TiN Decoration of Single-Wall Carbon Nanotubes and Graphene by

ARTICLE pubs.acs.org/JPCC

TiN Decoration of Single-Wall Carbon Nanotubes and Graphene by Density Functional Theory Computations M. A. Gialampouki and Ch. E. Lekka* Department of Materials Science and Engineering, University of Ioannina, Ioannina, 45110, Greece ABSTRACT: Ti nanostructures on Single-Wall Carbon Nanotubes (SWCNTs) have attracted considerable attention due to their potential applications in electronic nanodevices and molecular adsorption. We report on Density Functional Theory (DFT) results referring to TiN (N = 1, 2, 3, 7, 13) supported on SWCNTs and graphene. Two new equivalent positions emerged that trisect the line joining the hexagon normal to the tube’s axis sides (TSH). These sites accommodate the dimers and trimers in compact linear and 2D triangular forms, respectively, and the Ti7 and Ti13 in 3D conformations. Ti adsorbates introduce new electronic states close to and at the Fermi level. Despite the significant charge transfer from adsorbates to substrates, these otherwise reduced TiN induce substantial charge screening in their surrounding substrate’s atoms and appear eventually as charged locations. These findings enlighten the early stages of Ti deposition, predict possible active sites, and may be of use for the design of metalcarbon coatings for applications in catalysis and nanoelectronics.

1. INTRODUCTION The combinations of Ti nanostructures with Carbon Nanotubes (CNTs) have attracted considerable attention due to the multiplicity of the potential technological applications of the resulting systems. Ti ultrathin and uniform films (thickness ∼1 nm) can be formed on Single-Wall Carbon Nanotubes (SWCNTs), manifesting unique electronic properties for applications in electronic nanodevices.1,2 In addition, these Ti-film/ CNT systems have been proved as efficient buffer layers for the formation Pt or Au nanowires.15 A theoretical study correlated these findings with the stability of the icosahedral Ti13 cluster (3D) on (5,5) SWCNT and the aggregation and wetting of the SWCNT upon further Ti13 cluster deposition.6 The situation becomes richer when combinations of smaller objects are involved. Excellent functionalities, e.g., in catalysis, gas sensing, or hydrogen storage, were found, depending on the size and the morphology of the Ti nanoarchitectures on carbon surfaces. Indeed, planar (2D), linear (1D), or sparsely distributed (0D) Ti, mainly studied on fullerenes, (8,0) SWCNT, and graphene, are predicted to have excellent molecular adsorption properties, thus being promising for hydrogen storage711 and CO sensor12 applications, while the 3D clusters were suggested to reduce the system’s hydrogen adsorption ability.10,11 The critical cluster size (Nc e 5 atoms) that switches the 3D conformation toward 2D was first theoretically introduced for TiN (N = 25, 13) adsorption on fullerenes C6010 and for Ti3 or Ti7 deposition on (10,0)-C160,13 as well as for Ti4 on (5,5) and (8,0) SWCNTs14 and TiN (N = 24) on graphene.15 However, in this latter case, which exhibits several potential applications, like in hydrogen storage, electrical charge storage in ultracapacitor devices, or as electromechanical resonators and transistors,1620 these studies are limited to Ti adatom depositions,8,9,2124 the properties of r 2011 American Chemical Society

TiN (N e 4) nanoclusters being restricted only to energetic and structural considerations.7,15 The present work focuses on the structural and electronic properties of TiN (N = 1, 2, 3, 7, 13) deposited on two representative SWCNT cases, one metallic (4,0) and one semiconducting (8,0). The aim of the study is to uncover the energetically favored configurations and the corresponding TiN/ CNT bonding characteristics and, in conjunction with the evaluation of possible charge transfer between the metal and the CNTs, to predict potential active sites. In addition, we also address the TiN/graphene case, a new system with multifunctional potential applications, which can be considered as a largediameter SWCNT with zero energy gap semiconductor.

2. THEORETICAL METHODS AND COMPUTATIONAL DETAILS We performed the standard KohnSham self-consistent Density Functional Theory method in the local density approximation using the SIESTA code.25,26 Core electrons were replaced by norm-conserving pseudopotentials in the fully nonlocal KleinmanBylander form, and the basis set was a linear combination of numerical atomic orbitals constructed from the eigenstates of the atomic pseudopotentials.2529 In the Ti case, the 3s and 3p electrons were explicitly included in the computations.28,29 An auxiliary real space grid equivalent to a plane-wave cutoff of 100 Ry was used. The Zig-Zag (4,0) and (8,0) SWCNT with 32 (0.335 nm) and 64 (0.639 nm) atoms (diameter), respectively, were placed in a Received: March 6, 2011 Revised: June 3, 2011 Published: June 30, 2011 15172

dx.doi.org/10.1021/jp202130g | J. Phys. Chem. C 2011, 115, 15172–15181

The Journal of Physical Chemistry C

ARTICLE

tetragonal supercell with periodic boundary conditions along the tube axis. To avoid the adatomadatom interactions, the tube axis height (0.852 nm) was set twice as large as the onedimensional tube’s lattice constant, while the other two dimensions were fixed at 4.260 nm. In the graphene case, the periodic boundary conditions were applied in two directions to mimic an infinite slab with 120 atoms, while the Brillouin zone k-grid cutoff was set to 2 nm. For the Ti deposition case, we treated the adatom, two planar (dimer and trimer) and two 3D configurations, the Ti7 bipyramidal decahedral and Ti13 icosahedral clusters, which were theoretically found to be stable magic clusters.3035 Aiming to explore any size effect possibilities, in the larger clusters’ cases (Ti7 and Ti13), we performed calculations using four different tubes having lengths of 0.852, 1.278, 1.704, and 2.556 nm. We found that with the exception of the smallest tube’s case (0.852 nm) the obtained results are practically identical. For the geometry optimization, the structure was considered fully relaxed when the magnitude of forces on the atoms was smaller than 0.02 eV/Å. The binding energy (Eb) was calculated using the following expression Eb ¼

ðESWCNT þ ETiN Þ ETiN =SWCNT N

ð1Þ

where ESWCNT is the total energy of the pure SWCNT (or graphene); ETiN is the free-standing TiN cluster’s total energy (N = 1, 2, 3, 7, 13); and ETiN/SWCNT is the total energy of the TiN/SWCNT (or TiN/ graphene) system.

