Initial Stages of Growth of Nitrogen-Doped Single ... - ACS Publications

Article pubs.acs.org/JPCC

Initial Stages of Growth of Nitrogen-Doped Single-Walled Carbon Nanotubes Stefan Taubert and Kari Laasonen* Department of Chemistry, Aalto University, FI-00076 Aalto, Finland S Supporting Information *

ABSTRACT: The dynamics of carbon and nitrogen atoms on the Fe55 nanoparticle is investigated by means of molecular dynamics simulations at the density-functional tight-binding level. A time range of at most 0.4 ns is covered in the molecular dynamics simulations. Different degrees of adatom coverage are considered. Nitrogen and carbon atoms express different dynamics. Adsorbed monomers and large fragments are rather immobile whereas dimers and trimers move fast. Nitrogen-containing fragments are less strongly bound to the iron cluster and are therefore more mobile than carbon-only fragments with equal amount of atoms. On the iron nanoparticle surface, five-membered rings are formed first and then six-membered rings. The present simulations provide insight into the atomistic mechanisms involved in the nanocatalyzed synthesis of nitrogendoped carbon nanotubes. The tendency of nitrogen atoms as parts of carbon fragments to repel the iron surface is confirmed by performing short molecular dynamics simulations at the density-functional theory level.

1. INTRODUCTION Carbon nanotubes (CNT) are helical microtubules composed of six-membered carbon rings.1 Growing carbon nanotubes on transition metal clusters made of, e.g., iron, nickel, or cobalt is today a routine task.2 Controlling the size and the topology, i.e., the diameter and the (n,m) chirality, of the tubes is, however, not trivial.3 The topology of the CNTs determine their metallic or semiconductor character as well as the optical properties, and thus it would be of importance to control the chirality and diameter in the synthesis.3 The catalytic growth mechanism of carbon nanotubes, as well as the nature of the active iron nanoparticles, remains elusive. For single-walled carbon nanotubes (SW-CNT), the vapor− solid−liquid (VLS) mechanism4 is often assumed. In the VLS model, the gaseous carbon precursor dissociates on the surface of the nanocatalyst and forms a carbide. Supersaturation of carbon in the nanoparticle drives diffusion of carbon atoms to the surface where they aggregate to form a cap. The CNT then grows from the surface of the nanoparticle.5 The n and p doping of CNTs by means of nitrogen and boron doping, respectively, was suggested on the basis of Car− Parrinello ab initio molecular dynamics (MD) calculations in 1993.6 The first boron and nitrogen containing CNTs were made in electric arc discharge in 1994 by Stephan and coworkers.7 Chemical vapor deposition (CVD) synthesis of nitrogen-doped CNTs was accomplished in 1997.8 VillalpandoPaez et al.9 synthesized nitrogen-doped SW-CNTs and found that increasing the amount of nitrogen makes the diameter of the CNTs smaller. Furthermore, they found that the amounts of point defects and reactive sites in the nanotube are proportional to nitrogen content. © 2012 American Chemical Society

In nitrogen-doped CNTs (N-CNTs), every single nitrogen atom has an effect on the molecular structure and on the electronic structure of the tube.10 Sumpter and co-workers11,12 have studied the growth of N-CNTs by means of experiment and density-functional theory (DFT) calculations. They found that nitrogen atoms are prone to localize at two-coordinated sites or as dangling C−N bonds.11 The substitution of a carbon atom to a nitrogen atom causes a local decrease in the diameter of the CNT.11 Since nitrogen atoms also stabilize neighboring pentagons in the CNT, the curvature can be largely affected, and with a high enough N concentration, the CNT can be closed which leads to short tubes.11 Susi et al. found that with too high amounts of nitrogen precursor the CNT growth was completely inhibited.13 Kang and Jeong14 found that the preferred substitution sites for nitrogen atoms in SW-CNTs depend on the chirality of the tube. Lin and co-workers observed that the nitrogen dopants prefer two-coordinated pyridine-like sites where the nitrogen atom is sp2 hybridized and one electron contributes to the π system. The amount of ammonia introduced in the reactor is critical for the synthesis. Recently, Susi and co-workers have synthesized N-CNTs in the presence of 100−200 ppm ammonia (NH3). The N-CNTs formed had up to 2 at. % nitrogen.13 Lin et al. reported N-CNTs with 1.7 at. % nitrogen.15 Zhu and co-workers3 used 500 ppm NH3 to produce carbon-only SW-CNTs with a small chirality distribution. The detailed mechanism of the CNT growth on iron nanoparticles is unknown, and so is the structure and composition of Received: June 28, 2012 Published: August 1, 2012 18538

dx.doi.org/10.1021/jp306376r | J. Phys. Chem. C 2012, 116, 18538−18549

The Journal of Physical Chemistry C

Article

the active nanoparticles.5 For a range of transition metals, Deck and Vecchio found that the transition metals that catalyze CNT growth also have a carbon solubility of at least 1 at. %.16 PérezCabero and co-workers conducted a Mössbauer study on catalytically active iron nanoparticles and found α-iron to decompose acetylene, while cementite, Fe3C, was found among the intermediates in the catalytic process, and therefore the CNT formation was suggested to happen via the iron carbide phase.17 Anisimov et al.18 studied the SW-CNT growth by ferrocene CVD in a carbon monoxide (CO) atmosphere and found that the cementite nanoparticles are inactive in the catalysis. Most of the active iron nanoparticles were found to be γ-Fe with the face-centered cubic (FCC) crystal structure.18 Kim and Sigmund19 have also found evidence of γ-Fe being the catalytically active iron phase. Yoshida and co-workers have, on the contrary, reported that CNTs do grow from iron carbide nanoparticles in the cementite phase.20 Recent X-ray photoelectron (XPS) studies of metal nanoparticles during CNT growth show that metallic iron predominates among the catalytically active nanoparticles, but the abundance of some iron carbide among the active nanoparticles cannot be ruled out.21 The growth of carbon-only CNTs on iron has been modeled at the density-functional tight-binding (DFTB) level by the Morokuma group using model clusters with 38,22 55,23 58, and 77 iron atoms.24 Time scales up to 300 ps were covered in the MD simulations. In this period of time, carbon atoms deposited on the surface of the metal cluster coalesce into chains. The chains first form five-membered rings which can function as a seed for a curved cap formation.25 Raty and co-workers studied the growth process over a rather short time period of 10 ps at the ab initio molecular dynamics level using density-functional theory.26 In the simulations, no carbide formation is observed, but the carbon diffuses on the surface of the iron nanoparticle. To reach time scales of several nanoseconds or longer, one has to apply empirical potentials in the molecular dynamics simulations.27,28 Ammonia, NH3, can been used as nitrogen source to produce N-CNTs. It has been shown computationally that ammonia dissociates, leaving N atoms on the surface of the iron nanocluster.29 In CVD experiments, nitrogen atoms have been introduced into SW-CNTs using ammonia as a precursor.13 The N-doped CNTs have also been produced using amines and amides as the nitrogen source.30 The dissociation barrier for NH3 on the Fe55 nanocluster has been found at 1.48 eV at the DFT level.29 A refined calculation yielded the overall dissociation barrier of 1.0 eV.31 The lowest barrier for dissociation of CO was similarly found to be 0.63 eV, while the barrier for CO2 formation via the Boudouard reaction (CO + CO → CO2 + C) was reported to be 1.04 eV.32 In recent calculations the barrier for CO dissociation on the Fe78 cluster was between 1.1 and 1.8 eV.33 Zhang et al. found that the lowest barrier for CO dissociation on a γ-Fe(111) surface is 2.58 eV.34 The present paper aims at providing insight into the role of nitrogen atoms in the growth of nitrogen-doped carbon nanotubes. The diffusion of carbon and nitrogen atoms on the surface of a Fe55 nanocluster that take place prior to growth of nitrogen-containing single-walled carbon nanotubes is modeled at the DFTB level. The Fe55 cluster is ∼1 nm across and can therefore be taken as the smallest relevant size of catalytic nanoparticle for carbon nanotube synthesis. In fact, the catalytically active particles are larger, with diameters from

