Interaction between Iron and Graphene Nanocavity: Formation of Iron

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Interaction between Iron and Graphene Nanocavity: Formation of Iron Membranes, Iron Clusters, or Iron Carbides Shuang Chen, and Xiao Cheng Zeng ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b00904 • Publication Date (Web): 14 Mar 2017 Downloaded from http://pubs.acs.org on March 16, 2017

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ACS Applied Materials & Interfaces

Interaction between Iron and Graphene Nanocavity: Formation of Iron Membranes, Iron Clusters, or Iron Carbides Shuang Chen1 and Xiao Cheng Zeng*,2,3 1

2

Kuang Yaming Honors School, Nanjing University, Nanjing, Jiangsu 210023, China

Department of Chemistry, University of Nebraska–Lincoln, Lincoln, Nebraska 68588, United States 3

Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, Beijing, 100029, China

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] KEYWORDS: two-dimensional Fe membranes/monolayers, ultrafine Fe clusters, iron carbides, graphene edges, ab initio molecular dynamics simulations

ACS Paragon Plus Environment

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ABSTRACT: Motivated from a recent experimental study on filling of a graphene nanocavity by iron membrane at room temperature (Science 2014, 343, 1228.), we perform a comprehensive study of morphology changes of two-dimensional Fe membranes and iron carbides embedded in graphene nanocavities with specific sizes and shapes, using the first-principles calculations and ab initio molecular dynamics simulations. Our simulations show that Fe atoms tend to gradually seal the graphene nanocavity via growing a metastable Fe membrane until the nanocavity is completely covered. Notably, a densely packed Fe membrane in the graphene nanocavity shows higher structural stability than a loosely packed one as long as more number of triangular lattices can form to release high tensile strain. The Fe membrane under high tensile strain tends to collapse and turns into a three-dimensional Fe cluster upon detaching from the edge. The structural transformation of Fe nanostructures follows the melting recrystallization mechanism at ambient temperatures in high vacuum. Moreover, the iron carbide can also exist in the graphene nanocavity and once formed, can be highly stable even at 1200 K.


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1. INTRODUCTION Graphene, a two-dimensional (2D) atomically thin layer of carbon atoms in the honeycomb lattice, can be utilized as a coating material or a supporting substrate owing to its high mechanical strength and chemical stability. As a coating layer, for example, graphene has been used in atomic force microscopy measurement of structures of highly diffusive water1 or volatile organic molecules2 under ambient conditions, or used for protecting Pt(100) surface against O2 oxidation.3 As a supporting substrate, graphene has been used in transmission electron microscopy (TEM) imaging of structural evolution of ultrafine Fe clusters4 and other transition metal catalysts.5 Notably, when a nanocavity-containing graphene is under electron irradiation (e.g., in TEM experiment), intriguing phenomena related to the interaction between metal atoms and graphene nanocavity were observed, especially for the iron-graphene system.4, 6 It was found that when iron atoms or clusters are in contact with the edges of graphene nanocavity under the electron irradiation, the graphene nanocavity may be sealed with a single layer of Fe atoms.6 A better understanding of the formation of single-atom-thick Fe membranes and phase change between 2D Fe membranes and three-dimensional (3D) Fe clusters embedded in the graphene nanocavities is the primary aim of this computational study. Like bulk Fe, the 2D Fe membranes also exhibit ferromagnetic properties but with even higher magnetic moments.6-7 Indeed, the original discovery of 2D Fe membranes has motivated later experimental fabrication and theoretical prediction of free-standing ultrathin metal nanosheets.8-11 Generally speaking, fabrication of Fe membranes with single atomic layer thickness is quite challenging due to the excess of surface dangling bonds which tend to prohibit Fe atoms from forming a monolayer as graphene.6 Previously, Wang et al. predicted possible formation of 2D Fe monolayer constrained by graphene edge, which was inspired by the formation of 2D