Figure 1. Energy maps of the Ti adatom: (a) (4,0), (b) (8,0), and (c) graphene. Small (yellow) and big (blue) spheres stand for the C and Ti atoms, respectively. The color scale corresponds to the energy difference from the equilibrium adatom position whose value was set to zero. TSH, H, A, Z, S, and B locations are also shown. Schematic representation of the Ti adatom energetically favored positions on: (d) (4,0), (e) (8,0), and (f) graphene. Yellow and blue atoms stand for the C and Ti atoms, respectively.

3. RESULTS AND DISCUSSION 3.1. Ti Adatom, Dimer, and Trimer on SWCNT and Graphene. 3.1.1. Geometrical Aspects and Energetic Considerations.

Starting from the Ti adatom cases, we placed consecutively a Ti adatom on a 2D grid in the azimuthal angles (j) and the tube axis. With the adatom free to relax in its radial coordinate (F), we relaxed all the systems’ atoms by means of total energy minimization. The resulting contour energy maps referring to Ti on (4,0) and (8,0) SWCNTs are depicted in Figure 1a and Figure 1b, respectively. In the graphene case, Figure 1c, we applied the same approach but in Cartesian coordinates. The minimum energy value was set to zero, while the color scale indicates (going from blue to red) the gradual energetic increase. In Figure 1a, which refers to the (4,0) CNT, we can clearly see the existence of two equivalent adatom positions that are axially symmetric to the tube’s axis, called TriSectional Hexagon (TSH) sites hereafter. These sites are separated by a barrier of 0.23 eV, thus appearing as a dumbbell position. This adatom position has been also observed in the case of Cu on the Cu3Au(110)3638 and found to play an important role in the adatom’s diffusion and Cu epitaxial growth on this surface.3841 In the same figures, we provide also the sites suggested in ref 21, i.e., above the zigzag (Z-site) and axial (A-site) CC bonds for the SWCNTs, the bridge (B-site) on graphene, as well as the one on top of a C atom (S-site). Concerning the Ti on (4,0), it is visible in Figure 1a that the Z-site is located at a local minimum that differs from the TSH by 0.95 eV, followed by the S-site, with an energy difference of 1.33 eV, and the A-site, with 1.42 eV. We have to point out here that these values have to be treated only as indicative energy barriers of possible diffusion paths of the Ti adatom, within the quasiharmonic approximation. The determination of the true reaction path may be more complex, not to mention phononic contributions, requiring the assessment of the transition state (e.g., by

means of the Nudged Band minimization procedure42), which is very time consuming and beyond the scope of the present study that focuses on the structural and electronic properties of these systems. Nevertheless, based on these values, we can anticipate as plausible hopping mechanisms the one joining the two axially symmetric TSH sites of the same hexagon through the hexagon’s center (H-site) (TSHHTSH) requiring 0.23 eV, followed by those defined from one TSH site to the next hexagon’s TSH site through the Z-site (0.95 eV) or the S-site (1.33 eV). Finally the less possible diffusion mechanism appears to be the one that crosses the A position (1.42 eV). Turning to the case of the (8,0) SWCNT, we found that the H position is the preferential one, in agreement with a previous theoretical study21 (Figure 1b). The Z-site is the next energetically favored site, rendering the simple hopping mechanism between two consecutively H positions through the Z position as the most probable one, requiring 1.02 eV, followed by the hopping over the S-site (1.11 eV) and the A-site (1.29 eV), similarly to the adatom’s behavior on the (4,0) tube. In addition, it is worth noting that although these sites are less favored they, nevertheless, play an important role upon additional Ti atom deposition, as will be discussed later in this work. Finally, in the case of Ti adatom on graphene (Figure 1c), as it would be anticipated by geometrical considerations, the H-site is the energetically favored one, in agreement with other ab initio calculations.3,7,9,15,2224 Due to the hexagonal symmetry, the next lower-energy positions were found to be the B- and S-sites, exhibiting differences from the H-site of 1.11 and 1.02 eV, respectively, rendering the B- and S-sites practically equiprobable, in line with other theoretical studies.3,7,15,22,23 Accordingly, 15173

dx.doi.org/10.1021/jp202130g |J. Phys. Chem. C 2011, 115, 15172–15181


ARTICLE

Figure 2. Binding energy of the Ti adatom on (n,0) and graphene (blue diamonds) as a function of SWCNT’s size and graphene. Red square (2.2 eV on (8,0)) and purple cross (2.25 eV on (10,0)-C160) stand for refs 21 and 13. The references for Ti on graphene stand for black transparent diamond (2.7 eV),3 triangle (2.64 eV),15 star (2.17 eV),9 square (1.869 eV),22 crosses (1.41 eV, 1.62 eV),23 circle (1.51 eV),24 and (1.27 eV).7

higher diffusivity of Ti on graphene is expected, compared to the SWCNT cases, via simple hopping mechanisms, although due to these energy barriers significant localization of Ti on the carbon surfaces would be mainly expected at room temperature. Nevertheless, these results could be useful for the studies on Ti wetting or nucleation on carbon surfaces. Another interesting piece of information that we obtained from these calculations concerns the TiC bond lengths. We found that, due to the existence of the TSH position, the Ti adatom on the (4,0) forms two Ticarbon pairs with different TiC bond lengths: a short one (ds = 1.92 Å) corresponding to the closest atoms and a longer one (dl = 2.13 Å) (Figure 1d). Interestingly, albeit the uniqueness of the adatom site for the large SWCNTs, H-site, e.g., in the case of (8,0), there exist again two different TiC bonds lengths, one along the tube axis with length of 2.08 Å, to be compared with the value of 2.2 Å21 from previous calculation, and another one, which is longer, around 2.28 Å (Figure 1e). Finally, when the Ti adatom is relaxed on the H-site of graphene, the number of TiC bonds increases to six (Figure 1f), with bond length of 2.22 Å, in line with the available theoretical data 2.24,15 2.33,21 and 2.34 Å.24 Stimulated from the finding of the TSH site, we repeated the same procedure seeking the relaxed adatom positions also for the other cases of (n,0) SWCNTs (3 e n e 10). We found that on graphene and on the large SWCNTs (n g 6) the equilibrium adatom position is located on top of the center of the carbon hexagon (H-site) (Figure 2) in agreement with other theoretical studies. On the contrary, when deposited on the n < 6 SWCNTs, we found that the TSH sites are the equilibrium adatom positions. In addition, it came out that the Ti adatom’s binding energy decreases rapidly with n, reaching a plateau value of about 2 eV for n g 8 (Figure 2). This behavior is attributed to the curvature effect,7 the graphene thus appearing as a limiting case that is expected to be naturally located at the tail of the SWCNTs behavior. We note that the bond lengths correlate with the binding energies, the strong bonds corresponding to shorter TiC bond lengths. Aiming to obtain insight into the very early stages of coating, we studied the cases of dimer and trimer depositions on the same systems. The procedure we followed consisted of putting initially

