Growth of two-dimensional Au patches in graphene pores: a density-functional study
GGrowth of two-dimensional Au patches in graphene pores:a density-functional study
Saku Antikainen, Pekka Koskinen ∗ NanoScience Center, Department of Physics, University of Jyvaskyla, 40014 Jyvaskyla, Finland
Abstract
Inspired by recent studies of various two-dimensional (2D) metals such as Au, Fe and Ag, we study thegrowth of two-dimensional gold patches in graphene pores by density-functional theory. We find that at roomtemperature gold atoms diffuse readily on top of both graphene and two-dimensional gold with energy barriersless than . eV. Furthermore, gold atoms move without barriers from the top of graphene to its edge and fromthe top of 2D gold to its edge. The energy barriers are absent even at the interface of 2D gold and graphene,so that the gold atoms move effortlessly across the interface. We hope our demonstration for the propensity ofdiffusing gold atoms to grow 2D gold patches in graphene pores will inspire the fabrication of these patchesexperimentally.
1. Introduction
The great success with graphene has sparked muchadditional interest to other possible two-dimensional(2D) materials. The dimensionality can change theproperties of the material greatly, as evidenced par-ticularly well by graphene: it has extremely highcarrier mobility and thermal conductivity, and itdemonstrates the Quantum Hall effect.[1, 2] An-other example is the transition-metal dichalcogenideMoS : bulk MoS is an indirect bandgap semicon-ductor, while a monolayer MoS is a direct gapsemiconductor.[3, 4] Both graphite and bulk MoS consist of covalently bound layers that are held to-gether by the weak van der Waals (vdW) interac-tions. Bulk metals have no such layered structures,and thus the fabrication of two-dimensional metallicstructures is more problematic. However, the recentinterest in 2D metals has triggered several studies toinspect the possibility of their existence.For example, the simulations of 2D metalshave shown promising results about their stabil- ∗ Corresponding author
Email address: [email protected] (PekkaKoskinen) ity. For gold Yang et al. have predicted a sta-ble, two-dimensional lattice structure with hexagonalsymmetry.[5] In addition, bond strength was foundto increase greatly when going from bulk 3D Au to2D Au, analogously to the case of 3D diamond and2D graphene. Similar predictions were made for 2Dsilver, which also was found to prefer a hexagonallattice structure.[1] In addition to static properties,Koskinen and Korhonen have predicted the existenceof a liquid phase in a free-standing, atomically thin2D Au layer suspended by graphene pores.[6] How-ever, a free-standing two-dimensional layer of gold isyet to be produced experimentally. Zhao et al. havemanaged to create a single-atom-thick iron layer sus-pended in graphene pores[7]; this idea could be like-wise applied to other metals. Shao et al. suggestwith their simulations that a square lattice monolayerof Fe is energetically unstable, and that the experi-mentally observed Fe monolayers would instead bemade of a mixture of Fe and C.[8] The possibility ofa combination of carbon and metal is certainly worthinvestigating in further studies of 2D metals.In any case, earlier studies indicate that goldwould be a particularly suitable candidate for a 2Dmetal. In nanoscale, gold has been found to behave
Preprint submitted to Computational Material Science November 6, 2018 a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b ery differently from the inert bulk gold. For ex-ample, small gold clusters of sizes up to 20 atomshave been shown to exhibit catalytic activity in thecombustion of CO[9], and gold cluster anions ofsizes as large as 11 atoms have been shown tohave two-dimensional ground states.[10] This excep-tional planar stability has been attributed to the rel-ativistic effects on gold.[11] The studies of 2D Auhave been promising, but creating a free-standing2D monolayer of gold is experimentally problem-atic. Yet it has been shown that a gold atom inter-acts strongly with a graphene edge.[12] These prop-erties of gold, combined with the success of produc-ing an Fe monolayer suspended in graphene pores,give faith that two-dimensional structures could besynthesized with gold and perhaps even with othermetals.Here we have used density-functional theory(DFT) to investigate how Au atoms behave at thegraphene edge and thus to model the growth of a2D gold patch in a graphene pore. We performedDFT calculations to investigate the behavior of goldatoms in four different stages of the growth process:i) originating from some source of atomic gold, goldatoms move on top of a graphene sheet, ii) a goldpatch begins to form at the edge of the graphene,iii) gold atoms move on top of the gold patch, andiv) gold atoms move from the top of the gold patchto its edge, thereby growing the patch. We studiedthe adsorption of gold at different adsorption siteson top of the graphene and 2D gold sheets, as wellas at the edge of the sheets. In addition, we deter-mined the potential energy surfaces (PES) for themovement of gold atoms between various adsorp-tion sites. These potential energy landscapes indicateclearly that gold atoms prefer to move quickly fromthe top of graphene across the graphene-gold inter-face and to the edge of the 2D gold patch.