about 1.8 nm,35 but due to a high computational cost we use a slightly smaller model. Furthermore, we model diffusion and initial growth during almost half a nanosecond. Although the kinetics of the whole CNT formation process is not captured by the present DFTB calculations, insights into the fast dynamics of adsorbed atoms on the nanocluster surface can be obtained. The dynamics of carbon and nitrogen atoms during the clustering process on the surface of the catalytic iron nanoparticle is discussed based on the calculated DFTB-MD trajectories and DFT calculations.

2. COMPUTATIONAL DETAILS Molecular dynamics calculations were performed using the velocity-Verlet algorithm on a Born−Oppenheimer potential energy surface. The electronic structure was relaxed in every step, and the electronic energy and forces were evaluated at the DFTB level of theory.36−38 The self-consistent charge DFTB (SCC-DFTB)39 was used. The Slater−Koster files provided by the DFTB Web site40 were used.39,41 A time step of 80 au, i.e., 1.958 fs, was used. The atomic temperature was 1000 K, and a Berendsen thermostat was used with the scaling time of 1000 ps. The Fermi smearing together with an electronic temperature that was kept at Te = 10 000 K allowed for partial occupation of the valence orbitals in order to converge the SCC calculation. The same Te was used for similar simulations by Page et al.23 The calculations were done with the DFTB+ program package.42 The magnetic moments were kept collinear, and only the total magnetic moment was defined. The DFTB+ program is currently parallelized with openMP which limits the amount of cores that are used for one calculation. At most we can therefore use a maximum of 12 CPU cores for each MD simulation, and this limits both the tractable system size and the reachable time ranges. Short MD simulations were for comparison done at the density-functional theory (DFT) level using the grid-based projector-augmented wave method as implemented in the GPAW program.43,44 The Atomic Simulation Environment (ASE)45 was used as an interface to GPAW. Classical MD was performed in the NVT ensemble as implemented in ASE. The temperature was kept at 1000 K with a Berendsen thermostat. The energies and forces were obtained at the DFT level with GPAW. The PBE functional46 was used and the grid spacing was 0.2 Å. The threshold for convergence of the energy was 1 meV. The Fermi−Dirac distribution with the width of 0.1 eV was applied for the occupation numbers, and 26 virtual orbitals were included in the calculation. The magnetic moments were kept collinear in the DFT calculation. The results from the DFT calculations are presented in the Supporting Information. The bond lengths that are discussed in the Results and Discussion section are obtained by optimizing snapshot structures at the DFTB and DFT levels of theory, with the same convergence requirements as in the MD simulations. 3. COMPUTATIONAL MODEL SETUP The initial coordinates for the Fe55 cluster with Ih symmetry were obtained from the Web provided by Elliot et al.47,48 Initially, the cluster was optimized at the DFTB level. Carbon and nitrogen was attached at arbitrarily chosen atop sites on the Fe55 cluster. In the initial step, 27 carbon atoms and 4 nitrogen atoms were introduced, and the structure was relaxed prior to the molecular dynamics simulation. After 10 000 MD steps, corresponding to about 20 ps of time, another 10 carbon atoms 18539



Article

In eq 1, A is the frequency factor, R = 8.3145 J mol−1 K−1 is the gas constant, and ΔEa is the activation energy; one can obtain a measure of the time for each CO dissociation. Lyon and coworkers obtained the CO stretching frequency of 1865 cm−1 for CO on Fen with n = 18−30.52 Assuming the relevant frequency of vibration in the direction along the surface is maybe one-tenth of this, the Arrhenius frequency factor would become about 5.6 × 1012 s−1. Using this value as the Arrhenius frequency factor together with the dissociation barrier 1 eV (96.5 kJ mol−1) and the temperature T = 1000 K, one obtains the rate coefficient k = 5.1 × 109 s−1. For a dissociation barrier of 1.5 eV (144.75 kJ mol−1), the rate coefficient is k = 1.6 × 105 s−1. This means that one CO molecule dissociates every 19 ns (ΔEa = 1.0 eV) or every 6 μs (ΔEa = 1.5 eV). On a realistic Fe78 cluster, the dissociation barrier varies between 1.1 and 1.8 eV, depending on reaction channel.33 Combining the two observations above, there are tens or even thousands of CO molecules colliding with the iron particle between each dissociation. Furthermore, with a dissociation barrier of 1 eV, the CO molecules dissociate about 100 times faster than one carbon atom enters the growing CNT. If the dissociation barrier is 1.5 eV, the time scales of dissociation of CO and carbon atom addition to the CNT are about the same. The amount of ammonia is on the magnitude of 200 ppm in a typical experiment where nitrogen-doped CNTs is produced.13 Repeating the collision-theory calculation for NH3, this would mean that one ammonia molecule collides with the Fe55 cluster every 0.46 μs. The overall dissociation barrier for NH3 to produce one nitrogen atom and three hydrogen atoms has been found to be 1.0 eV31 or 1.5 eV.29 Assuming that the same Arrhenius prefactor can be used as for carbon monoxide above, the dissociation of one ammonia molecule would happen in 20 ns (ΔEa = 1.0 eV) to 6 μs (ΔEa = 1.5 eV). The dissociation of NH3 is a three-step process, and thus the prefactor is expected to be smaller than for CO dissociation, which would lead to a lower dissociation rate for ammonia as compared to carbon monoxide. Since the present discussion only provides a rough order-of-magnitude estimate for the inclusion speed for carbon and nitrogen into N-CNTs, the approximation should not be severe. To reach an enrichment of 1−2% of nitrogen atoms in the doped CNTs, one nitrogen atom should enter the CNT in 0.5−1.0 ms. Thus, it is enough that one nitrogen atom per 1000 colliding ammonia molecules reaches the CNT, in order to obtain the observed nitrogen enrichment. The question remains: what is the mechanism causing relatively more nitrogen atoms than carbon atoms ending up in the CNT, as compared to the relative abundances of carbon and nitrogen in the gas phase? A smaller dissociation energy for NH3 as compared to CO enables some enrichment of nitrogen. The present MD simulations indicate that the diffusion of carbon and nitrogen atoms and the formation of clusters with several carbon atoms take place on a picoseconds time scale. Since the carbon and nitrogen atoms rearrange much faster than the carbon monoxide dissociations take place, it is likely that there are enough vacant adsorption sites for carbon monoxide on the catalyst iron nanoparticles as long as carbon and nitrogen atoms are transferred to the growing CNT. 4.2. Analysis of the Trajectories. The behavior of nitrogen and carbon atoms adsorbed to the Fe55 cluster was investigated using model systems. The first model system contains 27 carbon atoms and 4 nitrogen atoms stochastically adsorbed on the surface of the iron cluster. This can be considered a low-coverage model. The diffusion and