Figure 3. Schematic representation of Ti2 and Ti3 on (4,0), (8,0), and graphene. Insets depict the less favored configurations. Small (yellow) and big (blue) spheres stand for the C and Ti atoms, respectively.

the first dimer’s atom at the equilibrium adatom position and scanning the second’s atom locations over a grid of the possible sites, all the system’s atoms being free to relax (including the first dimer’s atom). Figure 3a depicts a schematic representation of the equilibrated dimer on the (4,0) SWCNT case. We can see that the dimer’s Ti atoms relax on two consecutive TSH sites of the same hexagon (binding energy of 4.59 eV/atom), filling both dumbbell sites (Figure 3a), similarly to the case of the Cu dimer on the Cu3Au(110) surface.3638 We also found an alternative dimer location with the two Ti atoms residing on TSH sites that belong in two adjacent hexagons (4.52 eV/atom). In addition, a less stable configuration (4.14 eV/atom) also exists, with the two Ti atoms located on the HH sites over a Z position. These results are in line with the adatom energy map, in which the distance of TSHTSH over the A position is smaller than the one through the Z-site, and therefore, although less favored, the first conformation is preferred. In the same picture, we also note the TiC bond distances, ds and dl. It comes out that the short (ds) and long (dl) TiC bond lengths are 2.10 and 2.23 Å, respectively. This means that compared to the single adatom case a small change occurs in the dl distance, while the ds is enhanced by as much as 8%. Moreover, we found that the bond length between the Ti atoms is 2.29 Å, a value that is significantly larger than that from the free-standing case, which we evaluated at 1.91 Å, in excellent agreement with the experimental 1.91,11 1.94, and43 1.95 Å44 data. Interestingly, the deposition of a dimer on the (8,0) SWCNT alters significantly the predictions of the adatom energy map, according to which there was only one adatom site (H-site), permitting the accommodation of both dimer’s Ti atoms within a hexagon, thus occupying two TSH sites (Figure 3b). It is worth noting that this dimer’s accommodation induces significant local 15174


The Journal of Physical Chemistry C distortion in the (8,0) SWCNT that loses its circular view, appearing elongated and of ellipsoid-like shape close to the dimer area. The corresponding binding energy is 2.91 eV/atom followed (similarly to the (4,0) case) by another TSHTSH position (2.86 eV/atom) and a last one having Ti locations close to the HH (2.41 eV/atom) positions through the Z-site (inset in Figure 3b). The TiTi and TiC bond distances, at the energetically favored site, are 2.17 and 2.15 Å, respectively, while these values are smaller compared to the (4,0) case due to the tube’s curvature and to the dimer’s atoms tendency in residing at the TSH positions of the same hexagon. As could be anticipated, the dimer on graphene relaxes on two consecutive H positions, with a binding energy of 2.66 eV/atom. The energy gain for Ti2 formation compared to two isolated Ti adatoms is found 1.73 eV, in line with previous calculations of 1.32 eV of Ti2/graphene7 and 1.29 eV of Ti2/C60.11 The TiTi and TiC bond lengths are largely greater, 2.34 and 2.23 Å, respectively. Finally, it is worth noting that in all cases the dimer is more tightly bound on the (4,0), followed by the (8,0) case and graphene, in line with the Ti adatom’s behavior. In the trimer case on the (4,0), the Ti atoms relax mainly on the TSH sites, forming an equilateral triangle with a side of 2.52 Å (Figure 3d). This value is to be compared with the free-standing Ti3 case (2.295 Å) and with the literature values of 2.28 Å33 and 2.418 Å.30 The TiC bond lengths are ds = 2.11 Å and dl = 2.21 Å, both larger than in the adatom and dimer cases, while the corresponding binding energy is 3.65 eV/atom. In addition, we found an alternative trimer location corresponding to the one in which the three Ti atoms reside on three H-sites (3.51 eV/atom). On top of the (8,0), besides the apparent location of the trimer at the three consecutive H-sites, we found another conformation in which two of the Ti atoms are located at TSH sites and the third one is on top of a carbon atom (S-site) (Figure 3e). It turns out that this site is energetically favored, 2.48 eV/atom, compared to 2.32 eV/atom of the first case, while the triangle is distorted exhibiting a difference between its TiTi bond length (from 2.40 to 2.47 Å) as well as in its TiC bonds (average value is 2.16 Å), in line with the results of Ti3 on (10,0)-C160.13 The case of the Ti trimer on the highly symmetric graphene is illustrated in Figure 3f. As it can be seen, the trimer is accommodated on three neighboring hexagons forming a perfect triangle, in line with previous calculations.15 The binding energy is 2.39 eV/atom, while the TiTi and TiC bond distances are 2.44 and 2.24 Å, respectively. We also evaluated the linear chain (1D) conformation, and we found that this is not energetically favored, compared to the triangular one (2D) (3.40, 1.97, and 1.81 eV for the deposition cases of the (4,0), (8,0), and graphene, respectively). Summarizing, we found that the Ti adsorption sites depend on the SWCNT’s curvature. In the cases of SWCNTs with n < 6, the energetically favored position is the TSH, while for the bigger SWCNTs and graphene, the H-site is preferred. From the calculated energy maps of the equilibrium adatom sites, it came out that the energy difference between different adatom sites is inversely proportional to the tube’s curvature, becoming less than 1 eV for the larger SWCNTs and graphene, suggesting that adatom diffusion could be possible at finite temperatures. This new Ti adatom TSH position on (4,0), which is also found in the cases of Ti2 and Ti3 on both (4,0) and (8,0) SWCNTs, results in energy gain against clustering conformations on the H-sites. Finally, on all substrates, the trimer prefers the 2D triangular conformation rather than the linear one.