2. Methods
Our goal was to model the growth of a goldpatch at the edge of a graphene pore. More pre-cisely, we modeled gold atoms moving on top ofgraphene towards the edge so that when they metthe edge a gold patch began to form. The overallprocess was broken into four stages, sketched in Fig- ure 1. First, we used a 2D graphene sheet with asingle gold atom at various adsorption sites. Sec-ond, to model the growth of graphene-2D metal in-terface we used graphene nanoribbon with varyingnumber of gold atoms at the edge. We used botha zig-zag-edged graphene nanoribbon (ZGNR) andan armchair-edged graphene nanoribbon (AGNR).Third, we used a 2D gold sheet with a single goldatom at various adsorption sites. And fourth, tomodel the actual growth of the gold patch, we useda one-dimensional gold edge with an additional goldatom at the edge.The simulations were performed in the atomicsimulation environment [13] and using the density-functional code GPAW [14, 15], which is based onthe projector-augmented wave method (PAW) [16].The generalized gradient approximation exchange-correlation functional of Perdew, Burke, and Ernz-erhof (PBE)[17] was used throughout the calcu-lations. All calculations were made in local ba-sis mode (LCAO) with double-zeta polarized basis,and some additional calculations in Finite Difference(FD) mode.For the 2D structures (graphene and 2D Au), theconvergence of adsorption energy of a single Auatom on the 2D sheet was tested with respect to unitcell size and k-point sampling. The adsorption en-ergy was calculated according to the equation E ads = E + E Au atom − E relax , (1)where E is the energy of the 2D sheet without theadsorbate, E Au atom is the energy of a free Au atomand E relax is the energy of the relaxed system. To get E relax , the atoms of the 2D sheet were fixed, while theadsorbate was allowed to move until the forces onall atoms were <0.05 eV/Å. The calculations weremade with both LCAO- and FD-mode, but we choseLCAO-mode for the rest of the simulations becauseits accuracy turned out to be sufficient compared toFD-mode. We chose k-point sampling of × × for both of the systems; for 2D Au we chose cell sizeof × atoms and for graphene × atoms, as theadsorption energy was found to be sufficiently con-verged already at these values. We used a lattice con-stant of 1.42 Å for graphene and 2.76 Å for 2D Au;the 2D Au had a hexagonal lattice structure.[5] All2 igure 1: Overall picture of the growth process. On the left is an infinite 2D graphene sheet with a growing patch of gold in themiddle. The growth process is divided into four pieces, labeled 1-4: 1) a 2D periodic graphene sheet with top[t], hollow[h] andbridge[b] adsorption sites, 2) a 1D periodic graphene zigzag-edge and armchair-edge with gold at the edge, 3) a 2D periodic goldpatch with top[t], hollow[h] and bridge[b] adsorption sites, and 4) a 1D periodic gold edge. the structures were non-periodic in z-direction witha 6.0 Å vacuum on both sides.The edges of gold and graphene were modeled us-ing 1D periodic systems. The periodicity was in x-direction with 6.0 Å of vacuum in both y- and z-directions. For the 1D structures (1D Au, ZGNR,and AGNR), the convergence of adsorption energyof an Au atom at the edge with respect to the numberof rows of Au or C-atoms in the y-direction was con-firmed. In these convergence calculations the atompositions were kept fixed because at this stage wewere merely interested in the convergence of the ad-sorption energy with respect to the electronic struc-ture rather than the relaxation of the atoms. Theedge energy of the nanoribbon was obtained from theequation for the total energy of the nanoribbon: E total = − N · ε + L edge · ε edge , (2)where N is the number of atoms in the unit cell, ε is the cohesion energy of the infinite 2D sheet, L edge is the total edge length (2 times the cell x-length)and ε edge is the edge energy. We chose the number of atoms in a row to be 12 for AGNR and 10 forZGNR, as this produced nearly equal unit cell sizesand allowed for enough gold atoms to be placed atthe edge. Finally, to keep the cell sizes comparable,the unit