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membrane from a liquid drop supported by a thin wire.12 Meanwhile, Zhao et al. achieved a single-atomic-layer Fe membrane suspended in graphene nanocavity at room temperature,6 confirming the previous theoretical prediction.12 In Zhao et al.’s experiment, the graphene was grown by chemical vapor deposition over Ni/Mo substrate, and then the graphene monolayer was transferred onto standard lacey carbon (TEM) grid by using FeCl3 etching solution to detach it.6 During the above transfer process, the remnant Fe species from decomposed FeCl 3 were left as single atoms or small clusters at the edge of pores or as 2D crystalline membranes suspended across perforation in clean graphene.6 Later, from the TEM inspection, Zhao et al. proposed that of Fe membrane suspended in graphene nanocavity exhibits a square lattice with a lattice constant of 2.65 Å,6 contrary to predicted close-packing triangular lattice by Wang et al.12 This apparent inconsistency in predicted lattice structures of the Fe membranes has led to other theoretical studies to determine the realistic structures of Fe monolayers embedded in graphene nanocavities.7, 13 Thomsen et al. showed that the free-standing Fe monolayer is structurally more stable in triangular form than in square or honeycomb form.7 In any case, the predicted lattice parameters of different structures are all within the range of 2.3−2.5 Å,7 less than the proposed square-lattice parameter of 2.65 Å from the TEM experiment.6 To reconcile this apparent disagreement with the experimental suggestion, Thomsen et al. proposed that the structures of Fe membranes can switch between square lattice and triangular lattice, due to the interaction with different graphene nanocavities and a lower edge formation energy for the square lattice.7 They also showed that iron carbide formed in graphene nanocavity would be energetically favorable based on the binding energy calculations.7 Later, Shao et al. adopted the 2D particle-swarm-optimization (PSO) algorithm implemented in the CALYPSO code, combined with density functional theory (DFT) structure optimization,


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to generate low-energy 2D single-atom-thick Fe-C layers with possible square lattices to resolve the inconsistency between TEM observation and theoretical investigation, with consideration of different chemical compositions and stoichiometry.13 They suggested that the formation of iron carbide (Fe1C1) square lattice with Fe-Fe bond length of 2.62 Å13 is consistent with the TEM experiment-predicted square lattice constant.6 Another 2D distorted-square Fe2C2 lattice was found via the PSO search, which has the lowest energy and is dynamically stable.13 In the PSO search, a well-studied iron carbide Fe3C was also considered. Overall, the structures can maintain 2D only when the ratio of Fe to C is no larger than 1.13 In view of structure uncertainty of the 2D Fe membranes embedded in the graphene nanocavities, we have performed the first-principles computation and ab initio molecular dynamics (AIMD) simulations to examine various structures of 2D Fe membranes. A relatively stable iron carbide structure is also found within the graphene nanocavity. As shown in Figure 1, the Fe membrane embedded in graphene nanocavity appears to be metastable, as the energy of Fe membrane is appreciably higher than that of 3D Fe cluster counterpart. Also consistent with the previous TEM experiment, the Fe membrane can collapse into a disordered cluster under the electron-irradiation-like condition.6 Here, we use the AIMD simulations to induce the structural transformation of Fe membranes to mimic the electron-beam irradiation in realistic TEM experiment. We find that the structural transformation from the 2D membranes to 3D clusters undergoes a melting-recrystallization process with |ΔEM→C| amount of energy being released (see Figure 1). This simulation study provides an account of relative stability among 2D Fe membranes, 3D Fe clusters, and iron carbides within the graphene nanocavity.


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0.8 0.6 0.4 0.2

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Figure 1. Structures of 2D Fe membrane and 3D Fe cluster, both within a graphene nanocavity, and their relative stability. The structural transformation from 2D Fe membrane to 3D Fe cluster can release |ΔEM→C| amount of energy, which can be approximately estimated from the energy difference between pure 2D Fe membrane and 3D Fe cluster with the same number of atoms (see the Supporting Information for details).