ARTICLE

Figure 4. Electronic density of states: (a13) pure carbon substrates, (b13) Ti adatom, (c13) Ti dimer, and (d13)Ti trimer on (4,0), (8,0), and graphene, respectively. Dotted, solid, and dashed lines correspond to the total, Ti3d, and C2p electronic contributions. The Fermi level has been set to zero energy.

3.1.2. Electronic Structure. Figure 4 depicts the electronic density of states (EDOS) of (4,0), (8,0), and graphene cases. The first row corresponds to the pure carbon substrate cases, while the subsequent rows correspond to the total, the C-2p, and the Ti-3d projected EDOSs in the presence of a Ti adatom (second row), dimer (third row), and trimer (fourth row), respectively. From Figure 4a1, we conclude that the (4,0) exhibits metallic features mainly due to an enhanced and broad peak around 0.3 eV. Upon Ti addition, the metallic character of (4,0) persists, while the enhanced peak is altered; we note the hybridization between C2pTi3d electrons at the Fermi level (Figures 4(b1, c1, d1)) and at the energy area below 0.3 eV and up to 1.5 eV, which is also filled. From the projected EDOS referring to C, we find almost equivalent spin contributions, while the major contributions are located around 1.0 eV (Figures 4a1d1). Similar behavior is found in the trimer case at the Fermi level, the occupation of Ti-3d electrons is enhanced for both spin populations (Figure 4d1). The symmetric behavior of the spin majority and spin minority states is attributed to the symmetry of the trimer equilateral triangle, while it is worth noting that when the dimer relaxes close to the TSH sites belonging to neighboring hexagons (inset in Figure 3a) (less favored case having 0.5 eV energy difference from the TSH sites of the same hexagon) it exhibits strong spin updown differentiations (total magnetic moment M = 1.94 μB). Figure 4a2 refers to the (8,0) SWCNT; we can see that upon Ti, Ti2, or Ti3 deposition the tube’s semiconducting character is altered. In particular, in the Ti adatom case, this is due to the introduction of new Ti3d peaks with spin majority states close to the Fermi level, in which the C atoms also participate, while the spin minority states at the Fermi level are due only to the C substrate (Figure 4b2). This is in agreement with previous band structure calculations21 suggesting that the (8,0) is metalized upon Ti adatom adsorption. In the dimer case (Figure 4c2), Ti2 introduces new Ti3d spin minority states at the Fermi level, while less pronounced new Ti3d spin majority states are manifested 15175



Figure 5. Electronic wave functions close to the Fermi level: (a) pure (4,0) and Ti on (b) (4,0), (c) (8,0), and (d) graphene. Small (yellow) and big (blue) spheres stand for the C and Ti atoms, respectively.

around 0.3 eV (Figure 4c2). In the case of Ti2, the spin minoritymajority states differences (yielding M = 0.37 μB) are restricted to energies below 0.5 eV, while these differences are enhanced significantly (M = 1.70 μB) when the dimer is accommodated at the H-sites. As far as the trimer is concerned (Figure 4d2), the filling of the (8,0) SWCNT’s energy gap is due to new Ti3dC2p hybridizations occurring for both spins, while the spin symmetry is altered when the cluster relaxes closer to the H-sites (M = 1.33 μB), in line with the dimer case. Turning on the graphene case, we found similar behavior with the (8,0) tube; i.e., upon Ti adatom adsorption, there was alteration of its characteristic zero gap semiconducting character due to C2pTi3d electron hybridizations (Figures 4(a3, b3)). The spin majority exhibits a new peak located at 0.5 eV that is mainly due to Ti3d electrons, while, although less pronounced, the C nearest-neighboring atoms participate also (Figure 4b3). Indeed, the corresponding wave function at this energy state has clear Ti3dz 2 character (inset of Figure 4b3). In the spin minority PDOS, the Ti3d electrons occupy mainly the states above the Fermi level. These electronic features of the Ti adatom on graphene are in very good agreement with previous DFT calculations.22,23 Similarly to the adatom case, the dimer on graphene exhibits spin updown differences (M = 1.23 μB) that are mainly due to the Ti3dTi3d hybridizations resulting in the manifestation of a second new energy state around 1.0 eV (spin up) and 0.8 eV (spin down) (Figure 4c3). In the nonmagnetic trimer case, we see two new main peaks below the Fermi level (1.3 and 0.5 eV) that are separated by a pseudogap (1.0 eV). These states are due to Ti3dC2p hybridizations, and they are present at and above the Fermi level (Figure 4d3). Concluding, in all cases, Ti introduces new energy states close to the Fermi level that are attributed to Ti3dC2p hybridizations, thus altering the electronic character of the bare substrates.

