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Thermodynamics and Kinetics of Graphene Growth on Ni(111) and the Origin of Triangular Shaped Graphene Islands Danxia Wang, Yifan Liu, Deyan Sun, Qinghong Yuan, and Feng Ding J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09814 • Publication Date (Web): 29 Jan 2018 Downloaded from http://pubs.acs.org on February 3, 2018

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Thermodynamics and Kinetics of Graphene Growth on Ni(111) and the Origin of Triangular Shaped Graphene Islands Danxia Wang,1+ Yifan Liu,1+ Deyan Sun,1 Qinghong Yuan,1,2* Feng Ding2,3,4* 1

State Key Laboratory of Precision Spectroscopy, Department of Physics, School of

Physics and Material Science, East China Normal University, Shanghai 200062, P. R. China 2

Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hong Kong

S.A.R. China 3

Center for Multidimensional Carbon Materials, Institute for Basic Science, Ulsan

689-798, South Korea. 4

School of Materials Science and Engineering, Ulsan National Institute of Science

and Technology, Ulsan 689-798, Republic of Korea

Abstract: To understand the origin of the triangular shaped graphene, we systematically investigated the thermodynamics and kinetics of graphene growth on Ni(111) surface. It was found that the fcc staking of graphene on the substrate is more energetically favorable than other stacking sequences. Under the near thermo-equilibrium condition, a graphene island will present a truncated triangular shape with alternative zigzag (ZZ) and ZZ-klein edges, either its growth is on the top of the terrace (on-top mode) or embedded into the metal lattice (inlay mode). While, if the growth process is controlled by kinetics of carbon atom incorporation, the shape of a graphene island will be triangular because of the significant growth rate difference between the ZZ

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and ZZ-klein edges. This study reveals the atomic details of graphene growth on Ni(111) surface, and the deep insights into the mechanism of graphene CVD growth may lead to the rational design of experiments for the growth of desired graphene and other 2D materials.

Introduction: A graphene island grown on a substrate surface may present various shapes, such as hexagonal,1-2 pentagonal,3 rectangular,4-5 triangular,6-7 circular8 and irregular shapes,9 depending on the combination of numerous experimental parameters, such as feedstock type, pressure and flow, temperature of growth, content of hydrogen in the environment of growth, type of substrate and substrate annealing process etc. It was broadly reported that the symmetry of the catalytic substrate played a very important role in affecting the shape of graphene islands. For example, on a surface with a four-fold symmetry, e.g. Cu(100), graphene islands were mostly found to have a rectangular or square-like shape.4-5 On a surface with top layer atoms having a six-fold symmetry, such as Ir(111), Rh(111), Pt(111), Cu(111), and Ni(111) etc., the graphene islands normally presented a hexagonal shape.10-14 However, in some cases, triangular shape graphene islands were also observed on the Ni(111)15-16 and Cu(111)7 surfaces. To understand the determination of the various shape of graphene islands on a substrate, besides the general consideration based on the concept of symmetry-breaking,17 detailed study of the growth process of various graphene edges at the atomic level is required. In all crystal growth, the shape of a crystal is determined by two competitive factors, thermodynamics and kinetics. The thermodynamics controlled growth always leads to shapes with facets having low formation energies, which is dominating when the growth is very slow or the island size is very small. While the kinetics controlled growth normally presents shapes with only facets having the slow growth rate. This occurs when the growth rate of the crystal is very fast or the crystal size is large. The competition of the two factors normally leads to various shapes of graphene islands, or the transition between different shapes upon the change of the growth conditions. ACS Paragon Plus Environment

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For example, graphene islands with a triangular or hexagonal shape can be selectively obtained by adjusting the initial feedstock dose, reaction temperature, and post-annealing

procedure. To

better

understand

the

competition

between

thermodynamics and kinetics on the shape determination of graphene islands on Ni(111) surfaces, we systematically explored the formation energies and growth kinetics of various graphene edges on a Ni(111) surface via both on-top and inlay growth modes. Thermodynamically, zigzag (ZZ) and ZZ-klein edges with fcc stacking on Ni(111) surface were found to be much more stable than armchair (AC) and AC-klein edges. Kinetically, AC and AC-klein edges grow much faster than ZZ and ZZ-klein edges, and ZZ-klein edge grows faster than ZZ edge, which finally leads to a triangular graphene island with only ZZ edge. Our calculations demonstrated that growth process reached thermodynamic equilibrium leads to hexagonal graphene islands but growth process dominated by kinetics results in triangular shaped graphene islands.