were introduced at atop sites, and the calculation was restarted. The original trajectory with 27 carbon atoms was simultaneously continued. After 10 000 more steps a further 10 carbon atoms were inserted into the model with 37 carbon atoms. The MD simulation was restarted with the new 47 carbon atom model, and the previous models with 27 and 37 C atoms were continued. All the time, only 4 nitrogen atoms were included. The cluster with 47 adsorbed carbon atoms was already so crowded that the subsequent model only got 7 more carbon atoms. Because of the rather fast clustering of carbon atoms in the model with 54 carbon atoms, 11 more carbon atoms were added to create the last model system. This way, trajectories were obtained with the following stoichiometries and time ranges: Fe55N4C27, 412 ps; Fe55N4C37, 409 ps; Fe55N4C47, 294 ps; Fe55N4C54, 214 ps; Fe55N4C65, 113 ps. The nitrogen concentration is thus quite large as compared to the abundance of less than 2 at. % found in N-CNTs experimentally.13,15 Since the model systems described above do not contain enough carbon atoms to construct a CNT, a different kind of model was constructed in order to get insight into the role of nitrogen atoms in the early growth of the nanotube. Diffusion and aggregation of carbon and nitrogen have to take place on the catalyst prior to CNT growth. We constructed a model of a growing N-CNT by taking a snapshot structure from the trajectory with 37 carbon atoms and 4 nitrogen atoms and attached a short carbon nanotube on top of it. The nanotube was constructed with the Gabedit program,49,50 and the coordinate files of the nanotube and the iron carbide nitride cluster were merged. Care was taken to avoid superposition of atoms. The structure was optimized at the DFTB level, and then a molecular dynamics run was started with the same computational parameters as the previous MD simulations. A similar approach has previously been used by Page et al., but they constructed the starting structure by attaching a C40 segment of the C60 fullerene directly on top of the bare Fe55 cluster.23 In order to observe the effect of nitrogen atoms in the CNT growth, we performed a series of simulations with 4, 5, 6, and 7 nitrogen atoms and a total of 138 or 148 carbon atoms in the capped models.

4. RESULTS AND DISCUSSION 4.1. Time Scales of Carbon Monoxide and Ammonia Dissociation on Iron Clusters. The MD simulations discussed below cover at most almost 0.5 ns. This is a short time in comparison to the time scales of the growth of CNTs in experiments. The typical growth rate of SW-CNTs in CVD experiments is on the order of 1 μm/s at a temperature range of 700−1000 °C.18 This corresponds to one carbon atom entering the tube in 1−10 μs. In a typical CVD experiment, the carbon monoxide pressure is ∼1 atm as the reactor operates at ambient pressure.51 Using standard textbook collision theory and ignoring the steric factor, this yields a collision frequency of one CO collision every 5 ns per surface iron atom. On Fe55 with 42 surface iron atoms in the perfect icosahedral conformation, this equals 112 ps between each collision, assuming each surface atom is exposed to collisions with CO molecules. This rough estimate for the amount of carbon monoxide molecules colliding with the catalyst can then be compared to the time required for dissociation of CO on the nanoparticle surface. Using the Arrhenius rate law, the rate coefficient is expressed as k = Ae−ΔEa / RT

(1) 18540



Article

reactivity of the adsorbed atoms were modeled by molecular dynamics simulations over a time of 412 ps. Below, the trajectories with the smallest and the largest adatom coverage are discussed. In the discussion, the atomic sites are denoted as atop, bridge, or hollow sites. Atoms at atop sites are bonded only to one iron atom, whereas two-coordinated atoms are at bridge sites. Three- or four-coordinated sites are denoted as hollow sites. Also, the position of dimers can be described with the same notation, whereas trimers and larger fragments bind to several surface sites. All C−C bonds in the systems are in the range of 128−155 pm. The carbon monomers are adsorbed to rather stable hollow sites, and the time between site hopping is several tens of picoseconds; therefore, the distance between carbon monomers is at least 230 pm. Therefore, the C−C bonds discussed below are well-defined. 4.2.1. The Fe55C27N4 Model. At the temperature of 1000 K, at parts of the surface with low adatom concentration, the nitrogen atoms were in practice bound strongly to the Fe surface at three-coordinated sites. The nitrogen atoms repel carbon atoms at nearby adsorption sites, and in regions with high carbon coverage, the nitrogen atoms prefer atop sites until carbon atoms at adjacent bridge and hollow sites have moved further away. During the first 400 ps, in the low-coverage model the nitrogen atoms remained as strongly bound monomers. Initially, of the 27 carbon atoms, 19 were adsorbed as monomers. The carbon monomers bind at three-coordinated sites. The other 8 carbon atoms were adsorbed so close to another carbon atom that dimers were immediately formed. After 412 ps, 6 carbon monomers remained. At the end of the trajectory, one nitrogen atom was bonded to the largest carbon fragment, consisting of 16 carbon atoms. The Fe−C and Fe−N bond lengths depend on the coordination number of the adsorbed atom. In structurally relaxed structures, nitrogen monomers prefer three-coordinated sites, and the Fe−N bond lengths are 178−190 pm at the DFT level. At the DFT level, the bond lengths are shorter than at the DFTB level. The DFTB structure is therefore less compact, and the nitrogen atoms are often found at bridge sites with Fe−N bond lengths of 182−187 pm. Carbon monomers are mostly found at four-coordinated sites. At the DFTB level, also bridged sites are found, with Fe−C bond lengths of 213−214 pm. The Fe−C bond lengths are 217−222 (183−192) pm at fourcoordinated site at the DFTB (DFT) level. At three-coordinated sites, the Fe−C bond lengths are 210−216 (181−185) pm at the respective levels of theory. Carbon dimers are more loosely bound than monomers, with average Fe−C distances of 226−228 pm at the DFTB level. At the DFT level, the corresponding Fe−C distance is 186−188 pm. The carbon−carbon bond in C2 units trapped in hollow sites is 132 pm. The C−C bond length at the DFTB level of 129 pm is on the other hand shorter, albeit in closer agreement with the DFT bond length of 131 pm. In Figure 1, the amount of nitrogen monomers, carbon monomers, dimers, and trimers, as well as the number of carbon atoms in the largest carbon fragment, are plotted as functions of the time. In this low-coverage model, the nitrogen atoms remain as monomers for the first 400 ps of simulation time. The amount of dimers grows at the beginning when individual carbon atoms encounter and dimerize. The carbon dimers are more mobile than the monomers, and they are therefore prone to form trimers upon encountering monomers. The exponential growth of the largest fragment coincides in