ARTICLE

In particular, Ti additions on the (8,0) SWCNT and graphene change their semiconducting character to conducting, while the introduction of magnetic features is directly related to the deposition of the adsorbates closer to the H-sites. More insight into the bonding characteristics can be obtained from the detailed inspection of the corresponding system’s wave functions (WFs). In the present study, we focus basically on the highest occupied states (HOS) of (4,0), (8,0), and graphene, i.e., close to the Fermi level, due to their importance in Ti or molecular adsorption.8 In all cases, we used an isosurface wave function value of 0.05. Figure 5a depicts the HOS of the (4,0) SWCNT; we can see the characteristic π covalent bonding between the neighboring carbon atoms (shown in Figure 5a by the dashed yellow line on the π bond between the A and B carbon atoms). In Figure 5b we give the same system but in the presence of a Ti adatom anchored at the TSH position. We see that the two lobes of the Ti3d orbital (one blue and one red) are hybridized with the p lobes of the two nearest-neighbor C atoms (A and B atoms), forming two strong directional σ-like covalent bonds (shown in Figure 5b by solid yellow lines between Ti and A (B) carbon atoms). Importantly, the presence of the Ti adatom changes locally the pure HOS (4,0) characteristic π bond, which is aligned along the tube axis (Figure 5a): a new three C atoms hybridized orbital is formed that is now normal to the tube’s axis (shown in Figure 5b with a dashed yellow line). We point out that significant charge transfer occurs from the Ti adatom toward the bonded carbon atoms (labeled with A and B), while the neighboring carbon atoms (D and F) are also reduced (Figure 5b). From the Mulliken charge evaluation, it came out that the Ti adatom loses approximately one electron. As a consequence, the resulting system is expected to be more reactive, but it may suffer from conductivity reduction along the tube axis. The case of Ti on (8,0) is of particular interest. In the spin-up case (Figure 5c (spin v)), we see no hybridizations between the neighboring SWCNT atoms and the dangling Ti3d electron. In addition, we can see strong depletion of the WF on the carbon atoms beneath the Ti adatom that is extended along the tube’s axis, contrary to the clear manifestation of the π bonding features of the C atoms at the opposite tube’s side. Importantly, the spin minority states (situated at 0.4 eV) are characterized by strong TiC interactions (Figure 5c (spin V)): in particular, two lobes of the Ti3d orbital are hybridized with the neighboring C2p atoms (dashed lines between atoms labeled A, B, and Ti), thus leaving the other two d lobes of the Ti adatom free and reactive. The rest of the C atoms exhibit the usual characteristic π bonding features. Compiling these results, we can conclude that the presence of a Ti adatom on the SWCNT induces significant changes in the electronic characteristics of the system. These alterations are associated with important charge transfer that is localized in the vicinity of the adatom, which eventually acts as an electron donor (approximately 1.1 electrons). As far as the graphene is concerned, in Figure 5d we give the spin majority (spin v) and minority (spin V) HOS states, in which we can see TiC hybridizations and CC π bonding characteristics. In the spin majority HOS (Figure 5d (spin v)), the two axially oriented Ti3d lobes are hybridized with the Cpz first neighboring atomic orbital (schematic representation by a dashed yellow line that connects Ti with A or B labeled atoms), while the characteristic π bonding orbitals that are formed between two graphene atoms are aligned parallel to the TiC bond (e.g., dashed line between two yellow C atoms). A strong 15176



Figure 6. HOS electronic wave functions of the Ti dimer on: (a) (4,0), (b) (8,0), and (c) graphene. Small (yellow) and big (blue) spheres stand for the C and Ti atoms, respectively.

σ-like covalent bond characterizes the spin minority HOS between the Ti3d lobes (red and blue) and the first neighbor C atoms (dashed yellow line between Ti and labeled A (B) atom) (Figure 5d (spin V)). Perpendicularly to this directional bond and parallel to the graphene layer, a π-like bonding between three C atoms is manifested, similarly to the Ti in the (4,0) case (Figure 5b). From the Mulliken charge analysis, we found that Ti is reduced by one electron in excess of the graphene sheet, in agreement with other theoretical calculations.23 In Figure 6a, we present the schematic representation and the HOS of Ti2 on the (4,0) SWCNT. We can see the strong hybridization between the three lobes of Ti3dTi3d electrons forming σ and π bonds, shown by yellow solid and dashed yellow lines, respectively. For both Ti atoms, the fourth lobe overlaps with the C2p electrons of the nearest atoms (labeled A and B). This charge distribution results in a very active site close to the dimer’s area, in line with the case of theoretically suggested Ti2 on fullerenes for improved hydrogen adsorption.10,11 In addition, from the Mulliken population analysis, each Ti atom loses about 0.8 electrons (1.6 for the dimer case). The rest of the HOS charge distribution remains almost unchanged and similar to the pure (4,0) case (Figure 5a). sA strong directional σ bond was also found between the dimer’s atoms on (8,0) SWCNT (Figure 6b (solid yellow line between Ti atoms)), while no TiC bonds are seen at this energy. Interestingly, the other three d electron lobes are left open (dangling bonds); very importantly, the WF of the first neighboring C atoms is marked by strong depletion, while on the diametrically opposite side of the dimer C atoms are uniformly bonded via π hybridization. The Mulliken analysis population yielded charge transfer (0.7 electrons/ atom) from the dimer to the substrate. Rich in findings was also the dimer on graphene case: significant localization of the WF over the Ti atoms that form a

ARTICLE

Figure 7. Ibid with Figure 6 but for the trimer case.

π-like TiTi bonding, especially in the spin majority case (Figure 6c). In line with the (4,0) case, TiC hybridizations are also present, contrary to the (8,0). In addition, for the spin minority case, π-like TiTi bonding that is aligned parallel to the graphene sheet between the Ti3d electrons is also found (Figure 6c). The Mulliken analysis population revealed again loss of Ti electronic charge of (0.7 electrons/atom) in favor of the substrate’s C atoms. The HOS of the trimer case on (4,0) SWCNT (Figure 7a) is characterized by hybrid orbitals between the TiTi d electrons as well as the Ti3dC2p electrons (denoted by dashed yellow lines), while the WF contributes even far from the Ti trimer. On the (8,0), the HOS are more localized around the trimer, exhibiting enhanced π-like bonding between the d lobes of Ti atoms and Ti3dC2p hybrid orbitals with the first neighboring C atoms (Figure 7b). The WF in the remaining tube is again heavily depleted. The HOS of the trimer on graphene (Figure 7c) exhibits behavior similar to the spin majority case of the dimer on graphene (Figure 6c). The three Ti atoms manifest strong and well-localized WF distribution enhancement; the first neighboring C atoms are bonded to the trimer, while very interestingly the pz electrons of the rest of the C atoms exhibit dangling bonds. From the Mulliken population analysis, we found significant charge transfer from the trimer toward the (4,0), (8,0), and graphene by as much as 1.80, 1.84, and 2.1 electrons, respectively, this charge being mainly redistributed to the first neighboring C atoms. 3.2. Ti7 and Ti13 3D Cluster Deposition Cases. 3.2.1. Equilibrium Structures and Stability. Metal nanoclusters exhibit interesting physical, chemical, and electronic properties compared to the bulk system. TiN nanoclusters (N e 130 atoms) have been widely studied both experimentally30,31 and theoretically.3235 All studies agree that Ti7 and Ti13 are the most stable configurations, exhibiting 5-fold symmetry and dense icosahedral structures, followed by Ti15 and Ti19. In Table I, we give the 15177