cell of 1D Au contained four gold atoms in arow.To study the actual growth of the gold patch, weadded Au atoms one by one to the edge and allowedthe system to relax between each added atom us-ing the Broyden-Fletcher-Goldfarb-Shanno (BFGS)algorithm for optimization[18]. For all the systemsdescribed above, we calculated the adsorption en-ergy of a gold atom at different sites. In addition,we studied the potential energy surface (PES) of goldatom on the 2D sheets and along the edges. To cal-culate the potential energy surfaces between variousadsorption sites, we used the nudged elastic band -method (NEB)[19] with 3 images between the startand end points, which was sufficient because the re-action paths were fairly simple.3 . Results We begun to model the growth process by inves-tigating the movement of a single gold atom on topof graphene. This is a good starting point becausemuch is already known of the diffusion of gold ongraphene.[20, 21] The obtained adsorption energiesof a single Au atom at hollow, bridge, and top siteson 2D graphene were calculated from Eq.(1). Theadsorption energies are very low, and top-site has aslightly higher energy (102 meV) than the bridge-site(96 meV) or the hollow-site (73 meV). The study ofAmft et al. [22] report similar numbers (top-site 99meV and bridge-site 81 meV) with the exception ofhollow site, where no binding was predicted. Alongwith PBE, they also tested other functionals to ac-count for the vdW interaction between the Au atomand graphene. While the introduction of vdW forcesincreased the adsorption energies, the order of the en-ergies remained the same, and the top site remainedenergetically most favorable. With or without ac-counting for vdW forces, their calculations showedthat the likely diffusion path is along the C-C bonds.Although vdW interactions are frequently importantin 2D materials, the usage of PBE is justified becausehere the main point of interest is the growth processof gold; within the scope of our work the effect of avdW functional would be minor.We studied the diffusion of Au atom on graphenefor three different paths: top-bridge (t-b), bridge-hollow (b-h) and hollow-top (h-t), and the results canbe seen in Fig. 2. No energy barriers were found on
Figure 2: a) Potential energy surface (PES) of Au atom on topof graphene and b) the unit cell used in calculations, with hol-low [h], bridge [b], and top [t] sites. Figure 3: a) Energy per atom of 1D gold, AGNR and ZGNR asa function of atomic rows. b) Edge energy of 1D gold, AGNRand ZGNR as a function of atomic rows. any of these separate paths. As the difference of en-ergies between top and bridge sites is very low (6meV), it is reasonable to expect a gold atom to movereadily on top of graphene from top site to top sitealong the bridges; the same conclusion was reachedin the aforementioned study of Amft et al. [22]
To investigate the growth of gold patch at grapheneedge we constructed zigzag and armchair graphenenanoribbons with 2-7 rows of C-atoms. Each rowcontained in AGNRs 12 C atoms and in ZGNRs 10C atoms. In Fig. 3a the energy per atom is calcu-lated and plotted as a function of rows. We fittedthe curve of Eq. (2) for 3-8 rows and thus obtainedthe edge energies, which can be seen in Fig. 3b. Intheir simulations of graphene nanoribbons, Koskinen4 t al. found the edge energies ε acedge = 0 . eV/Å and ε zzedge = 1 . eV/Å.[23] Our present results are in fairagreement with the earlier numbers, considering thatwe did no optimization at this point and that we fixedthe atom positions using constant bond length 1.42 Åof 2D graphene.Next we added a single gold atom at two differ-ent adsorption sites near the edge: at a hollow siteon the edge (in plane) and at a top site on top ofthe edge (out of plane). Three rows of C-atomswere used with fixed bottom-row atoms. The sys-tems were allowed to relax and the adsorption en-ergies were calculated. As a result, the top sitesturned out to be unstable, as during the optimiza-tion the Au atoms moved spontaneously to a hollowsite at the edge. From the edge adsorption energies( E acads = 5 . eV and E zzads = 4 . eV) we see thatthe binding is much stronger at the edge than on topof the graphene, which is expected due to the avail-able dangling bonds of edge carbon atoms. This is ingood agreement with previous literature.[12]Next we studied the movement of the Au atomalong the AGNR and ZGNR edges. The results ofenergy calculations on a path between two edge sitesare shown in Fig. 4. AGNR shows much higherenergy barriers ( ∼ ∼