2. COMPUTATIONAL DETAILS 2.1. Geometry Optimization of 2D Fe Nanostructures in Graphene Nanocavity. We consider Fe membrane and iron carbide nanostructures in various graphene nanocavities, whose shapes and sizes quite differ from those reported in previous computational studies.7, 13 Four types of graphene nanocavities (see Figure 2) are considered, including two square Nanocavity_S1 and Nanocavity_S2 with two armchair (AC) and two zigzag (ZZ) edges, and two


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hexagonal Nanocavity_H1 and Nanocavity_H2 with six ZZ edges. In addition, two different forms of iron carbides, namely, Fe1C1 and Fe2C2, are embedded in the square graphene Nanocavity_S2 and Nanocavity_S3 (see Figure 3). First, we optimize these nanostructures by using the DFT method implemented in the Vienna ab initio simulation package (VASP) 5.3.5. For the DFT optimization, the Perdew-Burke-Ernzenhof (PBE) form14 of the exchangecorrelation functional within the framework of the generalized gradient approximation (GGA) is employed. The Grimme’s correction (D3)15 is also adopted to account for weak van der Waals interactions. The electron-ion interaction is described by the projector augmented wave (PAW) potentials16-17 with an energy cutoff of 500 eV. A vacuum layer of 20 Å is adopted in our slab models. For geometry optimization, the total energy change is set to be less than 10-5 eV and the magnitude of the largest force acting on the atoms is set to be less than 0.02 eV/Å. For more accurate estimation of electronic properties (single-point energies and magnetic moments) of the Fe-graphene systems, the convergence criterion of self-consistent field (SCF) computation is set at 10-6 eV. In addition, the spin-polarized DFT calculations are combined with the LDA+U method introduced by Dudarev et al.18 to improve the description of on-site Coulomb interaction of localized d electrons of Fe atoms with the Hubbard parameters U and J set as 4.0 eV and 1.0 eV, respectively. For different nanocavities, the Fe-Fe bond length in the optimized 2D Fe membranes nearly all falls within the range of 2.1-2.4 Å. Furthermore, these 2D Fe membranes tend to form stable triangular lattice (see discussion below), consistent with previous theoretical investigations.7,

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Hence, this treatment of the d electrons of Fe atoms can describe the Fe-

graphene systems considered well. 2.2. Thermal Annealing of Fe Nanostructures in Graphene Nanocavity. To further analyze thermal stability of 2D Fe membranes and iron carbides suspended in graphene nanocavities at


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ambient temperatures in vacuum, AIMD simulations are carried out for some specific slab models. All the AIMD simulations are performed within the framework of the Kohn−Sham formulation of DFT by using the Gaussian plane-waves (GPW) method implemented in the QUICKSTEP program of the CP2K software package. The PBE-D3 functional is employed with a cutoff radius of 20 Å for all dispersion calculations. To describe the d electrons of Fe atoms more accurately, the spin-polarized (i.e. unrestricted Kohn−Sham) computations are also used. A polarized double-ξ quality Gaussian basis in conjunction with the norm-conserving Goedecker−Teter−Hutter (GTH) pseudopotential is used. The auxiliary plane-wave basis set is defined by an energy cutoff of 330 Ry, accompanied by a cutoff of 33 Ry for Gaussian basis set collocation. The SCF convergence is set to 10-6 a.u. The time step in AIMD simulations is set as 1 fs. The temperature is controlled by a Nosé-Hoover chain thermostat. To exhibit the structural transformation of Fe membranes and iron carbides in graphene nanocavities, the slab models are directly taken from the optimized structures (see subsection above), followed by 10-ps AIMD simulations in the constant-volume and constant-temperature ensemble with temperature controlled at 300 K, 600 K, and 1200 K, respectively.