ARTICLE

Table I. Binding Energy (Eb) for Free-Standing and Deposited Ti7 and Ti13 on (4,0), (8,0), and Graphenea dTiTi (Å)

Ti7

a

la

Eb (eV)

system

(3.94 ( 0.28), 4.18, 3.286, 3.13* 30

33

32

lp

2.518*

2.438*

2.625,32 2.62,33

(2.552.62)31

dTiC (Å) -

Ti7/(4,0)

1.68*

2.67*

2.63*

Ti7/(8,0)

0.82*

2.56*

2.57*

2.18 2.21

Ti7/graphene

0.82*

2.61*

2.60*

2.21

Ti13

(4.66 ( 0.41),30 3.669,32 4.17,34,35 4.81,33 3.85*

l01

l11

2.567,34 2.53*

2.699,34 2.66*

-

32

(2.522.98)31 2.76*

2.17

33

Ti13/(4,0)

1.13*

2.701, 2.65, 2.59*

Ti13/(8,0)

0.62 *

2.59*

2.67*

2.22

Ti13/graphene

0.67*

2.57*

2.71*

2.20

Bond lengths (dTiTi and dTiC) as indicated in Figure 8. The distances of refs 3133 correspond to the average l bond values.

Figure 8. Schematic representation of Ti7 and Ti13 nanoclusters: (a, e) free-standing, (bd) Ti7 supported, and (fh) Ti13 on (4,0), (8,0), and graphene, respectively. Small (yellow) and big (blue) spheres stand for the C and Ti atoms, respectively.

binding energies (Eb) and the structural characteristics of Ti7 and Ti13, i.e., TiTi and TiC bond lengths, along with the available literature data for comparison. We note here that the binding energies of the supported cases refer to the energetically favored configurations of the relaxed systems (calculated by means of eq 1). It comes out that in the case of the Ti13 free-standing cluster the Ti atoms are more tightly bound than in Ti7, due to the higher symmetry of the former, in agreement with available theoretical data.3235 The supported clusters on the SWCNTs and graphene exhibit three characteristic features: (a) they remain stable and compact, in agreement with the findings referring to Ti13

on (5,5) SWCNT,6 (b) their binding energies/atoms are higher when anchored on the (4,0), while their evolution with the tube size converges to the graphene’s value, in analogy with the adatom’s behavior (Figure 1), and (c) in all substrates, the Ti13 is less tightly bound than Ti7. We recall here that the adatom exhibits the stronger bonding of all cases. In Table I, we also compare the characteristic cluster bond lengths as indicated in Figure 8: as it can be seen, in the case of Ti7, la refers to the bond lengths between the pentagon atoms and the axis atoms, while lp stands for the bond lengths between two successive pentagon atoms (Figure 8a). In the Ti13 case, we adopted the labeling used in ref 34: we denote with lij the lengths of the bonds formed between the atoms in the ith and jth shells with respect to the central cluster atom that is indexed by zero (Figure 8e). In the free-standing clusters cases, we found an overall good agreement with the available data (Table I), while Ti7 seems to be more compact than Ti13. The relaxed clusters on the carbon substrates were obtained by optimizing various possible rotations. It came out that they exhibit modifications in their bond lengths while preserving the basic structural characteristics and shapes. In the case of Ti7, we found two possible relaxed positions: one with the cluster’s axis along the tube’s axis and inclined by approximately 45° and another one aligned transversely to the tube axis with the same inclination. The energetically favored cluster’s arrangement on the (4,0) is the first one, a finding that may be correlated with the tube’s curvature (Figure 8b), while the second alignment is characteristic of the (8,0) case (Figure 8c). On the (4,0) the Ti7 cluster appears slightly distorted. Four Ti atoms are bonded with C atoms, appearing like two dimers with elongated bond lengths: one dimer occupying the two dumbbell positions that are located within the hexagon, similar to Figure 3a, and another one located at the next energetically favored dimer position that corresponds to two TSH sites of consecutive hexagons. In both cases, the average TiC distance, 2.18 Å, is longer than that of the adatom’s but comparable to the average distance of the dimer. In the case of Ti7 on the (8,0), we found that the cluster is aligned with its axis transversely to the tube axis. In particular, in this case four Ti atoms bind with the (8,0) C atoms (three Ti atoms close to the TSH positions of three neighboring hexagons and one Ti atom close to one S-site), having an average bond length of 2.21 Å (Figure 8c). On graphene, Ti7 is also distorted 15178



Figure 9. Electronic density of states of Ti7 and Ti13 on the different substrates studied. Dotted, red solid, black solid, and dashed lines correspond to the total, Ti3d, C2p, and C0 2p electronic contributions. The Fermi level has been set to zero energy.

and inclined by approximately 45°, forming 2-TSH, 1-S, and 1-H bonds with the C atoms that belong to three different hexagons (Figure 8d). The case of the icosahedral Ti13 cluster on the (4,0) is of particular interest due to the geometrical constraints; i.e., its size is almost double compared to the tube’s diameter. We found three possible adsorption cases: (a) while half of the cluster remains unaltered, the other half dissolves above the SWCNT, (b) two Ti atoms of the cluster penetrate into the SWCNT, and they break the CC bonds and incorporate the tube, thus altering locally the surface chemistry (inset in Figure 8f), and (c) a fully relaxed configuration that preserves very well the cluster’s shape on top of four neighboring hexagons (Figure 8f). Interestingly, the energetically favored case is the second one; nevertheless, given that in the present study we focus on the deposition of clusters above the SWCNTs we shall consider only the last case for further investigation. In Figure 8f, four Ti atoms bind the cluster with the tube: three are located at TSH and at the A-site. This configuration results from the tube’s geometry in conjunction with the cluster’s shape, while the presence of the Ti13 on the SWCNT results in elongation of the CC first neighbors from 1.45 to 1.48 Å. On (8,0), the Ti13 cluster preserves its asperity in agreement with Ti13 on (5,5),6 while it relaxes with one of its triangular sides parallel to the surface behaving like a trimer located on neighboring TSH sites (Figure 8g). On the contrary, on graphene the Ti13 triangular site is distorted, with two atoms bonded close to H-sites (Figure 8h) like an elongated dimer (Figure 3c). Nevertheless, in both (8,0) and graphene cases, the TiC bond lengths are almost equal and comparable to those of the adatomgraphene system (Table I). In addition, we note that the relaxation of the Ti13 cluster above the SWCNT results in an increase of the neighboring CC bond distances by 0.025 Å, compared to the pure SWCNT case. 3.2.2. Electronic Structures and Charge Distributions. In Figure 9, we present the EDOS for the cases of deposited clusters on the two SWCNTs and graphene. Aiming to reveal the

