Diffusion, Nucleation, and Self-Optimization in the Forming Process of

Article pubs.acs.org/JPCC

Diffusion, Nucleation, and Self-Optimization in the Forming Process of Graphene in Annealed Nickel−Carbon Alloy Yifan Li, Yan Wu, Yi Zhou, Jie Li, Yunrui Duan, Tao Li, Zhenyang Zhao, and Hui Li* Key Laboratory for Liquid−Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, People’s Republic of China S Supporting Information *

ABSTRACT: Reactive molecular dynamics simulation is used to explore the forming mechanism of graphene in an annealed nickel− carbon alloy. Results show that after internal carbon atoms diffuse to the surface of the alloy spontaneously with a large diffusion coefficient, graphene nuclei are formed due to the catalysis of nickel atoms. The nuclei can grow into large graphene and then the large graphene optimizes itself when annealing time is sufficient, accompanied by some nickel−carbon compounds and unstable nickel clusters in this alloy. The substrate, carbon concentration, annealing temperature, and alloy thickness could affect the morphology of the obtained graphene. Our simulation provides insight into the structural evolution of annealed nickel−carbon alloys at the atomistic level and will be valuable to the preparation of graphene.

1. INTRODUCTION Graphene, a monolayer of sp2-hybridized carbon atoms organized in a honeycomb lattice,1,2 has grabbed appreciable attention due to its good thermal conductivity, high current density,3−5 quantum Hall effect (QHE),6−9 super hydrophobicity,10,11 etc. These properties have generated significant interest for practical applications, such as ballistic transistors, field emitters, transparent conducting electrodes, and sensors,12 making graphene one of the important components of future materials. Now, most graphene is prepared by mechanical exfoliation from graphite,13 thermal graphitization of a SiC surface,12,14−17 and chemical vapor deposition (CVD).18 But each of these approaches has drawbacks. The exfoliated graphene obtained by mechanical exfoliation suffers from the limitation that the structure has a lot of defects.2 The reduction of SiC relies on the ability to walk a narrow thermodynamic tightrope.19 Even metal-catalyzed CVD, which has a good performance in the preparation of high-quality graphene, also has the disadvantages of high cost and low yield, which are not conducive to industrial preparation. Therefore, researchers have continued to explore new ways to fabricate graphene. In recent years, some researchers directly annealed a mixture of active metals and carbonaceous materials, providing a new method to prepare graphene. For example, Peng et al.20 synthesized bilayer graphene by annealing stacked polymers and nickel films at 1000 °C in an experiment. Subsequently, Tosic et al.21 produced graphene nanoribbons by annealing nickel nanowires and graphene quantum dots. In these preparations, nickel was the most commonly used active metal, because Amini et al.22 revealed that the graphene obtained in nickel−carbon alloys was pristine and defect-free, © XXXX American Chemical Society

better than that obtained in other alloys. Moreover, other suitable reaction conditions, such as the appropriate annealing temperature23 and high carbon concentration,24 could promote the growth of graphene. The new annealing method simplifies the preparation of graphene in a low-cost way, and the size of the obtained graphene can be adjusted by controlling the size of the mixture, so this method is expected to have good prospects in future applications. However, all these previous studies focused on the morphology and performance of the resulting graphene, but the fundamental mechanism of graphene formation in the annealed alloy has not been revealed and identified. In this paper, we applied reactive molecular dynamics simulation to study the structural evolution of nickel−carbon (Ni−C) alloys during annealing. The kinetic details of atom diffusion, nucleation, and self-optimization were demonstrated, and the effects of precursor concentrations, annealing temperatures, and initial alloy structures were systematically investigated. Our simulation provides an indepth understanding to the fundamental mechanism of graphene synthesis in the annealed Ni−C alloy and will be significant to further improve the preparation method of the novel material.