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Figure 2. Possible atomic structures of suspended Fe membranes in four different graphene nanocavities (grey color): (a) Nanocavity_S1, (b) Nanocavity_S2, (c) Nanocavity_H1, and (d) Nanocavity_H2. The four graphene nanocavities are designed to have two shapes: square (S) with two armchair (AC) and two zigzag (ZZ) edges and hexagonal (H) with six zigzag edges. For Nanocavity_S1, two series of Fe membranes are generated by adding Fe atoms one by one: high-symmetry (HS) and low-symmetry (LS) series. The color panel in (a) illustrates a color code for different coordinate number Ncoord of each Fe atom (marked by different color). In (d) the defective graphene structure is highlighted in green while the Fe atoms are also highlighted in orange.


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3. RESULTS AND DISCUSSION Here, we refer to the structures of body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) of bulk Fe crystals to derive four 2D structures (see Figure S1 in the Supporting Information), which include two square lattices, taken from BCC Fe(100) with the lattice constant of 2.87 Å and FCC Fe(100) with the lattice constant of 2.46 Å, and two triangular lattices, taken from rhombic BCC Fe(110) with the lattice parameters of 2.48 Å and 70.5° and rhombic HCP Fe(001) with the lattice parameters of 2.35 Å and 60°. Clearly, the suggested square lattice constant (2.65 Å) from the TEM experiment is larger than that of FCC Fe(100) (2.46 Å) and smaller than that of BCC Fe(100) (2.87 Å). Note that in the previous experiment, although the local electron energy-loss spectroscopy (EELS) spectra were used to exclude other possible compounds for these 2D Fe species, e.g., carbides and oxides, it was indicated that if only a few carbon atoms present in the lattice, they may not be detected due to the EELS detection limit.6 So the experimentally observed 2D Fe nanostructures still have a possibility of being iron carbide. When considering single-layer-thick iron carbides in graphene nanocavities, we adopted the square Fe1C1 lattice and distorted square Fe2C2 lattice generated by Shao et al.13 With reference to the mentioned square Fe, Fe1C1, and Fe2C2 lattices above, we attempted to seal the graphene nanocavities by either a single-atom-thick Fe layer, or Fe1C1 layer, or Fe2C2 layer with different shapes or sizes, named as square Nanocavity_S1, Nanocavity_S2, Nanocavity_S3, hexagonal Nanocavity_H1 and Nanocavity_H2, respectively (see Figures 2 and 3). For the studied graphene nanocavities, we considered the preferential alignment of Fe square lattice with graphene edge. The best lattice match is for the Fe(110) plane to align with an armchair edge of graphene.6 If an Fe(110) plane to armchair alignment exists, the other match is for the Fe(110) plane to meet with


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the zigzag edge.6 For the square Nanocavity_S1 (Figure 2a), Nanocatity_S2 (Figure 2b) and Nanocavity_S3 (Figure 3a) which all have two armchair and two zigzag edges, we reserve the graphene edges which would preferentially align with square Fe, Fe1C1, and Fe2C2 lattices. All nanocavities considered match the experimental size, and they are not larger than 3 × 3 nm2 and can hold Fe membranes not more than 10 atoms wide.6 Furthermore, Nanocavity_H1 and Nanocavity_H2 with six zigzag edges are considered as these types of graphene perforation can be produced experimentally19 and may have the possibility to hold square Fe membrane.7

Initial

Final

(a) Fe1C1 in Nanocavity_S3 (b) Fe1C1 in Nanocavity_S2 (c) Fe2C2 in Nanocavity_S2 Figure 3. Possible iron carbide (FenCn) monolayers suspended in graphene nanocavities: (a) Fe1C1 in Nanocavity_S3, (b) Fe1C1 in Nanocavity_S2, and (c) Fe2C2 in Nanocavity_S2. The initial and final structures of each iron carbide in graphene nanocavity indicate the structures before and after DFT optimization. The graphitic C atoms in green stand for defective C structures.