ARTICLE

Figure 10. HOS electronic wave functions of Ti 3D clusters (Ti7, Ti13) on: (a, d) (4,0); (b,e) (8,0); and (c,f) graphene. Small (yellow) and big (blue) spheres stand for the C and Ti atoms, respectively.

CTi7/13 bonding particularities, we calculated selectively the PDOS for the C atoms located at a distance of 0.5 nm from the cluster’s center, denoted by C0 2p. As it can be seen, these systems exhibit metallic character, in line with the dimer and trimer cases (Figure 4). The Ti7 on (4,0) exhibits an enhanced peak around 0.6 eV that is due to the C0 2p and the C2p hybridizations, while the Ti3d participate too. We note that the C0 2p partial EDOS exhibits an overall agreement with the pure (4,0) EDOS (Figure 4a1). On the (8,0) and graphene, the occupied states are broadened, while Ti3dC2p hybridizations emerge (Figures 9(a2,a3)). We note again that the major contributions at the Fermi level are basically due to C0 . In addition, similar behavior is exhibited by Ti13 with an enhanced state close to the Fermi level, which also exists in the free-standing cluster,3335 indicating the strong cluster stability (Figures 9(b1b3)). Finally, the presence of Ti7 and Ti13 alters the semiconducting character of the (8,0) and graphene, in line with the Ti adatom cases (Figure 4). It is worth noting that in these hybridic systems the spin majority and spin minority states are symmetric, indicating the absence of magnetic features, except for the case of Ti13 on graphene that could be related with the H-site occupation of the Ti atoms (M = 1.17 μB), similarly to the Ti2 and Ti3 behavior. Enhancement of magnetic features upon one-layer Ti coating on the (8,0) H-sites has been also found by other theoretical studies.45,46 More insight concerning the bonding characteristics and charge distribution is obtained by inspecting the wave functions. Figure 10 depicts the HOS energy states for the cases of Ti7 (Figures 10ac) and Ti13 (Figures 10df) on the three systems studied. The insets in Figures 10ac depict the same quantity for the pure substrates for comparison, while the WF isovalues are the same in all cases. As it can be seen in all cases, the WF at this energy is mainly accumulated on the cluster, while significant alterations occur in WF distributions of the substrates. In particular, in the Ti7 on (4,0) case (Figure 10a), we note the π-like bonds between the metal atoms, while most of the TiC hybridizations are characterized by directional bonding. Importantly, the C atoms away from the cluster preserve their bonding 15179


The Journal of Physical Chemistry C character (C0 bonds), while the WF participation of the C atoms that are close to the Ti7 area is significantly reduced. The remaining π CC substrate bonds at this location are now aligned vertically instead of along the tube’s axis (inset of Figure 10a). Moreover, this WF reduction in the vicinity of the cluster is more pronounced in the larger tube (8,0), in which the presence of the Ti7 induces an empty area around the cluster (Figure 10b), while the opposite side of the tube preserves the characteristic CC bonding, in analogy to the dimer case (Figure 6). Finally, Ti7 on the graphene substrate demonstrates these effects even more clearly: the WF is localized pronominally on the cluster, while the substrate’s C atoms are practically empty, indicating significant charge transfer at this energy (Figure 10c). Indeed, from the calculation of the Mulliken population, it came out that there is a gradual decrease of the electronic charge transfer of the Ti atoms, going upward from the substrate that reaches negligible values for the topmost Ti cluster atoms. This electronic deficiency is maximum in the bonded with the substrate Ti atoms, estimated at 0.67, 0.55, and 0.43 electrons/ atom for the (4,0), (8,0), and graphene, respectively. The case of Ti13 exhibits many resemblances with the one described above. It has to be noted, however, that at this energy there are practically no TiC bonds. In the case of Ti13 on graphene, the WF is mainly localized on the cluster, especially for the spin-down case. Similarly to the Ti7 case, the Mulliken population analysis revealed enhanced charge transfer of the Ti atoms that are bonded to C atoms, 0.78, 0.57, and 0.47 electrons/ atom for the (4,0), (8,0), and graphene, respectively, in line with the results concerning Ti13 on C60.10,11 Interestingly, in all cases, the cluster’s core atom gains 0.37, 0.30, and 0.22 electrons, for the three substrate cases, (4,0), (8,0), and graphene, respectively.

4. CONCLUDING REMARKS In this communication, we present DFT results of a detailed study referring to the alterations induced in the structural and electronic properties of two selected zigzag SWCNTs and graphene upon deposition of TiN (N = 1, 2, 3, 7, 13) nanostructures. Starting from the Ti adatom case, we found that the adsorption sites vary with the SWCNT’s radius: for n < 6, two equivalent positions located at the trisectional points of the line that is normal to the tube’s axis and joins two faces of a C hexagon are found to be energetically favored (TSH sites), while in the cases of larger-diameter SWCNTs, as well as in graphene, the position on top of the hexagon’s center is preferred (H-site). The analysis of the adatom’s contour energy maps yielded that the energy barriers between the adatom positions are higher for the SWCNTs and lower for graphene than 1 eV, respectively. In addition, we found that the energy height separating the two TSH sites of the same hexagon is an order of magnitude lower. These findings suggest that at room temperature the probability for adatom diffusivity would be limited and restricted mainly in oscillations between these TSH sites. Nevertheless, although these sites are not contributing to diffusion, they play an important role in a subsequent Ti atomic and/or cluster deposition process or an eventual coating. Indeed, we found that the TSH positions permit the accommodation of dimers and trimers in compact linear and 2D triangular forms, respectively, while the Ti 7 and Ti 13 clusters remain stable and compact in 3D conformations. Turning on the electronic properties of the supported TiN on the substrates studied, we found that the presence of Ti adatoms