2. METHODS Molecular dynamics (MD) simulations were performed using the reactive force-field ReaxFF,25,26 which has been confirmed to provide accurate descriptions of bond breaking and bond Received: July 6, 2017 Revised: September 5, 2017 Published: September 5, 2017 A

DOI: 10.1021/acs.jpcc.7b06620 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C forming for Ni−C systems27,28 because the energies, reaction paths, and reactive events calculated by ReaxFF accord well with those obtained by quantum mechanics (QM) calculations.29 The van der Waals and Coulomb interactions were considered for every pair of atoms. The speed of atoms followed the Gaussian distribution. All the MD simulations were conducted in the canonical NPT ensemble using the Lammps MD package30 with a time step of 0.5 fs, and the Nose−Hoover method was applied to control the annealing temperature in the thermostat. The damping coefficients used to control temperature and pressure are 50 and 100 fs, respectively. The atom trajectory was recorded every 0.5 ps. Each system was simulated for enough time to reach equilibrium, and each simulation was repeated several times to ensure that the result is reliable. Simulation models were built on the basis of some experimental results. In previous research, El Mel et al.31 and Tosic et al.21 produced graphene layers by annealing Ni−C systems in experiments, and Peng et al.20 demonstrated that the flat surface favors the formation of large graphene; thus, the flake Ni−C model, which has a large and flat surface, was built and optimized. As shown in Figure 1, the initial models of Ni−

the Ni−C system. The pair distribution function describes the distribution of distances between pairs of atoms in the material.

3. RESULTS AND DISCUSSION The kinetic process of graphene forming in a Ni−C alloy is shown in Figure 2. There are 70% carbon atoms and 30% nickel atoms in the initial alloy, and its side and front views are displayed at 0 ps. Figure 2a provides the evolution of the surface morphology of this alloy, which was placed on a fixed substrate at an annealing temperature of 1000 K, revealing four steps in the formation of graphene. At the first stage, randomly distributed atoms began to diffuse freely, and free carbon atoms tended to form carbon chains at 1 ps due to the strong bonding energy between carbon atoms. Soon afterward, a few elongated carbon chains were folded into isolated carbon rings spontaneously. These isolated carbon rings were easy to connect with free carbon chains or free carbon atoms as a nucleus, and the nucleus expanded into a small piece of graphene at 25 ps as the connected carbon chains folded again into new carbon rings around it. The atomic diffusion and graphene nucleation were also found and proved by Jiao et al.,24,33 indicating the reliability of the data in this paper. Small pieces of graphene were more stable than carbon chains due to the mutual restraint between carbon rings; thus, they easily grew larger and merge with other ones and eventually became a large piece of graphene when the time is up to 500 ps. After that, the size of the large graphene remained unchanged, but the graphene self-optimized itself into a more regular shape and its internal defects reduced as the time of annealing continued to 3000 ps, suggesting that the quality of the resulting graphene was improved by extending the annealing time. When the Ni− C alloy was annealed without substrate, as shown in Figure 2b, carbon atoms aggregated and graphene was also formed after the same four steps, although more annealing time was required. Comparing the two pieces of graphene obtained in the two systems, the graphene grown on the substrate has a better morphology, indicating that a suitable substrate has a favorable effect on graphene formation. In the process of graphene formation, the first step, diffusion, is very important. In order to study the atomic diffusion during graphene formation, Figure 3a shows the side views of the Ni− C alloy before and after annealing. The comparison between two structures reveals that the annealing process allowed carbon atoms to diffuse and accumulate on two large surfaces, while most nickel atoms were located between the two carbon layers. These results are consistent with the previous research that proved carbon atoms prefer to gather in groups rather than diffuse randomly in Ni−C alloys.34 The mean square displacement (MSD) in Figure 3b proves that the separation of nickel and carbon atoms is caused by their different diffusion abilities. Since the slope of the MSD represents the diffusion coefficient, carbon atoms had a large diffusion coefficient at the beginning of annealing, seeing that the slope of the carbon MSD is large. Thus, most carbon atoms diffused to the alloy surface quickly and then stayed there to form carbon chains and rings to minimize the surface energy of the system, for the reason that the surface energy of graphene (46.7 mJ/m2)35 is smaller than that of nickel (1900 mJ/m2).36 The diffusion coefficient of carbon atoms decreased with the formation of graphene, because carbon atoms in the graphene were not free to move due to the surrounding restriction, while the diffusion coefficient of nickel atoms was almost constant. In the stage of graphene self-optimization, the diffusion coefficient of carbon

Figure 1. Initial models and their optimized geometries for the nickel−carbon alloy (a) with a substrate and (b) without a substrate. Golden and blue spheres represent nickel and carbon atoms, respectively.