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After geometry optimization, we find that all square lattices are structurally unstable because nearly all square lattices turn into either triangular lattices or mixed triangular-square lattices, except the highly stable Fe1C1 square lattice in Nanocavity_S3 (Figure 3a). We obtain two different Fe membranes in graphene Nanocavity_S1, including a high-symmetry (HS) one with 27 atoms (Figures 2a and S2a) and a low-symmetry (LS) one with 28 atoms (Figures 2a and S3a). Then we add Fe atom one by one into the graphene Nanocavity_S1 to form new 2D Fe networks. Interestingly, two series of HS and LS Fe membranes with (27-30, 33) and (28, 30-37) Fe atoms, respectively, are obtained in graphene Nanocavity_S1, as summarized in Figures 2a, S2, and S3. To further address the issue on the square versus triangular lattices of the Fe membranes suspended in graphene nanocavities, we estimate coordination number (Ncoord) of each Fe atom (only the nearest neighbors are considered) by using the Fe-Fe bond distance cutoff of 2.87 Å, i.e., the BCC Fe(100) lattice constant (Figure S1a). As shown in Figure 2, the square-lattice pattern appears to be highly unfavorable in graphene nanocavity as few Fe atoms have the coordination number of 4 except the case of high-symmetry Fe membrane with 27 atoms in graphene Nanocavity_S1 where eight Fe atoms exhibit Ncoord = 4, indicating this Fe membrane retains a portion of square lattices. From Figure S2a, it can be seen that distribution of the Fe-Fe bond length for the high-symmetry Fe membrane with 27 atoms in Nanocavity_S1 exhibits a high peak at about 2.2 Å, while distribution of the Fe-Fe bond angle exhibits high peaks at 86° (indicating the square lattice) and 52°. These features are attributed to the small size of Nanocavity_S1 which cannot accommodate square Fe membrane so well. So we put a square Fe membrane into a larger Nanocavity_S2 to achieve a better alignment of Fe membrane with the graphene edges. As indicated by the coordination number again in Figure 2b, two additional


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possible square lattices for the Fe membranes with 30 and 36 atoms are identified in the squareshaped graphene Nanocavity_S2. In Figures S4a and S4b, both Fe membranes exhibit the most probable Fe-Fe bond length of ~2.1 Å, while distribution of the Fe-Fe bond angle exhibits a peak at about 90°. But for the 30-atom Fe membrane a higher peak is seen at 60°, while a higher peak at about 70°is seen for 36-atom membrane. Because the size effect of graphene nanocavities on the formation of square Fe membrane is still not so clear, we turn our attention to the hexagonal Nanocavity_H1 and Nanocavity_H2. As shown in Figures 2c and 2d, Fe atoms in central regions of the Fe membranes almost have Ncoord = 5. Further, from Figures S4c and S4d, Fe-Fe bond angle lacks the distribution of about 90°. Hence, the regular-hexagon-shaped Nanocavity_H1 and slim-hexagon-shaped Nanocavity_H2 with all-zigzag edges do not keep the 2D Fe membranes with square lattice. The shape effect of the graphene nanocavities on the formation of square Fe membrane appears to be slightly stronger than the size effect. Except the aforementioned high-symmetry Fe membrane with 27 atoms in Nanocavity_S1 and Fe membranes with 30 and 36 atoms in Nanocavity_S2, all the other Fe membranes considered (Figures S2−S4) have the distribution of the Fe-Fe bond length largely within the range of 2.1−2.4 Å and the distribution of the Fe-Fe bond angle largely within 50−60° (while with little distribution beyond 90°). These results indicate that for many Fe membranes generated in different graphene nanocavities, the square-lattice structure with the lattice constant of 2.65 Å is not as favorable as suggested from the TEM experiment.6 Most Fe membranes exhibit shorter Fe-Fe bond length within the range of 2.1−2.4 Å of the triangular lattice, consistent with two previous theoretical studies.7, 13 The square lattice seldom emerges in these membranes, and if emerging, the square lattices tend to mix with triangular lattices or