80 meV).This might be attributed to the two carbon atomsthat the Au atom will have to move across on theAGNR path as opposed to one on the ZGNR path.In other words, in zigzag graphene nanoribbons thedangling bonds are equidistant, whereas in armchairgraphene nanoribbons they are separated alternat-ingly by longer and shorter distances.Next we begun to model stepwise the formationof the 2D gold patch to the graphene edge by addinggold atoms one by one. The gold atoms were addedto various top sites near the graphene edge (an ex-ample is seen in Fig. 4b). A total of 7 atoms wereadded to AGNR edge and 5 atoms to ZGNR; all op-timized systems are shown in Fig. 5. In AGNR, thefirst three gold atoms settled for the edge sites (suchas ones shown in Fig. 4d). The fourth atom also fitin the same row, but the fifth and sixth atoms startedforming a second row of 2D gold. The seventh atomreplaced another Au atom in the first row and nudgedit to the second row (Fig. 5h). In other words, the 2Dgold patch did not necessarily grow from the edge,
Figure 4: a) PES of Au atom moving along ZGNR edge and b)the unit cell used in ZGNR calculations, with top [t] and edge[e] sites. c) PES of Au atom moving along AGNR edge and d)the unit cell used in AGNR calculations, with top [t] and edge[e] sites. but it could grow also at the graphene-gold inter-face by nudging previously settled gold atoms fartheraway.For comparison, we also studied different 6- and7-Au atom systems at armchair edge (Fig. 5g and5i, respectively). Here the six atoms were placed indifferent starting positions before optimization. Thissix-atom system (Fig. 5g) was found to have lowerenergy than the one-atom-at-a-time grown system ofFig. 5f. Again with the addition of the 7th Auatom, we found no energy barrier when moving tothe edge. Interestingly, while the unit cells were keptroughly the same size with both AGNR and ZGNR,all 5 atoms fit in the first row with ZGNR. However,this came at the expense of large out-of-plane distor-tions (Fig. 5o). For ZGNR, we also studied an ad-ditional tetragonal geometry, where two gold atomswere bound out of the GNR plane at the edge (Fig.5l). This system was found to have higher energythan the other two-atom ZGNR system (Fig. 5k) by2.65 eV. Thus, energetically the interface prefers pla-nar growth.5 igure 5: Unit cells of AGNR and ZGNR systems with various amounts of gold at the edge, with top and side views for eachsystem. The red circle indicates the position in which the most recent Au atom was added (the atom that models the actual growth),and the arrow points to the final position after optimization.
After investigating the graphene-2D gold inter-face, we moved on to investigate a gold atom movingon top of 2D gold sheet. The adsorpion energies wereobtained for an Au atom on top of hollow, bridgeand top sites. Here we found that the hollow site hasthe highest adsorption energy (1.37 eV), bridge siteis quite close (1.28 eV) and top site has the lowestadsorption energy (0.91 eV). Compared to the caseof gold on graphene, adsorption energies are muchhigher, which can be understood by the different na-ture of chemical bonding. And while on grapheneAu preferred the top site, here it preferred the hollowsite.To illustrate the movement of the Au atom on 2DAu, we once again performed potential energy sur-face calculations, the results of which can be seen inFig. 6a. Here the Au atom follows the path hollow-bridge-top-hollow. PES suggests that Au atom mov-ing on top of 2D Au would most likely hop betweenthe hollow sites via bridge sites, with a mere 90 meVenergy barrier. Compared to graphene, the energybarriers here are still higher, especially on the paths involving the top site.