C alloys were built by randomly replacing nickel atoms with carbon atoms. Then these initial structures were optimized to reach a stable configuration with the low potential energy of the system. The optimized alloy is amorphous, and nickel and carbon atoms were mixed randomly and disorderly. This modeling is similar to that used in previous simulations.24,32 The size of the initial alloy is 35 × 35 × 5.25 Å3; thus, there are two large surfaces in the z-direction for graphene formation. The atom number of initial alloys is 800. Some Ni−C alloys were placed on a single-layer fixed graphene, as shown in Figure 1a. In these systems, the periodic boundary condition was only implemented perpendicular to the substrate, and virtual walls were built on the nonperiodic boundary to avoid escaping atoms. Other Ni−C alloys were annealed without a substrate, as shown in Figure 1b. Periodic boundary conditions were implemented in the x- and y-directions, and the nonperiodic boundary condition was applied in the z-direction to ensure the presence of two large surfaces. A 6 GPa external pressure was applied to control the thickness of this alloy. Four temperatures (600, 800, 1000, and 1200 K), four carbon concentrations (50%, 70%, 90%, and 99%), and four alloy thicknesses (three, five, seven, and nine atomic layers) were chosen to investigate the effects of annealing temperatures and alloy structures on graphene formation. In addition, in the analysis, the conversion rate of graphene is the percentage of the number of carbon atoms in the graphene to the total number of carbon atoms in B


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The Journal of Physical Chemistry C

Figure 2. Representative snapshots of graphene formation on the surface of the annealed nickel−carbon alloy (a) with a fixed graphene substrate or (b) without substrate. There are 30% nickel atoms and 70% carbon atoms, and the annealing temperature is 1000 K. The carbon atoms are blue and the nickel atoms are golden, while the substrate is red in the side view and light gray in the front view for clarity.

Figure 3. (a) The side views of the nickel−carbon alloy before and after annealing. Mean square displacement changes of nickel and carbon atoms during (b) 0−100 ps and (c) 500−1000 ps, respectively. (d) Several representative concentration distribution profiles of carbon and nickel atoms along the z-direction.

atoms reduced to zero, which means the diffusion of carbon atoms had been stopped, while nickel atoms were still diffusing, as shown in Figure 3c. However, since the surface had been occupied by carbon atoms, nickel atoms could only concentrate

on the inside of carbon atoms. This is also proved by the atomic concentration distribution curves in Figure 3d. The concentration distribution of carbon atoms (the red line) peaks on both surfaces of the alloy (the surface positions are marked C


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structure resulted from diffusion. As active metal atoms were protected by chemically stable carbon atoms in the final structure, the annealing method that formed graphene directly on the surface of the Ni−C alloy can also be used to prepare a metal coating to prevent corrosion.37,38 To further study the process of graphene nucleation after diffusion of carbon atoms, the details of carbon ring formation, which is the actual simulation result obtained during the annealing process, is shown in Figure 4, because the carbon ring can be seen as a nucleus of graphene. Figure 4a shows the whole process of a carbon chain (marked in red) folding into a carbon ring with the catalysis of nickel. Initially, some carbon atoms in the chain were restricted by surrounding atoms, while others were in a free state. The free end of the carbon chain tended to swing at high annealing temperatures, and it was possible for two carbon atoms in this carbon chain to combine with the same nickel atom, forming a six-membered ring (6-m ring) containing the nickel atom. The two carbon atoms C1 and C2 got close to each other as the simulation continued, and then they were connected and the nickel atom was released. This result is consistent with the previous research of Jiao et al.39 Nickel atoms between two carbon layers could be viewed as the catalyst for the nucleation of graphene, which has been proved in the CVD formation process of graphene,40 carbon nanotubes,41,42 and carbon fibers.43 The carbon rings formed by folded carbon chains were not always five-membered or sixmembered; some of them contained more carbon atoms. The multivariate ring could further adjust or split itself into one or several five-membered or six-membered rings, as shown in Figure 4b,c. Some carbon rings disappeared again after their

Figure 4. Representative snapshots of a nucleus (a polygonal carbon ring) (a) forming, (b) self-adjusting, and (c) dividing into two rings in the formation of graphene. The carbon atoms selected to show atomic movements in detail are marked in purple and green to distinguish between the first and second carbon rings, while the unselected carbon atoms are blue. Nickel atoms are golden.

by the dotted line) even at 1 ps, suggesting that diffusion and aggregation occurred very early, and this phenomenon can be seen as the premise of graphene formation. The peaks become tall and narrow with annealing, meaning that most carbon atoms were gathered to the alloy surface eventually. The two concentration distribution peaks of nickel atoms (the dark blue line) appear between the concentration distribution peaks of carbon atoms, and the distance between carbon and nickel peaks is about 0.45 Å, suggesting that a regular nickel−carbon