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become distorted, consistent with the experimental TEM images of square lattices surrounded by triangular lattices near the edge of graphene nanocavity.6 Next, we focus on the structural rearrangement of Fe membranes with increasing Fe atoms in graphene Nanocavity_S1 (see Figure 4). By adding Fe atoms one by one to grow the Fe membranes, the coordination number of Fe atoms increases, leading to higher fraction of triangular lattices (Figure 4b). In principle, one expects the formation energies decrease as the triangular lattices enlarge. However, the formation energies per Fe atom for high-symmetry Fe membranes markedly increase (from -3.0 eV/atom to -2.6 eV/atom) as the number of newly added Fe atoms increases, while the formation energies per Fe atom for low-symmetry membranes are nearly unchanged (fluctuate at around -3.1 eV/atom). A reason for this contrast is that Fe atoms within the high-symmetry membranes are fully confined into the 2D plane as shown by the side views (insets in Figure 4a). As such, with increasing the number of Fe atoms, both hydrostatic and shear strains (whose definition can be found in Li and Yip’s work20 and also see the Supporting Information for details) within Fe membranes increase (as shown in Figures 4c and 4d), resulting in less negative formation energy. However, Fe atoms in the low-symmetry membranes can relax both within the plane and out of the plane (side views of Fe membranes with 33 and 37 atoms, shown in insets of Figure 4a) so that the formation energies per Fe atom change little with increasing the number of Fe atoms. As shown in Figures 4c and 4d, the strains of Fe membranes would also increase as the number of Fe atoms increases for low-symmetry membranes, but the associated energy increase may be compensated by out-of-plane relaxation.


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(b) Coordination Number (Ncoord) of Each Fe Atom 20

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(a) Variation of Formation Energy per Fe Atom with Number of Fe Atoms for Different Fe Membranes in Graphene Nanocavity_S1

y (Å)

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37 Fe Atoms

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Figure 4. Summary of high-symmetry (HS) and low-symmetry (LS) Fe membranes in graphene Nanocavity_S1 with increasing number of Fe atoms (after geometry optimization): (a) variation of formation energy per Fe atom of Fe membranes with number of Fe atoms. For Fe membranes with 27, 33 (HS and LS), and 37 atoms, their (b) coordination number (Ncoord) plots, (c) hydrostatic strain plots, and (d) shear strain plots of each Fe atom are presented. Top and side views of these specific Fe membranes are also highlighted in insets.

Although Fe membranes can form in graphene nanocavities, they are generally metastable with respect to 3D Fe clusters with the same number of atoms as indicated from the computed relative energies of different Fe nanostructures (Figure 1). In fact, the previous calculations showed that the free-standing square or triangular Fe monolayers exhibit imaginary frequencies in the phonon dispersion curves,13 also indicating less stability of 2D Fe monolayers. When an Fe atom is placed on a six-membered ring of graphene surface of the FeN-in-graphene-Nanocavity_S1 (N = 30-36), to be compared with the Fe membranes with N+1 Fe atoms in the same base system, one can view that the newly adsorbed Fe atoms can show two possibilities after geometry optimization: (1) directly moving into graphene nanocavity to join in the Fe membranes or (2) staying on the six membered rings of graphene as shown in Figure S5. By comparing the formation energies for both cases, we conclude that the Fe atom prefers to join the Fe monolayer in graphene nanocavity, rather than to be adsorbed on the graphene surface. On the other hand, the Fe membranes also exhibit catalytic capability to induce defective graphene edges (highlighted in green) via C-C rotation in Figure 2d. Shao et al. used ab initio PSO technique and identified two stable iron carbides, Fe1C1 and Fe2C2, suspended in graphene nanocavities. Especially, the Fe1C1 in graphene nanocavity exhibits square lattice with the lattice