Methods The Ni(111) substrate was represented by an ABC-stacked four-layer slab model with the bottom layer fixed to mimic the bulk Ni atoms. The graphene edge is simulated by one edge of graphene nanoribbon (GNR) in which the other edge is saturated by H atoms. Considering the small lattice mismatching between the graphene (2.46Å) and Ni(111) surface (2.492Å), the lattice of Ni(111) is slightly compressed to match with the graphene’s lattice. The vacuum layer inside the super-cell is larger than 10 Å to avoid the interaction between adjacent unit cells. A cell size of 2.46×15.96×20.00 Å3 is used to calculated the formation energy of ZZ/ZZ-klein edges on Ni(111) surface, in which 2.46 Å represents the direction of ZZ/ZZ-klein edge. A cell size of 4.26×15.96×20.00 Å3 is used to calculated the formation energy of AC/AC-klein edge on Ni(111), where 4.26 Å represents the direction of AC/AC-klein edge. The Brillouin zone for the cell size of 2.46×15.96×20 Å3 and 4.26×15.96×20 Å3 were sampled by a k-point mesh of 9×1×1 and 5×1×1, respectively. For the kinetic calculations, the unit cell was expanded to avoid the ACS Paragon Plus Environment


interaction between the neighboring reactive sites, and a Monkhorst 1×2×1 k-point mesh was adopted. All calculations were performed by using spin-polarized density functional theory (DFT) implemented in Vienna Ab Initio Simulation Package (VASP).18 The exchange-correlation functional was the Perdew−Burke−Ernzerhof (PBE)19 based on generalized gradient approximation (GGA). The projected-augmented wave (PAW) potential was used to describe the interaction between valence electrons and ion cores, and the energy cutoff was set to 400 eV. The van der Waals interaction was considered by using DFT-D2 which is considered to be good enough to describe the interaction energy between graphene and the metal substrate.20 All structures were fully relaxed by the conjugate gradient method with a convergence criterion of 10-4 eV for total energy. The climbing-image nudged elastic band (CI-NEB) method21 was used in searching the minimum energy paths and the transition states.

Results Thermodynamic equilibrium structure of graphene island on Ni(111) substrate. For free standing graphene, there are only two typical edges: AC and ZZ edge. While for graphene grown on Ni(111) surface, the edge structure becomes complicated due to the passivation of the underlying substrate. Graphene with one sublattice on top of the upper-layer Ni atoms and the other either in fcc or hcp sites of the Ni lattice have been proposed as the two most favorable stacking structures.22 The two structures differ only in position with respect to the second layer of Ni, as shown in Figure 1A and B. Based on the different stacking of graphene layer, the Ni(111) passivated AC and ZZ graphene edges can be classified as AC-fcc, AC-hcp, ZZ-fcc, ZZ-hcp and ZZ-top. For AC-fcc and AC-hcp edges, edges on both sides have the same structure because of the lattice matching between the [-110] direction of Ni(111) surface and the zigzag direction of graphene. As shown in Figure 1, the AC-type edges in both sides of graphene ribbon have the same binding site on the Ni(111) substrate. However, case is quite different for ZZ-type edge structures due to the broken-symmetry. For example, fixing one ZZ edge in a fcc or hcp position (ZZ-fcc ACS Paragon Plus Environment