Figure 5. (a) The average populations of six polygonal carbon ring sizes in the substrate system as a function of the simulation time. (b) The conversion rate of free carbon atoms to graphene in the substrate system as a function of the simulation time. (c) The average populations of six polygonal carbon ring sizes in the system without substrate as a function of the simulation time. (d) The conversion rate of free carbon atoms to graphene in the system without substrate as a function of the simulation time. The X-m ring (abbreviated from X-membered ring) represents the carbon ring composed by X carbon atoms. D


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Figure 6. Angular distribution functions of (a) the regular nickel crystal and (b) the nickel cluster in the annealed alloy, where corresponding configurations at different angles are inserted. (c) The variation of the pair distribution function over time for the nickel−carbon alloy. (d) The number of C−C, Ni−C, and Ni−Ni bonds as a function of the simulation time.

obtained graphene, especially in the grain boundary between different nuclei. Fortunately, 7-m rings reduced slightly and 6-m rings increased significantly in the self-optimization stage, indicating that grain boundaries and defects disappeared gradually and the large graphene became more perfect. The number of 5-m rings did not decrease, bringing some advantages to the obtained graphene. As proven by previous simulations, appropriate 5-m rings made graphene nanosheets stable,44−47 and the combination of 5-m rings and 6-m rings bring wrinkles and protrusions for the obtained graphene.46 These wrinkles and protrusions make graphene uneven, increasing the difficulty of graphene stacking; thus, the obtained graphene may disperse to obtain a large specific surface area. The conversion rate of carbon atoms to graphene (Figure 5b) reveals that 60% of free carbon atoms was bonded rapidly to form the large graphene at the growth stage of graphene, and then another 6% of carbon atoms was incorporated into the large graphene slowly in the process of graphene selfoptimization, suggesting that the graphene formation stage could be predicted according to the speed of carbon atom conversion. The average populations of polygonal carbon rings in the system without substrate are displayed in Figure 5c, demonstrating that the obtained graphene had more 5-m rings than 6-m rings and that the ring number grew slowly, which further illustrates the importance of the substrate on the perfect configuration and the rapid growth of graphene. The conversion rate of carbon atoms in this system is only 56%, as shown in Figure 5d, 10% less than that in the system with substrate, proving that a suitable substrate can also improve the utilization of the carbon element. Nickel is another important element of this annealed alloy; therefore, it is necessary to study its final structure. The angular distribution functions of the regular nickel crystal and the nickel cluster in this alloy are displayed in parts a and b of Figure 6, respectively. Different from standard angles (60°, 90°, and 120°) in the nickel crystal, nickel−nickel (Ni−Ni) bond angles

Figure 7. Potential energy as a function of the simulation time in the process of graphene formation; the two inset graphs are potential energy changes of carbon atoms and nickel atoms, respectively.

appearance due to the system’s thermal fluctuation, but others became the effective nuclei to promote the growth of graphene, causing the area of graphene to expand gradually. The average population change of carbon rings (Figure 5a) reveals the growth and self-optimization of graphene in the substrate system. As expected, graphene was quickly generated in the growth stage with a rapid increase of ring number, and the initial graphene was mainly composed of five-membered rings (5-m rings), 6-m rings, and a few seven-membered rings (7-m rings), meaning that there were some defects in the E


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Figure 8. (a) The final morphology of graphene obtained in four alloys that have different proportions of carbon atoms; from top to bottom, carbon proportions are 50%, 70%, 90%, and 99% respectively. (b) Potential energy as a function of the simulation time in the formation process of the four pieces of graphene. (c) Final concentration distribution profiles of the four alloys. (d) The conversion rate of carbon atoms to graphene in the four alloys as a function of the simulation time.