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constant of 2.62 Å,13 nearly the same as the square lattice constant suggested from the TEM experiment.6 Although the TEM experiment measurement excluded possibility of iron carbide,6 our simulations support existence of free-standing iron carbide in graphene nanocavity. It is possible that under the TEM electron irradiation, C atoms can gain high enough energy to be displaced from the edge of graphene nanocavity. If so, the displaced C atoms may encounter Fe atoms and form the iron carbide. To confirm this possibility, we chose the larger-sized graphene Nanocavity_S2 to be filled by different iron carbide, Fe1C1 and Fe2C2, with reference to Shao et al.’s work13 (Figures 3b and 3c). After structural relaxation, both nanostructures change a great deal. Iron carbides lose their original connection between Fe and C atoms. The graphene nanocavities become defective (highlighted in green in Figures 3b and 3c). To make a better alignment for the square Fe1C1 with the graphene edges, a smaller Nanocavity_S3 was employed (Figure 3a). After structural relaxation, a highly-ordered square iron carbide in graphene nanocavity is obtained. Here, the Fe-Fe bond length is within the range of 2.4−2.8 Å with an average value of 2.58 Å, much longer than that of pure Fe membranes discussed above, and also quite close to the experimentally estimated square lattice constant of 2.65 Å.6 The size match between 2D Fe nanostructure and graphene nanocavity plays a significant role in generation of some specific nanostructures. To further demonstrate thermal stability of Fe membranes and possible formation of iron carbide in graphene nanocavities, we performed three series of 10-ps AIMD simulations in the NVT ensemble at 300 K, 600 K, and 1200 K, respectively. Three studied systems include the HS Fe membrane with 27 atoms in graphene Nanocavity_S1, LS Fe membrane with 37 atoms in graphene Nanocavity_S1, and iron carbide, Fe1C1, in graphene Nanocavity_S3, as summarized in Figure 5. The Fe membrane with 27 atoms (Figure 5a) quickly collapses into 3D Fe clusters


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even at 300 K due to the preferential reduction of excess surface Fe dangling bonds of Fe membrane. The Fe membrane tends to detach from the edge of graphene nanocavity, and but leaves a single Fe atom or a short Fe wires in contact with the graphene edge. The computed time-dependent mean-square-displacement (MSD) curves based on the 10-ps AIMD simulations at three temperatures are also shown in Figure 5a. We found that the Fe membrane with 27 atoms in graphene Nanocavity_S1 behaves like viscous liquid at 300 K or 600 K. After fitting the MSD curves, diffusion coefficients are found to be on the order of 10-6 cm2/s. At the elevated temperature of 1200 K, the 27-atom Fe membrane becomes liquid-like with a diffusion coefficient of 1.42×10-5 cm2/s.


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(a) 27 Fe Atoms in Nanocavity_S1

(b) 37 Fe Atoms in Nanocavity_S1

(c) Fe1C1 in Nanocavity_S3

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Lindemann Index

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Figure 5. Initial and final structures (after 10 ps of each AIMD simulation) of Fe membranes with (a) 27 and (b) 37 atoms in graphene Nanocavity_S1 and (c) iron carbide, Fe1C1, in graphene Nanocavity_S3 based on the AIMD simulations at 300 K, 600 K and 1200 K, respectively. The corresponding MSD-time curves for fitting diffusion coefficients and Lindemann indexes are also present to analyze the phase behavior of Fe membranes or iron carbide in graphene nanocavities.