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or ZZ-hcp) makes the opposite ZZ edge of graphene to be in a top position, leading to a ZZ-top edge structure as shown in Figure 1A and B. Such a ZZ-top edge structure is reported to be unstable, and a ZZ-klein structure with extra edge atoms sitting at the fcc or hcp position of Ni(111) surface is supposed to be formed and stabilize the ZZ-top edge, as shown in Figure 1A and B.23 Similar edge structure, such as AC-klein edge, has also been proposed on Ni(111).24 Therefore, for AC-type edge structures, there exist AC and AC-klein structures as shown in Figure 1A and 1B. In addition to the on-top mode, graphene islands can also be embedded into the topmost of the Ni(111) surface via fcc or hcp stacking,25 leading to an inlay mode as shown in Figure 1C and D. For graphene grown via inlay-fcc mode (Figure 1C), both ZZ and ZZ-klein edges co-exist. There are two types of zigzag steps (ZZ-step) for the attachment of ZZ/ZZ-klein edges, e.g. step-I and step-II as shown in Figure 1E. Both ZZ and ZZ-klein edges can be attached to step-I or step-II. The same case is for graphene grown via inlay-hcp mode (Figure 1D).

Figure 1. Illustration of graphene edges’s structure via different mode (on-top and inlay) and stacking sequence (fcc and hcp) on Ni(111) surface. (A) fcc graphene on Ni(111) via on-top mode, ZZ, ZZ-klein, AC, AC-klein edges are considered, (B) hcp graphene on Ni(111) via on-top mode, (C) fcc graphene on Ni(111) via inlay mode,



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(D) hcp graphene on Ni(111) via inlay mode, (E) three types of metal step on Ni(111) surface.

To compare the stability of different graphene edges, we calculated the formation energies of the above mentioned 16 edge structures. The formation energy of graphene edge, Ef, was calculated by using the following formula:23

E f = ( Etot − Esub − nC × EC − nH × EH − nC × Evdw + EZPE ) / L

(1)

where Etot is the energy of GNR-Ni(111) slab, Esub is the energy of the supported metal substrate, EC is the energy of C atom in isolated graphene, EH is the energy of H atom in H2, EZPE is the zero-point energy due to C-H bonds (0.307 eV/H for zigzag edge and 0.315eV/H for armchair edge). nC and nH are the number of C and H atoms in the GNR, respectively, and L is the length of unit cell along the periodic direction of GNR. To single out the edge formation energy, we also subtract the adsorption energy of C atom obtained for the monolayer graphene/Ni(111) interface with fcc stacking (0.13 eV per C atom). As shown in Table 1, both on-top and inlay growth modes were considered. In each mode, there are four edge structures, e.g. ZZ, ZZ-klein, AC, AC-klein, passivated via fcc and hcp stacking, respectively. By comparing the formation energies, we can see that graphene edges formed via fcc stacking always have lower formation energies than those formed via hcp stacking. For graphene grown via on-top mode, the energy difference between fcc and hcp stacking is ~0.4 eV/nm, and the difference becomes larger (> 0.7 eV/nm) when graphene adopts inlay growth mode. Our conclusion about fcc stacking graphene edges are more energetically favorable is consistent with previous studies.15 For each fcc stacked graphene, ZZ type edge structure (including ZZ and ZZ-klein) is more stable than the AC type one (including AC and AC-klein). For example, as for on-top graphene with fcc stacking, the formation energies of ZZ and ZZ-klein edge are 3.40 and 4.11 eV/nm, respectively. While the formation energies of AC and AC-klein edge are 5.90 and 4.93 eV/nm, respectively.