Figure 1. Number of carbon monomers, dimers, and trimers as well as the number of carbon atoms in the largest fragment in the Fe55C27N4 model during the 412 ps trajectory.

time with the rapid decrease in the amount of carbon dimers, as seen in Figure 2. Visual inspection of the trajectory revealed that the growth of the largest fragment at this instance of time takes place by addition of dimers. With low carbon coverage, only one larger carbon cluster is formed. This suggests that C2 dimers play a central role in the nucleation of the CNT precursor. In Figure 2, some representative snapshots from the 412 ps trajectory of the Fe55C27N4 are shown. At 307 ps, the majority of the adsorbed fragments are concentrated to one-half of the iron nanocluster, leaving the other half of the cluster surface with only carbon and nitrogen monomers. At this time, the largest fragment on the cluster surface starts growing exponentially, as seen in Figure 1. The tendency of carbon fragments to localize has been observed also for larger nanoparticles. Ding and Bolton have found that the nucleation of carbon fragments takes place at areas where the iron is locally supersaturated with carbon.53 4.2.2. Fe55N4C65. In the following, the high-coverage model with 65 carbon atoms is discussed in order to provide comparison to the low-coverage model with 27 carbon atoms. Both models contain four nitrogen atoms. In the model with 65 carbon atoms, there are already three CN units. The CN molecules are formed in previous trajectories with lower carbon coverage through encounter of carbon and nitrogen monomers. No dinitrogen molecules are formed in the simulations. The C−N bond lengths in snapshots optimized at the DFTB (DFT) level are 118−119 (116−123) pm. The C−C bond length of a carbon dimer is 130−133 (131−135) pm at the DFTB (DFT) level. This can be compared to the bond lengths of CN and C2, which are 116 and 124 pm, respectively, as optimized at the SCC-DFTB level. As expected, the bonds of the adsorbed diatomic species are elongated due to the bonding interaction with the iron cluster. Dimers, trimers, and tetramers mostly occupy bridge sites. Pentamers and larger fragments induce a larger reorganization of the metal surface, modifying the surface such that the fragments are partly bound within the outermost iron layer of the particle, rather than adsorbing on top of the surface. The snapshot at 98 ps from the DFTB-MD trajectory of Fe55C65N4 has several of these fragments. See Figure 3. These larger fragments are rather immobile. 18541



Article

Figure 2. Snapshots from the 412 ps MD trajectory of Fe55C27N4: (a) 0 ps, (b) 97 ps, (c) 257 ps, (d) 307 ps, (e) 307 ps showing the almost empty part of the cluster, and (f) 407 ps.

the trajectory, a carbon trimer is formed from three carbon monomers. One of the added carbon atoms relaxes from an atop site and forms a bond to a nearby carbon atom at a hollow site. The amplitude of the C−C vibration in the dimer is high with bond lengths between 115 and 155 pm, indicating that the dimer is rather hot. The hot dimer forms a bond to a third carbon atom within 70 fs, or seven oscillations, forming a hot trimer. After temperation, the bond lengths in the formed trimer oscillate between 129 and 140 pm. The local heating caused by collisions of gaseous molecules with the surface may momentaneously induce faster dynamics. 4.3. Diffusion of Carbon and Nitrogen on the Iron Surface. The transport of carbon and nitrogen atoms on the iron cluster surface is partially governed by the thermal motion of the iron atoms. Especially when the adatom coverage is low, there is a large exchange of iron atoms between the layers of the iron cluster. On the other hand, carbon and nitrogen monomers are rather strongly bound to individual iron atoms on the surface. The nitrogen atoms are more strongly bound to the iron surface than the carbon atoms. As discussed in the previous sections, the Fe−N and Fe−C bond lengths depend on coordination number of the carbon and nitrogen atoms and also on the bonds between carbon atoms. Carbon or nitrogen monomers are most strongly bound to the irons. A rough estimate of the site-hopping frequency is obtained by plotting the atomic indexes of the iron atoms that are within 250 pm from a certain carbon or nitrogen molecule as a function of the time. The permanent exchange of a bonding iron atom to another is counted as a site hop. For carbon monomers, the time spent at each site is 35−70 ps, whereas nitrogen monomers change site every 40−70 ps. The hopping frequency for two-atom fragments is analyzed by plotting the neighbor iron atoms for one of the carbon

Figure 3. Snapshots from the DFTB-MD trajectory of Fe55C65N4, at t = 98 ps.