vanishing and large graphene appearing, and it would be used to determine whether there is a piece of graphene in the annealing Ni−C alloy. In order to study the structural transformation by analyzing the change of atomic bond numbers, Figure 6d shows bond numbers as a function of the simulation time. It can be seen that both the number of carbon−carbon (C−C) and Ni−Ni bonds grew with annealing, while the former had a larger quantity and increased faster due to the large proportion and diffusion coefficient of carbon atoms. The interaction of Ni−C was weakened obviously according to the decrease of the Ni−C bond, suggesting that homogeneous elements were segregated with annealing. But the number of Ni−C bond did not drop to zero when the system was balanced, which means that there were some Ni−C compounds in the final alloy. In a previous study, Jacobson et al.49 identified the Ni−C compound as a source of grain rotation in epitaxial graphene; thus, the variable directions of graphene nuclei and boundary defects of the large graphene obtained in annealed Ni−C alloys may be caused by Ni−C compounds. To reveal the energy change during annealing, the potential energy curve is plotted in Figure 7. The potential energy of the total system has a rapidly decreasing tendency during the first 500 ps, indicating that the diffusion, nucleation, and growth of graphene are spontaneous because the emergence of carbon

Table 1. Potential Energy Changes of Nickel Atoms in the Formation Process of the Four Pieces of Graphene with Different Carbon Concentrations % C concn of alloys potential energy changes of Ni atoms (kcal/mol)

50 1619.2

70 1109.5

90 882.4

99 121.2

in the annealed system were concentrated around 60° and 110°, and two common nickel structures in the stable annealing alloy are inserted into Figure 6b. The smallest configuration of the nickel cluster is a triangle composed by three nickel atoms, which is consistent with the nickel crystal. However, the diagonal angle between two nickel triangles distributes in the range of 60° and 110°, suggesting that nickel clusters do not reach the most stable situation and are easily deformed. The configuration of nickel clusters may be affected by the defect of surface graphene, as Gao et al.48 proved. The pair distribution function shown in Figure 6c reveals the overall structural change of the Ni−C alloy. With annealing, the first and third peaks become sharper, and the second peak becomes more insignificant. These phenomena indicate a structural transformation making atoms arrange in order. Moreover, comparing pair distribution functions and direct dynamics snapshots (in Figure 2a) at several moments, the disappearance of the prepeak can be seen as a sign of the initial structure F


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Figure 9. (a) Final graphene obtained at different annealing temperatures; from top to bottom, the annealing temperatures are 600, 8000, 1000, and 1200 K, respectively. (b) Final concentration distribution profiles of the four alloys. (c) Potential energies as functions of the simulation time in the formation process of graphene. (d) The conversion rate of carbon atoms to graphene in the four alloys as a function of the simulation time.

rings reduces the systematic potential energy and enhances the stability of the Ni−C system. The declining rate of energy slows down after 500 ps and the system potential energy reaches its minimum at 2000 ps, suggesting that the self-optimization of the large graphene is also spontaneous, although it takes a longer time. The optimized graphene reaches equilibrium as the potential energy remains unchanged, illustrating that the large graphene obtained by annealing is stable and not easy to damage. Although the total energy decreases with annealing, the potential energy of a certain element is not always declining. As shown in the insets in Figure 7, the potential energy of carbon atoms has the same downward trend as the total potential energy because the resulted graphene is stable. However, the potential energy of nickel atoms increases due to the unstable nickel cluster, suggesting that the formation of graphene may be hampered when the proportion of nickel atoms is too large. Figure 8 illustrates the effect of the carbon proportion on graphene formation. Four alloys with different carbon concentrations (50%, 70%, 90%, and 99%) were annealed to prepare graphene at 1000 K. The initial models of the four alloys are shown in Figure S1 of the Supporting Information. Figure 8a shows that the obtained graphene has a large area and few defects as the carbon concentration increases from 50% to

90%, because carbon atoms interconnect easily at high concentrations. However, the morphology of the graphene deteriorates when the carbon concentration increases to 99%, since some carbon atoms do not fold into graphene nuclei due to the insufficient nickel catalyst, which indicates that there is an optimum carbon concentration (90%) for graphene formation. Similar results have also been demonstrated in the process of carbon nanofiber nucleation.50 As illustrated in Figure 7, the potential energy of nickel atoms increases with annealing, and Table 1 shows that the energy increases more when the nickel concentration of the alloy is high. Figure 8b illustrates that the increased potential energy of nickel atoms prolongs the time required to reach equilibrium and form graphene, proving that the formation of graphene will be hampered when the proportion of nickel atoms is too large. The lateral concentration distribution in Figure 8c certifies that the proportion of carbon atoms does not affect the position of graphene, but graphene conversion rates shown in Figure 8d further demonstrate that the Ni−C alloy with 90% carbon atoms is more suitable for the growth of graphene, since the graphene conversion rate in the alloy with 90% carbon concentration is 86%, which is much higher than that of other alloys. G