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For graphene grown via inlay-fcc mode, although both ZZ and ZZ-klein edges could attach to step-I or step-II our calculations demonstrated that the ZZ edge prefers to attach to step-I and the ZZ-klein edge prefers to attach to step-II. (as shown in Table S1) For graphene grown via inlay-hcp mode, the opposite trend is observed. ZZ edge attached to step-II has lower formation energy and ZZ-klein edge attached to step-I has lower formation energy. (shown in Table S1) Both ZZ and ZZ-klein edges formed via inlay-hcp mode have higher formation energies than that formed via inlay-fcc mode. AC edges in both inlay-fcc and inlay-hcp are attached to step-III but the binding sites are quite different (as shown in Table S1). The calculated formation energies of AC (3.74 eV/nm) and AC-klein (4.04 eV/nm) edges are much higher than the ZZ and ZZ-klein structures (both are 2.99 eV/nm). Our calculated formation energy of ZZ edge is ~1.90 eV/nm lower than the value (5.30 eV/nm) reported by Gao et. al.24, and 0.75 eV/nm lower than the value reported by Shu et. al.26 We believe the difference is attributed to the different theoretical model. In the work published by Gao et.al., graphene nanoribbon with two pristine ZZ edges are used and both edges are passivated by the underlying metal substrate. This is quite different from our theoretical model in which only one ZZ edge of the GNR is passivated by the metal substrate and the other one is passivated by H atoms. From Figure 1, we can see that the two ZZ edges in GNR can’t be simultaneously passivated by the fcc position of the Ni(111) surface. For example, if one edge is passivated by the fcc adsorption site the other edge should be passivated by the top adsorption site. According to our calculations, the top adsorption edge has much higher formation energy (6.52 eV/nm) than the fcc adsorption edge (3.40 eV/nm). Therefore, taking the average formation energy of the ZZ-fcc and ZZ-top edges as that of the ZZ-fcc one will definitely overestimate the formation energy of ZZ-fcc edge. This explained why the calculated formation energy of ZZ edge in Gao’s work is higher than what we reported here. However, the formation energy of ZZ edge reported by Artyukhov et. al.17 (3.0 eV/nm) is quite similar to our calculated value (3.40 eV/nm). And a similar theoretical model was used in their work.



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Table 1 the formation energy of ZZ, ZZ-klein, AC, and AC-klein edges on Ni(111) susrface with different stacking and growth mode. (unit: eV/nm) Edge type

ZZ

ZZ-klein

AC

AC-klein

fcc

3.40

4.11

5.90

4.93

hcp

3.73

4.46

6.27

5.40

fcc

2.99

2.99

3.74

4.04

hcp

3.69

7.06

5.05

5.99

Stacking On-top

Inlay

To obtain the equilibrium shape of graphene nanoisland on Ni(111) surface, we plot the thermodynamic Wulff construction shape of graphene based on the calculated edge formation energies. Since the fcc stacked graphene has lower formation energy, we only considered graphene which adopts fcc stacking. As shown in Figure 2, graphene nanoislands grown via fcc stacking of both on-top and inlay modes show hexagonal shape with alternative ZZ and ZZ-klein edges. For on-top growth mode, the hexagonal shape of graphene is not regular since one edge is larger than the other one.

Figure 2. Thermodynamic Wulff constructions of graphene nanoislands grown via (a) on-top mode and fcc stacking, (b) inlay mode and fcc stacking. Blue and red lines represent ZZ and ZZ-klein edge, respectively.


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Kinetic growth of graphene edge on Ni(111) substrate Under some experimental conditions, the growth process of graphene is hard to achieve thermodynamic equilibrium due to the very fast growth rate. In this case, the kinetic process of graphene growth is crucial to determine the shape of graphene nanoisland. Here, only the growth kinetics of graphene with fcc stacking is considered because of the lower formation energy. To explore the energetic process of graphene edge growth, the formation energy (EF) of each structure formed in the growth process is defined as:

EF = EC +GNR @ sub − EGNR@sub − N × EC

(2)

where the EC+GNR@sub is the energy of Ni(111) substrate with adsorbed graphene ribbon and C adatom, EGNR@sub is the energy of Ni(111) substrate with adsorbed graphene ribbon. EC is the energy of C atom in graphene and N is the number of C atoms incorporated in the graphene edge. If there is no C atoms added or N=0, then EF=0. Therefore, all the initial structure in each growth path has a formation energy of 0 eV. For addition of the first C atom, the C atom is initially adsorbed to a stable site of the metal terrace near the graphene edge (labeled as 1C-near in Figure 3-7), and the formation energy of 1C-near is calculated by using Eq. (2) with N = 1. Then the C atom is incorporated into the graphene edge by overcoming the transition state (labeled as 1C-TS in Figure 3-7). The free energy of 1C-TS is obtained by CI-NEB calculation and the formation energy of 1C-TS is calculated by the energy difference between 1C-TS and 1C-near. After the incorporation of the first C atom, 1C-in structure is formed and its formation energy is also calculated by using Eq. (2) with N = 1. The formation energies of all the other NC-near, NC-TS and NC-in (N=2-4) are calculated similarly. Here, the formation energy (EF) is related to the Ef defined in Eq. (1) since the energy of C atom in graphene are used as the reference energy in both cases. The kinetic growth of ZZ edge with on-top and fcc stacking. Each growth cycle of ZZ edge involves the formation of a new hexagon row, here we only considered the



addition of the first five C atoms because the subsequent addition of C atoms is repeatable.27 By exploring several possible growth ways (see Figure S1 in SI), we identified the most favorable one which is shown in Figure 3a and 3b. The C atom to be incorporated into the ZZ edge is placed in a fcc site near the ZZ edge (1C-near in Figure 3b), then it attaches to the ZZ edge by overcoming a transition state (1C-TS in Figure 3b) and form a structure like ZZ-klein (1C-in in Figure 3b). The energy barrier and the formation energy for the first C addition is 0.74 and 1.22 eV, respectively. After the addition of the first C atom, the second C atom near the ZZ edge (2C-near in Figure 3b) approaches and binds with the first incorporated C atom, forming the 2C-in structure shown in Figure 3b. This process needs overcoming an energy barrier of 1.36 eV, and the formed structure has a formation energy of 1.18 eV. The incorporation of the third C atom into the ZZ edge needs overcoming an energy barrier of 0.63 eV, forming a “Y” shaped structure (3C-in in Figure 3b) with a formation energy of 0.96 eV. On the basis of the “Y” structure, the incorporation of the fourth C atom leads to the formation of the first hexagon (4C-in in Figure 3b) on ZZ edge. And an extra energy of 1.00 eV is needed for this progress. Addition of the fifth C atom can have two possible ways, one is to form two hexagons, and the other is to form two connected “Y” shape struture. Our calculations demonstrate the later one is more favorable, and this process has an energy barrier and formation energy of 1.22 and 0.59 eV, respectively. Based on the calculated energy barriers and formation energies, we can obtain the overall energy path for the growth of ZZ edge, as shown in Figure 3a. It can be seen that the overal barrier for the addition of the first five C atoms is 3.38 eV. After the addition of the five C atoms on ZZ edge, the formed structure (5C-in in Figure 3b) has two reactive sites on both sides, which was regarded to be energetic favorable for the addition of the subsequent C atoms.28 Hence, it can be concluded that the kinetic barrier for ZZ edge growth is 3.38 eV. It should be noted that the relative energies of each new C adatom with respect to the previous configuration are different from each other. For example, the relative energy of 1C-near with respect to ZZ-GNR is 1.22 eV but the value becomes 0.81 eV for 2C-near with respect to 1C-in. This can be attributed to the change of local ACS Paragon Plus Environment

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environment of the adsorption site caused by the different graphene edge structure.

Figure 3. (a) Energy profile and (b) optimized geometries involved in the kinetic process of ZZ edge growth via on-top mode and fcc stacking sequence. The growth process of incorporating five C atoms into ZZ edge on Ni(111) terrace is considered, and the structures including reactant, intermediates and transition states.