Figure 4 presents the amount of fragments of different sizes as a function of simulated time for the Fe55N4C65 system. Comparing Figure 4 with Figure 1, it is evident that the higher adatom coverage speeds up the forming of larger fragments on the nanoparticle surface considerably. With a high adatom coverage, carbon monomers are very short-lived and the size of fragments larger than tetramers grow fast. In the catalysis process, the collisions of precursor molecules with the catalyst particles brings heat to the system.54 Although the heat required for dissociation is not accounted explicitly for in our models, some heating is locally caused by the inserted adatoms relaxing from atop positions since the most stable positions for monomers are at hollow sites. The following example from the Fe55N4C65 simulation illustrates this. Early in 18542



Article

Figure 4. Growth of carbon fragments in the system with 65 carbon atoms and 4 nitrogen atoms on the surface of Fe55. (a) The number of carbon monomers, carbon dimers, carbon trimers, five-membered rings, and six-membered rings. (b) The number of atoms in fragments consisting of five or more atoms.

atoms in C2 and for the carbon atom in CN. CN molecules are much more mobile than nitrogen monomers and slightly more mobile than carbon dimers. The time between site hops is 6−14 ps for CN units and 10−22 ps for C2 units. Therefore, it is possible that nitrogen atoms are more easily incorporated into N-CNTs as CN. Since the adsorption site of trimers is not well-defined, the estimate about their mobility is based solely on inspection of the MD trajectories. Trimers are observed to move faster than monomers but slower than dimers. Tetramers and larger fragments are clearly less mobile than trimers. The cyanide units differ from carbon dimers on the nanoparticle surface. The carbon atom in CN is more strongly bound to the iron atoms while the nitrogen often is perpendicular to the particle surface. CN units therefore can reside for longer times on atop sites and also diffuse over iron atoms that are pulled up from the surface. Carbon dimers rarely move over iron atoms via the atop site but rather between iron atoms via bridge sites. Also as part of larger carbon fragments, dangling CN bonds point out of the surface facet plane and the fragment becomes more loosely bound to the iron particle and can consequently move on the surface. When a nitrogen atom becomes part of a carbon chain and nitrogen is not the terminal atom, the fragment is again more closely bound to the surface. In Figure 5, the effect of nitrogen as terminal atom on the one hand and as part of the carbon chain on the other hand is seen in the snapshot at 149 ps in the MD trajectory of 54 carbon atoms and 4 nitrogen atoms on Fe55. The weaker interaction between nitrogen-containing fragments and the cluster and the consequently increased motion of the fragment can increase the diffusion rate of the adatoms. Therefore, the CNT might nucleate faster on the iron particle when nitrogen is present. In Figure 6, the amount of monomers, carbon dimers, and CN molecules on the Fe55 cluster with different degree of carbon coverage is plotted as a function of time. Nitrogen atoms are strongly bound to deep sites of the nanoparticle surface. Carbon atoms are slightly more mobile and form dimers or join larger fragments. At low adatom coverage, as in the Fe55C27N4 model, all nitrogen atoms remain as monomers during the first 400 ps, whereas with 10 more carbon atoms, only one nitrogen monomer remained after 409 ps. With 54 carbon atoms on the surface, all nitrogen atoms are bound to a

Figure 5. Nitrogen atoms bound to carbon in different conformations. The dimers are at bridge and hollow sites, respectively, where they are able to rotate rather much. Mostly the dimers are aligned with both atoms rather near the metal atoms, as in the picture. In the larger carbon fragments, the terminal nitrogen atom is most of the time almost perpendicular to the surface, while the nitrogen atom that is bound to two carbon atoms as part of a chain does not affect the interaction of the fragment with the surface much since the terminal carbon atoms are bound to iron atoms. The snapshot is taken after 149 ps of molecular dynamics of the Fe55C54N4 model.

carbon atom as CN units or as part of larger fragments within 41 ps. On the other hand, when the carbon fragments grow larger and only few carbon monomers remain, as in the model with 65 carbon atoms, the dynamics becomes slower. Large fragments are not very mobile, as are not monomers. After 113 ps, there is still one nitrogen monomer and one carbon monomer in the Fe55C65N4 system. The predominant route to mobile nitrogen atoms is to form CN units from a carbon and a nitrogen monomer. These CN units are on several occasions then incorporated into larger fragments, which is seen as the decrease in the amount of CN molecules in Figure 6d. 18543



Article

Figure 6. Number of carbon monomers, nitrogen monomers, carbon dimers, and free CN molecules in the systems with 27, 37, 47, 54, and 65 carbon atoms and 4 nitrogen atoms on the surface of Fe55: (a) carbon monomers, (b) nitrogen monomersn (c) carbon dimers, and (d) CN molecules.

The growth of fragments five atoms or more is visualized in Figure 7. The nucleation of larger carbon fragments almost

above, was only found once in the simulated trajectories. In Figure 6c, the importance of dimer formation at the early stages of carbon nucleation is seen. Comparing Figures 6a and 6c in the time window 0−50 ps shows this. The model with 47 carbon atoms is an especially good example of dimer formation early in the trajectory. The carbon dimers are more mobile than carbon monomers, and therefore trimers is in many instances formed via the reaction C2 + C → C3, whereas longer chains are formed through reactions like Cn + C → Cn+1, or, predominantly, through Cn + C2 → Cn+2 and by adding two larger fragments. In the model with 65 carbon atoms, the adatom coverage is large, and there are already at the beginning of the trajectory larger carbon fragments present. Therefore, the amount of carbon dimers declines rapidly. The majority of the adsorbed carbon monomers are also within a short period of time fused to larger fragments. 4.4. Ring Formation. The formation of sp2-hybridized carbon networks made up of primarily five- and six-membered rings is an important step toward the CNT. The ring formation takes place when two conditions are fulfilled. A long enough chain with a branch is needed. On the other hand, the catalyst surface need to be somewhat rearranged in order to fit an adsorbed ring. In the present simulations, ring condensation is observed to take place in a branched side chain with as few as only five atoms, the minimum number needed for a ring. Five-membered rings are predominantly formed. This is in line with the pentagon-first principle observed previously.22,55

Figure 7. Number of atoms in fragments built up of five atoms or more in the systems with 27, 37, 47, 54, and 65 carbon atoms and 4 nitrogen atoms on the surface of Fe55. When several fragments are in the same system, several lines are drawn. The sudden disappearing of lines at the same moment as one fragment in the same system grows indicates two large fragments coalescing.

always require carbon dimers to form first. Instantaneous trimer formation from three monomers, as mentioned in an example 18544