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four graphene obtained in alloy surfaces, illustrating that it is easier to prepare high-quality graphene by annealing the flaky alloy, since the graphene obtained in the three-layer alloy is more complete than that obtained in the nine-layer alloy. This result is due to the fact that carbon atoms in thick alloys do not easily diffuse to surfaces, so the growth of graphene is hampered. Lateral concentration distributions in Figure 10b reveal that graphene is mainly formed on the surface of Ni−C alloys, regardless of the alloy thickness, while graphene conversion rates shown in Figure 10c demonstrate that annealing the thin Ni−C alloy can increase the conversion rate of carbon atoms to graphene.

4. CONCLUSION In summary, this paper proves that there are four stages diffusion, nucleation, growth, and self-optimizationin the formation process of the large monolithic graphene in the annealed Ni−C alloy. Carbon atoms can diffuse to and occupy alloy surfaces rapidly due to their large diffusion coefficient and low surface energy, while nickel atoms inside the carbon layer play an important catalytic role in the graphene nucleation by folding carbon chains into carbon rings. Nuclei grow into large graphene consisting of 5-m rings, 6-m rings, and a few 7-m rings, and the morphology and defects of the obtained graphene can be self-optimized when the annealing time is extending. Nickel atoms form Ni−C compounds and unstable nickel clusters in the process of annealing. The alloy evolution is spontaneous, and the appropriate substrate, flaky alloy, optimized carbon concentration (90%), and high annealing temperature have positive effects on the integrity, stability, and conversion rate of the obtained graphene. This study certifies that the reactive force field can be used in molecular dynamics simulation to study the forming process of graphene, and it provides insight into the heterogeneous growth of the annealed Ni−C alloy at the atomistic level, which can help researchers to further improve the preparation method of graphene in a convenient and economical way.

Figure 10. (a) The final morphologies of graphene obtained in four alloys with different thicknesses; from top to bottom, there are three, five, seven, and nine atomic layers in the initial alloy. (b) Final concentration distribution profiles of the four alloys. (c) The conversion rate of carbon atoms to graphene in the four alloys as a function of the simulation time.

Annealing temperature also affects the formation of graphene. Figure 9 shows four pieces of graphene obtained at four different annealing temperatures: 600, 800, 1000, and 1200 K. Ni−C alloy contains 70% carbon atoms and 30% nickel atoms, and its initial geometry is shown in Figure S2 of the Supporting Information. The final morphology of the obtained graphene (Figure 9a) illustrates that the highest annealing temperature is conducive to producing high-quality graphene, since the graphene obtained at 1200 K is larger and more perfect than that obtained at 600 K, which is consistent with previous experimental results.51−53 Lateral concentration distributions of the four systems are shown in Figure 9b, revealing that the distance between two pieces of graphene which are located on two surfaces of the alloy increases with the increasing of annealing temperatures, because high temperatures can promote the atomic diffusion and segregation. The potential energy change (Figure 9c) proves that high temperatures could extend the time of graphene nucleation and growth, as shown by the dotted line, for the reason that atoms move actively at high temperatures and carbon nuclei redisperse easily due to thermal fluctuations in the system. However, the high annealing temperature can increase the conversion rate of carbon atoms to graphene; for example, the final conversion rate is only 50% at 600 K but is 75% at 1200 K, as shown in Figure 9d. Thus, it can be concluded that high annealing temperatures have a positive effect on the morphology and conversion rate of the obtained graphene. To study the effect of the thickness of Ni−C alloy on graphene formation, annealing on four alloys with different thicknesses was performed to prepare graphene at 1000 K. The thickness of alloys is adjusted by changing the number of atomic layers from three to nine in the model, and the four initial alloys are shown in Figure S3 of the Supporting Information. Figure 10a shows the final morphologies of the

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b06620. The initial structure of Ni−C alloys with different carbon concentrations. The initial structure of Ni−C alloy that is annealed at four different temperatures. The initial structure of Ni−C alloys with different thicknesses (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yifan Li: 0000-0001-5764-5350 Yan Wu: 0000-0002-4223-226X Hui Li: 0000-0002-1457-8650 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge the support from the National Natural Science Foundation of China (Grant No. H


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51671114). This work is also supported by the Special Funding in the Project of the Taishan Scholar Construction Engineering and National Key Research Program of China (Grant No. 2016YFB0300501)

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