The kinetic growth of ZZ-klein edge with on-top mode and fcc stacking. In contrast to ZZ edge growth where the C atoms addition in each growth cycle is dependent, the C atoms addition on ZZ-klein edge is independent and each growth site involves only two C atoms. As shown in Figure 4, each addition of two C atoms at the reactive site of the ZZ-klein edge is an independent growth process. Similar to ZZ edge growth, the first C atom was firstly placed at a fcc site near the ZZ-klein edge. By overcoming an activation barrier of 1.54 eV, the C atom is incorporated into the ZZ-klein edge and form a structure which has a hexagon (1C-in in Figure 4). Then the second C atom near the edge approaches to the incorporated C atom and form a new dendritic structure (2C-in in Figure 4), which has an energy barrier of only 0.44 eV. Such an addition makes the formation energy of the second C atom decrease from 2.2 to 0.68 eV. It is possible that the second C atom bind with the neighbor C atoms on ZZ-klein edge and form the second hexagon structure, but our calculation results demonstrated that such an addition way is less favorable since the formation energy of



the structure is as high as 2.3 eV. Therefore, the most favorable way of ZZ-klein growth is the repeatable addition of two C atoms at the reactive site. Based on the calculated energy, it can be seen that the energetic barrier for ZZ-klein growth is 2.64 eV, which is 0.74 eV lower than that of ZZ edge growth.

Figure 4. (a) Energy profile and (b) optimized geometries involved in the kinetic process of ZZ-klein edge growth via on-top and fcc stacking. The growth process involves incorporating two C atoms into ZZ-klein edge on Ni(111) terrace, and the structures including reactant, intermediates and transition states.

The kinetic growth of AC edge with on-top and fcc stacking. The thermodynamic energy calculations demonstrate that AC-klein edge is much stable than the AC one, thus we only consider the growth kinetics of AC-klein edge. The kinetic growth of AC-klein is quite similar to ZZ-klein edge since each growth process involves only two C atom. Figure 5 shows the optimized structures and calculated energy paths for the kinetic growth of AC-klein edges. The addition of the first C atoms at the AC-klein edge forms a hexagon structure, and the formation of this structure needs overcoming an energy barrier of 1.84 eV. And the addition of the second C atom forms a dendritic structure which is similar to the original one. The overall barrier for the AC-klein edge growth is 2.2 eV, which is much lower than that of ZZ and ZZ-klein edge.


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Figure 5. (a) Energy profile and (b) optimized geometries involved in the kinetic process of AC-klein edge growth with on-top and fcc stacking. The growth process involves incorporating two C atoms into AC-klein edges on Ni(111) terrace.

The kinetic growth of ZZ edge with inlay and fcc stacking. For graphene growth via inlay mode, the edges of graphene attach to the metal step, leading to a stronger binding between graphene edge and the substrate.29 This can be seen from the formation energy comparison listed in Table 1. ZZ edge with inlay mode has lower formation energy than that with on-top mode. Similar to ZZ edge growth on metal surface, the typical growth barrier for ZZ edge at the metal step also involves five C atoms and forms two connected “Y” shape structure. While the difference is, the addition of five C atoms at the inlay ZZ edge needs to kick out two Ni atoms from the metal step. As shown in Figure 6, the addition of the first three C atoms kicks out one Ni atom from the metal step and forming a “Y” shape structure (3C-in in Figure 6), the formation energy of the “Y” shape structure is 1.21 eV. The addition of the fifth C atom kicks out another Ni atom and forming a structure with two connected “Y”. The subsequent addition of C atoms will be repeatable processes like the addition of the fourth and fifth C atoms. The overall barrier for ZZ edge growth on Ni(111) step is 3.22 eV.



Figure 6. (a) Energy profile and (b) optimized geometries involved in the kinetic process of ZZ edges growth via inlay mode and fcc stacking sequence. The growth process involves incorporating five C atoms into ZZ edge on Ni(111) terrace.