Article

taken from a snapshot of the DFTB-MD simulation. Two slightly different starting structures were preoptimized at the DFTB level, and then MD simulations were started. In the first model, a nitrogen atom is within 1000 time steps moved into the CNT. It induces a defect in the tube, where the nitrogen atom is situated in between two seven-membered rings. Sumpter and co-workers11 found that nitrogen energetically prefers to be at two-coordinated sites or as dangling CN moieties in the carbon nanotube. In the present simulation, the nitrogen atom however remains stable throughout the whole simulation in a corner of two seven-membered rings and one five-membered ring and therefore three-coordinated. This can be seen in Figure 9. The first model described in the previous paragraph was simulated for 20 ps, after which 10 carbon atoms were added. The new model was simulated for a further 94 ps, as the first simulation was continued to reach a total of 112 ps. The tube itself does not grow during this short time. There is, however, a clear tendency of the carbon fragments to coalesce into a unified network that the CNT is part of. In the second simulation, a carbon fragment of 12 atoms is included in the carbon network during the simulation. The added fragment has one five-membered ring, but within 8 ps two ring condensations take place and the recently added fragment becomes a part of the network made up of sp2-hybridized carbon atoms. Subsequently, a CN unit is also bonded to the network. The nitrogen atom appears to repel the iron surface in the same way as observed previously in the model systems without a CNT, but the effect is less pronounced for the carbon network than what was observed for smaller fragments. The process is shown in Figure 10. To approach tube growth, 10 more carbon atoms were added to the above-mentioned capped model. Four different simulations were started, one with four nitrogen atoms as in the previous simulations, and three simulations with five, six, and seven nitrogen atoms, respectively. Also these models were allowed to grow after 10 000 steps by adding 10 carbon atoms. At most, there was thus 148 carbon atoms in the model. In the simulations with an increased amount of nitrogen atoms, the role of nitrogen is pronounced. The central observations on the role of nitrogen are summarized in the next section. 4.6. The Role of Nitrogen in Ring Formation. The formation of carbon rings described above follows in large the same patterns as previously observed in carbon-only DFTB simulations.22,23 The ring condensation process in nitrogencontaining fragments differs slightly from that in carbon-only

The attractive interaction between iron and carbon elongates the C−C bonds in the rings, enabling a slight bending of the ring, reducing ring strain. In Figure 8, the ring formation in the

Figure 8. Number of five- and six-membered rings in the simulated systems with 27, 37, 47, 54, and 65 carbon atoms and 4 nitrogen atoms on the surface of Fe55. All rings are carbon-only.

different model systems is shown as a function of time. As could be expected, the higher the adatom coverage, the faster is the ring formation. The time scale for ring formation in Figure 8 correlates with the size evolution of the largest fragments in Figure 7. The formation of carbon-only rings is not directly affected by the presence of nitrogen atoms, as long as the nitrogen atoms are not in the same fragment, but it follows the same features as previously observed in DFTB simulations.22,23 Also, ring formation via carbon diffusion deep in the surface22 is observed, as shown in the Supporting Information. The ring formation in nitrogen-containing fragments is discussed further below. The interaction between individual iron atoms and the carbon network can be very strong when the iron atom is strongly coordinated by carbon atoms. A special case is the formation of carbon-only porphyrin-like structures, as in Figures 11e−g. 4.5. Early Growth of Nitrogen-Doped SW-CNTs. To model the transport of carbon and nitrogen atoms to a carbon nanotube on the surface of an iron nanoparticle, a model was constructed where a short segment of a (9,0) nanotube was placed on top of Fe55C37N4. The nanocluster coordinates were

Figure 9. Snapshots from the DFTB-MD simulation of a growing N-CNT. (a−c) A CN unit has been bonded to the CNT and the nitrogen atom eventually is located at the corner of two seven-membered rings and one five-membered ring. The time elapsed during the illustrated process is 7.2 ps. 18545



Article

Figure 10. Snapshots from the DFTB-MD simulation of a growing N-CNT at indicated simulation times: (a, b) the addition of a 12-atom fragment to the CNT; (c, d) ring condensation; (e, f) CN unit added.

fragments. In the Fe55N4Cx, x = 27, 37, 47, 54, 65 model systems, no ring condensation with nitrogen involved was observed. Therefore, we increased the amount of nitrogen in the capped models discussed in the previous section and performed further DFTB-MD simulations. Some illustrative examples of nitrogen involved in ring condensation are summarized below. When a nitrogen atom is part of a branched chain, there is repulsion between the two branches that prevents ring formation. As discussed above, nitrogen-containing fragments are less bonded to the nanocluster surface than carbon-only fragments due to the CN bonds orienting away from the surface. This causes the nitrogen-containing fragments to be largely nonplanar. Increased sp2 hybridization in the chain induced by the formation of a ring makes also nitrogencontaining fragments more planar and thus aligned along the surface. Therefore, the formation of N-containing rings is promoted by the previous formation of another ring in the same fragment. An example of ring condensation in nitrogen-containing fragments is the formation of 6−6−5-ring fragment with N atom in the capped Fe55N6C148 model, which is shown in Figure 11. Addition of N-terminal NC2 fragment to a branched C-chain induces condensation of a four-membered ring, to which the nitrogen atom is connected directly. The cyclobutanyl ring is unstable and persists only for 0.6 ps, and 6.6 ps later a stable five-membered ring is formed. The five-membered ring induces sp2 hybridization in combination with favorable bond angles for a six-membered ring to form adjacent to the

cyclopentanyl ring. This enables the formation of a nitrogencontaining ring, as shown in Figures 11e,f. After a further 10 ps, a carbon side chain to the two-ring fragment binds to the nitrogen atom, closing up to a third ring. Thus, a three-ring fragment with a three-coordinated nitrogen atom is formed. This fragment is stable for at least an additional 90 ps throughout the MD trajectory. Another example of condensation of nitrogen-containing rings is shown in the snapshot series in Figure 12. The addition of a CN unit to the carbon chain increases the sp2 hybridization along the chain, as the more pronounced zigzag shape of the chain in Figure 12c as compared to Figure 12b shows. This change in topology is followed by condensation of a fivemembered ring within 3.4 ps. On the basis of the previous example, one could expect at least somewhat increased planarity of the whole fragment as a consequence of the ring formation, but as seen in Figure 12f, the terminal nitrogen stays out of the surface. The increased sp2 hybridization in the fragment is therefore too local to align longer side chains with terminal nitrogen atoms along the surface in the same fashion as the side chain with a −C−N−C− fraction. The examples above show that nitrogen atoms indeed slow down the formation of rings in the fragments on the surface of the iron nanoparticle. This might have implications for the nucleation rate of the N-CNTs, slowing down the process. 4.7. Structure of the Fe55 Particle. The icosahedral Fe55 is built up of two shells with 12 and 42 Fe atoms around one central atom. In all the MD trajectories, there is exchange of iron atoms between all three layers, while the carbon and 18546



Article

Figure 11. Snapshots from the DFTB-MD simulation of a growing N-CNT at indicated simulation times. The model is Fe55N6C148. (a−g) Formation of rings in a nitrogen-containing fragment. The nitrogen-containing ring is not formed until an adjacent stable carbon-only ring is formed.

