a particular defect in a single image capturetogether with color coded schematics of the specific tetravacancy structure. The energy is plotted relative to the lowest energy structure, thereconstructed extended tetravacancy, defined as zero. Inset shows two unobserved candidate tetravacancy structures that have high formation energy.(b) A single SW rotation (arrow) is sufficient to reversibly transform between two observed low energy structures. (c) Energy landscape for defectevolution, illustrated with the SW rotation. There is a barrier to the formation of the evolved defect, but also a barrier preventing its relaxation backto the lower energy structure. (d) Formation of a few high energy structures is possible due to staged evolution, as shown for the defectscorresponding to the points circled in red in (a). Bonds that undergo SW rotations are denoted with arrows. The red line only qualitatively showsthe energy barriers for evolution/relaxation and is purely illustrative.

Table 1. Mean Observation Lifetimes for the Four Most Frequently Observed Tetravacancy Defects

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the barrier for SW unwinding is less than the energy requiredfor a second SW rotation. This explains the inverse relationshipbetween energy and observation frequency that can be seen forthe red circled points in Figure 6a.Figure 6a shows the total frequency of observation of a

particular structure and as such does not take into accountwhether a structure is frequently observed due to its stabilityover a prolonged period or because it is a common transitionstate in defect evolution. To address this, we have calculated themean number of sequential frames in which a particular defectstructure is observed without undergoing any alteration andhave used the time stamp information from each capture tocalculate the defect lifetime. The majority of tetravacancystructures have an observation count that is too low to permit ameaningful average lifetime estimate; however, for the fourmost frequently observed tetravacancy structures we find themean lifetimes given in Table 1. It is useful to contrast theselifetimes to those of the three divacancy structures imagedunder similar imaging conditions,21 as these are known tooscillate between different configurations. We find that the 585divacancy (Figure 5a) has a mean lifetime of 29 ± 6 s, the 555-777 a lifetime of 20 ± 6 s (Figure 5b), and the 5555-6-7777divacancy a lifetime of 91 ± 24 s (Figure 5c). The 5555-6-7777was found to either exist for prolonged, several minute stretchesor for brief periods of 10−20 s, hence the large standard errorof the mean. The ∼20−30 s divacancy lifetimes are 3−4 timesless than those recorded for the three most frequently observedtetravacancy defects, suggesting that the observed tetravacancyconfigurations are relatively stable. The fourth tetravacancy inthe table has a lifetime that is not significantly larger than thosefound for the divacancies, so it is possible that thisconfiguration is a common transitional state.We now explore why these structures are the most frequently

observed, even though there exist alternative tetravacancystructures that also have a low formation energy. Figure 7shows a defect evolution hierarchy, illustrating the SW rotation

paths by which the various tetravacancy structures relax tolower energy configurations. Each of the colored, curved arrowsindicates an evolution path triggered when the bond indicatedundergoes a SW rotation. Exceptions to this are labeled (i)−(iii), which all require two bond rotations. It is evident that thethree most frequently observed configurations are the lowestenergy configuration for each path. However, below a certainenergy a defect can be effectively locked into a particular pathto minimize its energy; thus, it is not always possible for atetravacancy to reach the global energy minimum of thereconstructed extended vacancy structure. As an example, atetravacancy from group B would have to go through severalSW rotations, passing through group D configurations, before itcould relax to the lowest energy reconstructed extendedvacancy in group C. In this case it is more probable that itwill evolve to the local minimum, which for this example wouldbe the lowest energy structure in group B, helping to explainwhy this defect structure is so frequently observed in spite of itsrelatively high energy. The low energy dislocation pair and Y-vacancy structures require two SW rotations to form whenbranching off from group C, and interestingly these bothrequire the same intermediate structure that has not beendirectly observed.In order to address both the dynamic nature of the evolution

of the tetravacancy and the formation by migration andsubsequent coalescence of divacancies, we have conductedTBMD simulations to model divacancy aggregation andtetravacancy evolution. Earlier, we demonstrated that thetetravacancy structures observed suggest an agglomeration ofdivacancies, rather than sequential ejection of carbon atoms. Tofurther explore this, we have performed TBMD simulationswith sequential sputtering of individual atoms and alsosimulations with four monovacancies all present at theinitialization. Examples of the former case are shown in Figures8a and 8b, which are performed over 40 ps at 4300 and 4100 K,respectively. Figure 8a shows an initial state consisting of two

Figure 7. Pathways for SW rotations in tetravacancies that lead to the most frequently observed configurations (circled). Each colored arrowindicates a single SW rotation, except those numbered with Roman numerals which show the two SW rotations required in the panels on the right.The bond rotation required are indicated by black arrows. Configurations which can develop in one of two ways have numbered pathwayscorresponding to the respective numbered bond rotation. Once a tetravacancy forms a structure in one of groups A, B, or C, then the lowest energyprobable configuration is that at the end of the chain for that group, which also match with the most frequently observed structures. Structures ingroup D are able to evolve into either group B or C.