The kinetic growth of ZZ-klein edge with inlay mode and fcc stacking. Each growth process of ZZ-klein edge includes an addition of two C atoms and the kicking of one Ni atom. The addition of the first C atom forms a hexagon structure (1C-in in Figure 7) at the metal step by squeezing a Ni atom, while the addition of the second C atom kicks out the Ni atom and form a new ZZ-klein structure. Due to the kicked Ni atom, the energy of the 2C-in structure shown in Figure 7 increases about 1.9 eV. If the kicked Ni atom is diffused to a low energy site, e.g. defective site or kink site, the energy of this structure should decrease about 1.2 eV.30 If the second C atom attaches to the neighbor C atoms on ZZ-klein edge and form the second hexagon structure, the formation energy will increase to 2.63 eV. Therefore, forming two hexagons is not a favorable growth path. The whole barrier of the ZZ-klein edge’s growth via inlay-fcc stacking is 3.70 eV, as shown in Figure 7.


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Figure 7. (a) Energy profile and (b) optimized geometries involved in the kinetic process of ZZ-klein edge growth via inlay mode and fcc stacking sequence. The growth process involves incorporating two C atoms into ZZ-klein edge on Ni(111) terrace.

Kinetic Wulff construction of graphene nanoisland. The growth velocity, ν(χ), of graphene edge can be expressed as following:31 v ( χ )∞

4 sin( χ ) × exp(− E AC / kT ) + 2sin(30o − χ ) × exp(− EZZ / kT ) 3

(3)

Where χ is the title angle of an arbitrary graphene edge, EAC and the EZZ is the energy barrier of AC-type edge’s growth and ZZ-type edge’s growth respectively, and k is the the Boltzmann constant and T is the temperature of graphene growth. Based on Eq. (3), we can plot the kinetic Wulff construction of graphene nanoisland. As shown in Figure 8a and b, for on-top and fcc stacking graphene the shape of graphene island is a triangle shape with ZZ edges, while for inlay and fcc stacking graphene the shape of graphene island is also triangular but with ZZ-klein edges.



Figure 8. Kinetic Wulff constructions of graphene nanoislands grown via (a) on-top and fcc stacking, (b) inlay and fcc stacking. Blue and red lines represent ZZ and ZZ-klein edges, respectively. The growth temperature is set high (6500 K) in order to “compress” the plots in the radial dimension. Based on the above calculation results, we can conclude that graphene domain should have hexagonal shape if the thermodynamic equilibrium can be achieved during the CVD growth, while the triangular shape should be observed without a thermodynamic equilibrium growth condition. For example, under low growth temperature, the thermodynamic equilibrium is hard to be achieved and thus graphene nanoislands should have triangular shape. Under high growth temperature, thermodynamic equilibrium can be achieved and graphene nanoislands should be dominated by hexagonal shape. This is completely consistent with the experimental observations, Olle et. al. found that triangular graphene domains were observed under the growth temperature of 550 ℃ while hexagonal graphene domains were observed when the graphene domains were annealed under a temperature of 650 ℃.6 Yang et.al. also found that the epitaxial triangular graphene nanoislands were formed on Ni(111) surface at a temperature of 400 ℃, and the hexagonal graphene islands were observed at a growth temperature of 540 ℃.16 Conclusion The thermodynamics and kinetics of graphene island growth on Ni(111) surface were explored. The formation energies of 16 types of graphene edges of graphene island in different growth modes (on-top and inlay) and stacking sequence to the