Figure 12. Snapshots from the DFTB-MD simulation of a growing N-CNT at indicated simulation times. The model is Fe55N4C148. (a−g) Formation of rings in a nitrogen-containing fragment. For enhanced visibility, only the CN unit coupling to the CNT and the terminal nitrogen atom are represented by spheres.

retained, possibly due to the large portion of surface atoms. As the carbon coverage is increased, the exchange of iron atoms between the layers is decreased. Carbon and nitrogen atoms

nitrogen atoms remain bound on top of or within the surface layer. Thus, at the simulated temperature of 1000 K the Fe55 particle is very flexible. However, the shell structure is largely 18547



Article

sp2 hybridization due to branching of chains promotes the condensation of nitrogen-containing rings. The present results show that the quenching effect of nitrogen on the growth of N-CNTs cannot be completely explained by the diffusion processes on the surface of the catalyst particle. However, the formation of rings is at least partly inhibited by the presence of nitrogen, and this might be a factor slowing down the formation of N-CNTs.

and larger clusters are not very prone to diffuse on the iron surface, and therefore the surface iron atoms are more bound. The strong interaction between the adsorbed atoms and the nanocatalyst also induces a considerable rearrangement of the surface iron atoms, destroying the original high symmetry of the icosahedral Fe55. The surface of an active catalyst iron nanoparticle has a large variety of topologies, and the overall topology of the surface changes constantly. If the dissociation energy of carbon and nitrogen precursors depends strongly upon the surface topology, as preliminary calculations show,33 it is likely that low-barrier dissociation sites will be available often enough to enable an effective feed of building material from the carbide and nitride phase to the nanotube. The surface of the iron particle is easily deformed by the adsorbed atoms and fragments. It would be expected that the diffusion of carbon and nitrogen into the subsurface layer of the nanoparticle increases as more carbon atoms are adsorbed, since the barrier for diffusion is lower on more rough surfaces than on closed-packed ones.56 On the other hand, the iron atoms are partly immobilized due to the bonds to carbon and nitrogen atoms, and this reduces the transport of iron through the layers as the carbon coverage is increased.

■

ASSOCIATED CONTENT

* Supporting Information S

Full refs 13 and 44; brief characteristics of the MD simulations at the DFT level; snapshots showing ring formation following carbon addition from deep in the surface. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: kari.laasonen@aalto.fi. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Marko Melander, who provided data from his M.Sc. thesis regarding the dissociation energy of CO on Fe78. Toma Susi is acknowledged for valuable discussions regarding experimental issues. The Academy of Finland is acknowledged through the project 140115. Ample computing resources were provided by CSC IT Center for Science.

5. CONCLUSIONS We report molecular dynamics simulations at the DFTB level on the dynamics of carbon and nitrogen atoms on the surface of an iron nanoparticle. The features of the dynamics are qualitatively confirmed at the DFT level. The formation of larger carbon fragments almost always takes the route via C2 dimer formation. The carbon dimers are rather mobile, as are also the trimers and tetramers. Pentamers and larger fragments as well as monomers are less mobile. Therefore, the small fragments are the key ingredients in carbon nanotube precursor formation on the surface of the iron nanocatalyst. As the carbon fragments become large enough, they grow exponentially if there are enough carbon monomers and dimers available on the particle. At the same time, the amount of five- and six-membered rings increases rather fast. Since the carbon-diffusion driven fragment formation takes place on a picosecond time scale, it is likely that adsorption sites with a low enough barrier for CO dissociation are most of the time available on the nanocluster. The nitrogen atoms are less mobile and more strongly bound to the iron surface than the carbon atoms. On the other hand, CN moieties are slightly more mobile than carbon dimers. Carbon dimers are prone to bind to each other and to larger carbon fragments, whereas the CN molecules more rarely are attached to carbon structures. When nitrogen atoms are part of larger carbon fragments, the mobility of the fragment is increased. The tight-binding molecular dynamics simulations thereby indicate that nitrogen might increase the formation speed of early linear structures. However, ring condensation in nitrogen-containing fragments is slower than in carbon-only fragments. On the one hand, there is repulsion between nitrogen-containing branches and carbon-only parts of the fragment. On the other hand, the tendency of nitrogen-containing parts to be oriented out of the cluster surface reduces the planarity. Therefore, nitrogencontaining rings are only formed subsequent to the formation of a carbon-only ring in the same fragment. The first ring condensation induces planarity and enhances the sp2 hybridization, thereby driving further ring condensation. Also, the increased

■

REFERENCES

(1) Iijima, S. Nature 1991, 354, 56−58. (2) Ma, Y.; Wang, B.; Wu, Y.; Huang, Y.; Chen, Y. Carbon 2011, 49, 4098−4110. (3) Zhu, Z.; Jiang, H.; Susi, T.; Nasibulin, A. G.; Kauppinen, E. I. J. Am. Chem. Soc. 2011, 133, 1224−1227. (4) Saito, Y. Carbon 1995, 33, 979−988. (5) Harris, P. J. F. Carbon 2007, 45, 229−239. (6) Yi, J.; Bernholc, J. Phys. Rev. B 1993, 47, 1708−1711. (7) Stephan, O.; Ajayan, P. M.; Colliex, C.; Redlich, P.; Lambert, J. M.; Bernier, P.; Lefin, P. Science 1994, 266, 1683−1685. (8) Yudasaka, M.; Kikuchi, R.; Ohki, Y.; Yoshimura, S. Carbon 1997, 35, 195−201. (9) Villalpando-Paez, F.; Zamudio, A.; Elias, A. L.; Son, H.; Barros, E. B.; Chou, S. G.; Kin, Y. A.; Muramatsu, H.; Hayashi, T.; Kong, J.; Terrones, H.; Dresselhaus, G. Chem. Phys. Lett. 2006, 424, 345−352. (10) Ayala, P.; Arenal, R.; Rümmeli, M.; Rubio, A.; Pichler, T. Carbon 2010, 48, 575−586. (11) Sumpter, B. G.; Huang, J.; Meunier, V.; Romo-Herrera, J. M.; Cruz-Silva, E.; Terrones, H.; Terrones, M. Int. J. Quantum Chem. 2009, 109, 97−118. (12) Sumpter, B. G.; Meunier, V.; Romo-Herrera, J. M.; Cruz-Silva, E.; Cullen, D. A.; Terrones, H.; Smith, D. J.; Terrones, M. ACS Nano 2007, 1, 369−375. (13) Susi, T.; et al. Chem. Mater. 2011, 23, 2201−2208. (14) Kang, H. S.; Jeong, S. Phys. Rev. B 2004, 70, 233411:1−4. (15) Lin, H.; Arenal, R.; Enoux-Vedrenne, S.; Stephan, O.; Loiseau, A. J. Phys. Chem. C 2009, 113, 9509−9511. (16) Deck, C. P.; Vecchio, K. Carbon 2006, 44, 267−275. (17) Pérez-Cabero, M.; Taboada, J. B.; Guerro-Ruiz, A.; Overweg, A. R.; Rodríguez-Ramos, I. Phys. Chem. Chem. Phys. 2006, 8, 1230−1235. (18) Anisimov, A. S.; Nasibulin, A. G.; Jiang, H.; Launiois, P.; Cambedouzou, J.; Shandakov, A. D.; Kauppinen, E. I. Carbon 2010, 48, 380−388. (19) Kim, H.; Sigmund, W. Carbon 2005, 43, 1743−1748. 18548