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In addition, the Lindemann index value (0.1) can be used to characterize the melting transition of a solid.21 As shown in Figure 5a, the Lindemann index increases with temperature and reaches 0.09 at 1200 K, consistent with the diffusivity results for the Fe membrane with 27 atoms in graphene nanocavity. Here, the metastable Fe membrane will collapse into 3D cluster within the graphene nanocavity behaving like a viscous liquid or liquid initially and then following the melting recrystallization pathway to realize the structure change. The Fe membrane with 37 atoms in Figure 5b exhibits very different structural characteristics from the one with 27 atoms. At the end of 10-ps AIMD simulations, no obvious structure change is observed for the Fe membrane with 37 atoms at different temperatures, even as high as 1200 K. Notably, Fe atoms at the center of the Fe membrane show a tendency to aggregate, which means that they are not constrained into 2D plane. As shown in Figure 5b, Fe atoms in this membrane give lower MSDs and Lindemann indexes than those in the Fe membrane with 27 atoms. At 300 K, the diffusion coefficient is on the order of 10-7 cm2/s. As the temperature increases to 600 K and 1200 K, the diffusion coefficient is on the order of 10-6 cm2/s, indicating that this membrane behaves like a more viscous liquid. Combining the dynamic structural evolution of Fe membranes discussed above with the formation energy data in Figure 4a, we conclude that when a graphene nanocavity is gradually filled with more and more Fe atoms to form a membrane, the more densely packed Fe membrane is energetically more favorable than the loosely packed Fe membrane. Although the previous first-principles calculations showed that the free-standing Fe1C1 iron carbide monolayer is dynamically unstable due to existence of imaginary frequencies in phonon spectrum,13 the thermal stability of this free-standing Fe1C1 iron carbide monolayer is expected to be quite different from the iron carbide embedded in graphene nanocavity. As shown in Figure 5c, when


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this iron carbide Fe1C1 is embedded into the graphene Nanocavity_S3, it exhibits very high thermal stability. This iron carbide can be the most stable form among three systems considered, including two Fe membranes and one iron carbide in the graphene nanocavities. Note that the iron carbide behaves like solid at all three temperatures, even as high as 1200 K, and gives lower Lindemann index (in the range of 0.01−0.015) than that of Fe membranes with 27 and 37 atoms in graphene Nanocavity_S1. In sum, although Fe membranes are metastable, either the Fe membranes or iron carbides can exist in graphene nanocavities with specific sizes and shapes. Eventually, the Fe membranes tend to collapse into 3D Fe clusters, as observed in the TEM experiments.6 However, the iron carbide can be stable in graphene nanocavity.

4. CONCLUSIONS Our systematic first-principles calculations suggest that either 2D Fe membranes or iron carbides can exist in graphene nanocavities with specific sizes and shapes. Our AIMD simulations show evidence of structural evolution of ultrafine Fe nanostructures, such as phase change from 2D membranes to 3D clusters. If Fe atoms encounter the graphene edge, they tend to seal the graphene nanocavity to form 2D metastable Fe membranes. The graphene nanocavity can be filled with increasing number of Fe atoms until the Fe membrane is densely packed. Until then, the more densely packed Fe membranes exhibit higher stability than the loosely packed Fe membranes. Eventually, the metastable Fe membranes tend to collapse into 3D clusters by detaching from the graphene edge. This structural transformation of Fe nanostructures follows the melting recrystallization mechanism at ambient temperatures in high vacuum. On the other hand, the iron carbide can also exist in the graphene nanocavity, and once formed, it is highly


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stable even at 1200 K. Overall, our simulations offer comprehensive insights into rich structural behavior of Fe nanostructures in graphene nanocavity.

ASSOCIATED CONTENT Supporting Information: Estimation of relative energies and hydrostatic/shear strain components, reference structures of Fe membranes, coordination number of each Fe atom and distributions of Fe-Fe bond length/angle for Fe membranes, and formation energy comparison between Fe membranes with N+1 Fe atoms and Fe membranes with N atoms and with one more Fe atom adsorbed on graphene surface. The Supporting Information is available free of charge on the ACS Publications website at http://pub.acs.org. AUTHOR INFORMATION Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was supported by a grant from the Nebraska Center for Energy Sciences Research in the University of Nebraska-Lincoln, a fund from Beijing Advanced Innovation Center for Soft Matter Science & Engineering for summer visiting scholar, and by the University of Nebraska Holland Computing Center.

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TOC Graphic

Relative Energy per Fe Atom (eV/atom)

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Interaction between Iron and Graphene Nanocavity: Formation of Iron

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