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substrate (fcc and hcp) were calculated, and it was found that fcc stacking is always more favorable than the hcp one. For the fcc stacked graphene, the ZZ and ZZ-klein edges have lower formation energies than the AC and AC-klein edges. Therefore, a graphene island grown under the thermoequilibrium should present a hexagonal or truncated triangle shape with alternative ZZ and ZZ-klein edges. However, if the growth process is dominated by kinetics, the shape of graphene islands become triangular shape due to the very large growth rate difference between the ZZ and ZZ-klein edge. A graphene island grown via the on-top mode has a triangular shape with ZZ edges while the dominating edge becomes ZZ-klein if the island is grown via the inlay mode. This study proves that even for graphene nanoislands, their shapes are mostly determined by kinetics. Therefore, undersatnding the kinetics of 2D materials’ growth is of crucial importance for their synthesis.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org. Two other possible ways of ZZ edge growth (Figure S1); The formation energy and structure of another ZZ-klein edge binding on the terrace of Ni(111) (Figure S2), formation energy and structure of another ZZ-klein edge attaching at the step-II of Ni(111) (Figure S3); Energy comparison of 16 different edges on Ni(111) surface via different growth mode and stacking sequence (Table S1); The calculated energies of the growth path of different edge involved in Figure 3-7 (Table S2 - S7). AUTHOR INFORMATION Corresponding Authors *E-mail：[email protected] *E-mail：[email protected] Author Contributions D. Wang and Y. Liu contributed equally to this work. Q. Yuan and F. Ding designed the project, D. Wang and Y. Liu carried out the first principles calculations. Q. Yuan ACS Paragon Plus Environment


and F. Ding co-wrote the manuscript. All the authors participated in the data analysis, discussions of results and manuscript revisions. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was financially supported by National Natural Science Foundation of China (Grant Nos. 21673075), and the Research Project of Hong Kong Polytechnic University (1-BBAA). The computations were performed in the Supercomputer Centre of East China Normal University.

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Table of Content



C

ZZ-fcc

ZZ-K-hcp

Step ‐ II

AC-K-step-III

ZZ-K-step-I

AC-step-III

D AC-hcp

ZZ-top

Step ‐ I

ZZ-K-step-II

ZZ-hcp

B

E

ZZ-step-I

AC-step-III

AC-K-fcc

ZZ-top

AC-fcc

A

AC-K-step-III

ZZ-K-fcc

AC-K-hcp

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Page 22 of 29

ZZ-step-II


Step ‐ III

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

(a)

(b)

EFEnergy (eV) (eV) Relative


4

TS‐2C

TS‐3C

3

TS‐5C

TS‐4C TS‐1C

2

1C‐ter

1C‐in

5C‐ter

3C‐ter

2C‐ter

1 0

Page 24 of 29

4C‐ter

2C‐in

4C‐in

3C‐in

5C‐in

ZZ GNR

ZZ GNR

1C‐ter

TS‐1C

1C‐in

2C‐ter

TS‐2C

2C‐in

3C‐ter

TS‐3C

3C‐in

4C‐ter

TS‐4C

4C‐in

5C‐ter

TS‐5C

5C‐in


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46


F (eV) (eV) RelativeEEnergy

Page 25 of 29

3 TS‐2C

TS‐1C

2 1

2C‐ter

0 1C‐ter

-1

1C‐in 2C‐in

ZZ‐klein GNR


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

) H9 5HODWLYH((QHUJ\ H9


Page 26 of 29

d^rî d^rí

î rš Œ

í rš Œ í r]v rlo ]v î r]v


Page 27 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Energy (ev) EF (eV)

(a)

(b)


4

TS‐4C

TS‐3C

3

TS‐5C

TS‐2C TS‐1C

2 1

1C‐ter

4C‐ter

3C‐in’ 1C‐in

2C‐ter

2C‐in 3C‐ter

5C‐in 4C‐in 5C‐ter

3C‐in

0

ZZ GNR 1C‐ter

TS‐1C

1C‐in

2C‐ter

TS‐2C

3C‐in’

3C‐in

4C‐ter

TS‐4C

4C‐in


2C‐in

5C‐ter

3C‐ter

TS‐3C

TS‐5C

5C‐in


4

TS‐2C TS‐1C

RelativeEEnergy F (eV) (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Page 28 of 29

3

2C‐ter

2

1C‐in 1C‐ter

1 0

ZZ‐klein

-1


2C‐in

Page 29 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46


(a)

(b)

ZZ ZZ-klein


and the Origin of Triangular Shaped Graphene ... - ACS Publications

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