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monovacancies, which rapidly assembles into a divacancy.Following this an additional monovacancy is created (frame 3),which eventually merges with the divacancy to form areconstructed extended tetravacancy, with the surplus carbonatom moving into a bridge position over one of the bonds(frame 8). This atom is subsequently ejected from the lattice(frame 9). The TBMD simulation shown in Figure 8b startswith a divacancy and a monovacancy, which evolves into a 5-8-

4-9 structure (frame 4), similar to the extended armchair defect.Following this an additional monovacancy is added (frame 5),which enables the defect to reconfigure and eventually relax toan extended armchair tetravacancy. While these simulationsshow final minimum energy tetravacancy structures that agreewith experiment, and in particular result in the two mostfrequently observed structures, they do not transit through anyof the other tetravacancies states that are also observed. Figure

Figure 8. Selected frames from three TBMD simulations. (a) Initially two monovacancies are created, with an additional vacancy added after initialassembly into a divacancy (third frame). This evolves into a reconstructed extended vacancy with the extra carbon atom in a bridge position (eighthframe), which is subsequently ejected (ninth frame). (b) Initially a divacancy and a monovacancy are created, similar to the third frame in (a). Thevacancies assemble into the structure in the fourth frame followed by a further vacancy addition (fifth frame). This eventually developed into anextended armchair defect (tenth frame). (c) Initially, there are two 5-8-5 divacancies (first frame). These migrate to adjacent positions (third frame)and undergo several transformations by SW rotations (arrows in frames 3 and 4). The structure then evolves to the reconstructed extendedtetravacancy (fifth frame) through an intermediate structure (fourth frame), which we also observe in ACTEM.

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8c shows the system initialized with two 5-8-5 divacancies,performing a simulation over 100 ps at 5000 K. Theexpectation is that as they converge that they would overlapand evolve through intermediate states that matched some ofthe less frequently observed tetravacancy structures. It can beseen that once the vacancies begin to coalesce (frame 3), anintermediate configuration can soon be observed (frame 4).This is the same type of tetravacancy as imaged by TEM inFigure 4a and supports the proposed divacancy mergerdiscussed in Figure 5. The tetravacancy in frame 4 subsequentlystabilizes by a bond rotation into the minimum reconstructedextended tetravacancy state, as was illustrated in Figure 6b. Theelevation of the temperature from 4000 to 5000 K wasnecessary for the simulation in Figure 8c due to the lack of anadditional carbon adatom, which was present in the first twosimulations, as this adatom helps to reduce the otherwise veryhigh energy barrier for divacancy diffusion.44 Completeanimations of the TBMD results are presented in MoviesS1−S3 for Figures 8a−c, respectively.

■ CONCLUSIONWe have reported the use of ACTEM to investigate theprevalence of the many different structural permutations of thetetravacancy defect. We have shown that the most frequentlyobserved structures do not simply correlate with DFTcalculated formation energies but were sensitive to the specificsof the vacancy creation mechanism. These results demonstratethe advantages of modeling complex materials systems with thesupport of experimental observations for reference. Specifically,none of the reported theoretical literature describing graphenetetravacancies considered the most frequently observedstructural archetype observed in our ACTEM analysis: theextended reconstructed vacancy. Furthermore, the frequentlymodeled symmetrical Y-tetravacancy was rarely observed. Wefind instead that the more commonly imaged tetravacancieswere dependent upon the specifics of tetravacancy formation,which we demonstrate as likely to be due to the coalescence ofdivacancy defects. We hope that this work provides insightsinto the stability of higher order vacancies in graphene and theirtransitional dynamics mediated by SW rotations.

■ ASSOCIATED CONTENT*S Supporting InformationDetailed experimental and computational methods plus furtherTEM image data. This material is available free of charge via theInternet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authors*E-mail jamie.warner@materials.ox.ac.uk (J.H.W.).*E-mail gdlee@snu.ac.kr (G.-D.L.).NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSJ.H.W. thanks the support from the Royal Society and BalliolCollege, Oxford. A.W.R. has been supported by EPSRC(Platform Grants EP/F048009/1 and EP/K032518/1). Finan-cial support from EPSRC (Grants EP/H001972/1, EP/F028784/1, and EP/F048009/1) is acknowledged. E.Y. andG.-D.L. acknowledge support from the SupercomputingCenter/Korea Institute of Science and Technology Information

with supercomputing resources (KSC-2013-C3-058), the BK21plus program, and from the National Research Foundation ofKorea (NRF) grant funded by the Korean government (RIAMNo. 2010-0012670, MSIP No. 2013003535).

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Nano Letters Letter

dx.doi.org/10.1021/nl500119p | Nano Lett. 2014, 14, 1634−16421642