As the final stage, we investigated a gold atom atthe edge of 2D gold patch that was modeled by a 1Dgold ribbon. As with graphene, a 1D Au edge wasconstructed with 3-9 atomic rows, and the energy peratom was calculated and plotted with respect to thenumber of rows (Fig. 3a). The resulting edge ener-gies are shown in Fig. 3b.We studied the adsorption of a single Au atom onthe edge, with two adsorption sites of interest: hol-low site on top of the 1D Au, and an edge site on theside. The calculations were performed with 5 rowsof Au atoms while the two bottom rows were fixedduring the optimization. As a result, the adsorptionenergy at the edge site (2.27 eV) was found to be con-siderably higher than at the hollow site (1.62 eV). Itis notable that the optimization of an Au atom at ahollow site close to the edge brought the Au atommuch closer to the edge, almost to a bridge site.The movement of the Au atom at the edge wasstudied along two paths, along a path from the hol-6 igure 6: a) PES of Au atom on top of 2D gold and b) the unitcell used in 2D gold calculations, with top [t], bridge [b] andhollow [h] sites. c) PES of Au atom near the 1D gold edge andd) the unit cell used in 1D gold calculations, with hollow [h]and edge [e] sites. low site on top of the 1D Au to the edge site (h-e)and along a path between two edge sites (e-e). Theresults of the calculations are shown in Fig. 6c. Theatom was found to hop from the top to the edge eas-ily; the energy barrier was practically absent. Yet themovement along the edge however came with an en-ergy barrier of ∼
4. Discussion
The adsorption energies and the distances to thenearest neighboring atom of a single gold atom onvarious adsorption sites are summarized in Table 1.On top of graphene gold shows weak adsorption,while at the edge of graphene gold shows strong ad-sorption. There is also another possible adsorptionsite between the edge sites of ZGNR, as seen in Fig.4. But because the energy barrier separating the sitesis low (<10 meV), the lower-energy edge sites aremuch more likely to get occupied by the incominggold atoms.The overall picture of the growth process is quiteclear, at least when viewed via the potential en-ergy surface. Figure 7b illustrates one possible PES
Figure 7: a) PES of Au atom moving from the top of grapheneto the edge with different number of gold atoms at the edge.Each graph represents a different system as seen in Fig. 5 (theenergy on top of graphene is set equal for different systems,according to system in Fig. 5b). b) A sketch for the overall PESfor an Au atom contributing to the growth of the golden patch.Numbers 1-4 indicate the four stages shown in Fig. 1, with PESof stage 2 detailed in panel a. The blue path thus illustrates onepossible PES for a gold atom during the growth process. for a gold atom during its traversing to the edge.The extremely low energy barrier ( ∼
30 meV) showsthat a gold atom is likely to move readily on topof graphene. Moreover, it continues to move fromthe top to the edge without an energy barrier. Thesame trend continues even when more gold atoms areadded. Interestingly, there is also a possibility for thenew gold atoms to replace old gold atoms in the firstrow and nudge them farther to the second row, imply-ing that patches can grow also at the graphene-goldinterface.Furthermore, as with graphene, the energy barrierof a gold atom moving on top of 2D gold is verylow (90 meV on hollow-bridge-hollow path), and noenergy barrier was found when moving to the edgeof 2D gold. While atoms move to the edge effort-lessly, there still exists energy barriers when moving7 able 1: Au atom adsorption energies E ads (eV) and distances d (Å) to nearest atoms at different adsorption sites on graphene, 2DAu, AGNR, ZGNR and 1D Au. hollow bridge top edge E ads d E ads d E ads d E ads d et al. observed this kind of collapsefor a 2D Fe patch when the Fe particles were underprolonged electron irradiation; they found that the Fe membrane-armchair graphene interface remainedstable the longest, compared to Fe -zigzag grapheneinterface.[7] Nevertheless, the 2D Fe membranes re-mained stable for several minutes under the irradi-ation. The low energy barriers of our study (<0.5eV) indicate that room temperature (300 K) shouldbe enough for rapid diffusion and patch growth. Itcan be expected that the effects of temperature mightbe the greatest during the stage 2 of our study, at thegold-graphene interface, where the potential energydrops are the largest.We note that the choice of exchange-correlationfunctional affects more adsorption energies and lessdiffusion energy barriers. Since our main interesthere is on energy barriers, our choice to exlude vdWinteractions should be a reasonable approximation,as demonstrated in the study of Amft et al. [22] Over-all, the low energy barriers and the ease of the growthof the gold patch parhaps could be anticipated, butour study does further clarify the picture of the inter-action of gold and graphene edge.In summary, we have studied the growth of 2Dgold at graphene pores, modeled by graphene zigzagand armchair edges. Gold was chosen because of itsknown 2D stability. Yet, earlier studies have demon-strated that also other metals show fast diffusion ongraphene and strong binding to graphene defects[25,26, 27]. Our follow-up articles will concentrate onthese other metals, as well as other pore materi-als, such as hexagonal boron nitride, transition metaldichalcogenides, and black phosphorus.[28] Otherpore materials are worth investigating, although itis an evident risk that the pores with more com-ples edge morphologies pose serious challenges forthe stable growth of atomically thin 2D patches.[29]But although we focused only on Au and graphene8ores, we hope this study clarified the microscopicprocesses during the growth of a 2D metal patchin graphene pores and encourages experiments topush the limits for the patch sizes of stable 2D metalpatches. As shown by this study, gold makes an ex-cellent candidate for this because of its low diffusionbarriers and strong binding with the graphene edge;the chances for experimental realization at room tem-perature should be fair.
5. Acknowledgements
We acknowledge the Academy of Finland forfunding and CSC - IT Center for Science in Finlandfor computer resources.
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