Article

(20) Yoshida, H.; Takeda, S.; Uchiyama, T.; Kohno, H.; Homma, Y. Nano Lett. 2008, 8, 2082−2086. (21) Hofmann, S.; Blume, R.; Wirth, C. T.; Cantoro, M.; Sharma, R.; Ducari, C.; Hävecker, M.; Zafeiratos, S.; Schnoerch, P.; Oestereich, A.; Teschner, D.; Albrecht, M.; Knop-Gericke, A.; Schlögl, R.; Robertson, J. J. Phys. Chem. C 2009, 113, 1648−1656. (22) Ohta, Y.; Okamoto, Y.; Page, A. J.; Irle, S.; Morokuma, K. ACS Nano 2009, 3, 3413−3420. (23) Page, A. J.; Minami, S.; Ohta, Y.; Irle, S.; Morokuma, K. Carbon 2010, 48, 3014−3026. (24) Page, A. J.; Yamane, H.; Ohta, Y.; Irle, S.; Morokuma, K. J. Am. Chem. Soc. 2010, 132, 15699−16707. (25) Fan, X.; Buczko, R.; Geohegan, D. B.; Howe, J. Y.; Pantelides, S. T.; Pennycook, S. J. Phys. Rev. Lett. 2003, 90, 145501:1−4. (26) Raty, J.-Y.; Gygi, F.; Galli, G. Phys. Rev. Lett. 2005, 95, 096103:1−4. (27) Ding, F.; Bolton, K.; Rosén, A. J. Phys. Chem. B 2004, 108, 17369−17377. (28) Ding, F.; Rosén, A.; Bolton, K. Carbon 2005, 43, 2215−2217. (29) Lanzani, G.; Laasonen, K. Int. J. Hydrogen Energy 2010, 35, 6571−6577. (30) Nxumalo, E. N.; Letsoalo, P. J.; Cele, L. M.; Coville, N. J. J. Organomet. Chem. 2010, 695, 2596−2602. (31) Susi, T.; Lanzani, G.; Nasibulin, A. G.; Ayala, P.; Jiang, T.; Bligaard, T.; Laasonen, K.; Kauppinen, E. I. Phys. Chem. Chem. Phys. 2011, 13, 11303−11307. (32) Lanzani, G.; Susi, T.; Ayala, P.; Jiang, T.; Nasibulin, A. G.; Bligaard, T.; Pichler, T.; Laasonen, K.; Kauppinen, E. I. Phys. Status Solidi B 2010, 247, 2708−2712. (33) Melander, M. Private communication, M.Sc. thesis 2012, Aalto University School of Chemical Technology. (34) Zhang, Q.; Han, B.; Li, J. X.; Hoffman, J.; Lin, M.; DerecskeiKovacs, A.; Cheng, H. J. Phys. Chem. C 2011, 115, 12068−12076. (35) Nasibulin, A. G.; Pikhitsa, P. V.; Choi, M.; Kauppinen, E. I. Phys. Status Solidi B 2006, 243, 3095−3100. (36) Porezag, D.; Frauenheim, T.; Köhler, T.; Seifert, G.; Kaschner, R. Phys. Rev. B 1995, 51, 12947. (37) Seifert, G.; Porezag, D.; Frauenheim, T. Int. J. Quantum Chem. 1996, 58, 185−192. (38) Frauenheim, T.; Seifert, G.; Elstner, M.; Niehaus, T.; Köhler, C.; Amkreutz, M.; Sternberg, M.; Hajnal, Z.; Di Carlo, A.; Suhai, S. J. Phys.: Condens. Matter 2002, 14, 3015−3047. (39) Elstner, M.; Porezag, D.; Jungnickel, G; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Phys. Rev. B: Condens. Matter 1998, 58, 7260−7268. (40) http://www.dftb.org. (41) Zheng, G.; Witek, H. A.; Bobadova-Parvanova, P.; Irle, S.; Musaev, D. G.; Prabhakar, R.; Morokuma, K.; Lundberg, M.; Elstner, M.; Kohler, C.; Frauenheim, T. J. J. Chem. Theory Comput. 2007, 3, 1349−1367. (42) http://www.dftb-plus.info/home/. (43) Mortensen, J. J.; Hansen, L. B.; Jacobsen, K. W. Phys. Rev. B 2005, 71, 035109:1−11. (44) Enkovaara, J.; et al. J. Phys.: Condens. Matter 2010, 22, 253202. (45) Bahn, S. R.; Jacobsen, K. W. Comput. Sci. Eng. 2002, 4, 56−66. (46) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (47) Elliot, J. A.; Shibuta, Y.; Wales, D. J. Philos. Mag. 2009, 89, 3311−3332. (48) http://www-wales.ch.cam.ac.uk/wales/CCD/FS_Fe/iron_fs. html. (49) http://gabedit.sourceforge.net/. (50) Allouche, A. R. J. Comput. Chem. 2011, 32, 174−182. (51) Susi, T.; Zhu, Z.; Ruiz-Soria, G.; Arenal, R.; Ayala, P.; Nasibulin, A. G.; Lin, H.; Jiang, H.; Stephan, O.; Pichler, T.; Loiseau, A.; Kauppinen, E. I. Phys. Status Solidi B 2010, 247, 2726−2729. (52) Lyon, J. T.; Gruene, P.; Fielicke, A.; Meijer, G.; Rayner, D. M. J. Chem. Phys. 2009, 131, 184706:1−7. (53) Ding, F.; Bolton, K. Nanotechnology 2006, 17, 543−548.

(54) Lanzani, G.; Nasibulin, A. G.; Laasonen, K.; Kauppinen, E. I. Nano Res. 2009, 2, 660−670. (55) Wang, Y.; Page, A. J.; Nishimoto, Y.; Qian, H. J.; Morokuma, K.; Irle, S. J. Am. Chem. Soc. 2011, 133, 18837−18842. (56) Riikonen, S.; Halonen, L. Phys. Rev. B 2011, 83, 235423:1−5.

18549


Initial Stages of Growth of Nitrogen-Doped Single ... - ACS Publications

Recommend Documents