ARTICLE

influences mainly the electronic states close to the Fermi level, inducing metallic features to the semiconducting SWCNTs and graphene, the effect being more pronounced in the cases of the larger clusters. In addition, most of the new electronic states are characterized by strong hybridization between the Ti d and C p electrons, resulting in strong directional covalent bonding. Moreover, we found that in all cases there is significant charge transfer from the adsorbates to the substrates. Importantly, we found that these otherwise reduced TiN clusters induce substantial charge screening in their surrounding substrate atoms that renounce their electronic contributions, thus appearing, in most cases, as charged locations with dangling bonds. These findings are closely related with the early-stage mechanisms of Ti deposition and the presence and the functionality of possible active sites and can, thus, be used for the design of controlled metalcarbon coatings, suitable for technological applications for catalysis and nanoelectronics.

’ ACKNOWLEDGMENT This work was partially supported by the EC funding, GA no 264635-BioTiNet ITN. The authors would like to thank Prof. G. A. Evangelakis for stimulating discussions. ’ REFERENCES (1) Zhang, Y.; Dai, H. Appl. Phys. Lett. 2000, 77, 3015–3017. (2) Tombler, T. W.; Zhou, C.; Kong, J.; Dai, H. Appl. Phys. Lett. 2000, 76, 2412–2414. (3) He, Y.; Zhang, J.; Wang, Y.; Yu, Z. Appl. Phys. Lett. 2010, 96, 063108–063110. (4) Georgakilas, V.; Gournis, D.; Tzitzios, V.; Pasquato, L.; Guldie, D. M.; Prato, M. J. Mater. Chem. 2007, 17, 2679–2694. (5) Andriotis, A. N.; Menon, M.; Froudakis, G. E. Appl. Phys. Lett. 2000, 76, 3890–3892. (6) Park, N.; Sung, D.; Lim, S.; Moon, S.; Hong, S. Appl. Phys. Lett. 2009, 94, 073105–073107. (7) Durgun, E.; Ciraci, S.; Yildirim, T. Phys. Rev. B 2008, 77, 085405–085413. (8) Yildirim, T.; Ciraci, S. Phys. Rev. Lett. 2005, 94, 175501–175504. (9) Kim, C.; Jhi, S. H.; Park, N.; Louie, S. G.; Cohen, L. Phys. Rev. B 2008, 78, 085408–085412. (10) Yang, S.; Yoon, M.; Wang, E.; Zhang, Z. J. Chem. Phys. 2008, 129, 134707–134713. (11) Sun, Q.; Wang, Q.; Jena, P.; Kawazoe, Y. J. Am. Chem. Soc. 2005, 127, 14582–14583. (12) Mota, R.; Fagan, S. B.; Fazzio, A. Surf. Sci. 2007, 601, 4102–4104. (13) Fujima, N.; Oda, T. Eur. Phys. J. D 2009, 52, 87–90. (14) Yuan, S.; Wang, X.; Li, P.; Wang, C.; Yuan, S. J. Appl. Phys. 2008, 104, 013509–013512. (15) Felten, A.; Suarez-Martinez, I.; Ke, X.; Van Tendeloo, G.; Ghijsen, J.; Pireaux, J. J.; Drude, W.; Bittencourt, C.; Ewels, C. P. Chem. Phys. Chem. 2009, 10, 1799–1804. (16) Li, D; Kaner, R. B. Science 2008, 320, 1170–1171. (17) Westervelt, R. M. Science 2008, 320, 324–325. (18) Li, X.; Wang, X.; Zhang, L.; Lee, S.; Dai, H. Science 2008, 319, 1229–1231. (19) Bunch, S. J.; Van der Zande, A. M.; Verbridge, S. S.; Frank, I. W.; Tanenbaum, D. M.; Parpia, J. M. Science 2007, 315, 490–493. (20) Patchkovskii, S. J.; Tse, S.; Yurchenko, S. N.; Zhechkov, L.; Heine, T.; Seifert, G. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10439–10444. (21) Durgun, E.; Dag, S.; Bagci, V. M. K.; Gulseren, O.; Yildirim, T.; Ciraci, S. Phys. Rev. B 2003, 67 (R), 201401–201404. (22) Chan, K. T.; Neaton, J. B.; Cohen, M. L. Phys. Rev. B 2008, 77, 235430–235441. 15180



ARTICLE

(23) Lindan, P.; Duplock, E.; Zhang, C.; Thomas, M.; Chatten, R.; Chadwick, A. Dalton Trans. 2004, 3076–3084. (24) Rojas, M. I.; Leiva, E. P. M. Phys. Rev. B 2007, 76, 155415–155422. (25) Sanchez-Portal, D.; Ordejon, P.; Artacho, E.; Soler, J. M. Quantum Chem. 1997, 65, 453–461. (26) Artacho, E.; Sanchez-Portal, D.; Ordejon, P.; Garcia, A.; Soler, J. M. Phys. Status Solidi B 1999, 215, 809–817. (27) Soler, J.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745–2779. (28) Junquera, J.; Paz, O.; Sanchez-Portal, D.; Artacho, E. Phys. Rev. B 2001, 64, 235111–235119. (29) Junquera, J.; Zimmer, M.; Ordejon, P.; Ghosez, P. Phys. Rev. B 2003, 67, 155327–155338. (30) Salazar-Villanueva, M.; Tejeda, P. H. H.; Pal, U.; Rivas-Silva, J. F.; Mora, J. I. R.; Ascencio, J. A. J. Phys. Chem. A 2006, 110 (34), 10274–10278. (31) Zhao, J.; Qiu, Q.; Wang, B.; Wang, J.; Wang, G. Solid State Commun. 2001, 118, 157–161. (32) Lian, L.; Su, C. X.; Armentrout, P. B. J. Chem. Phys. 1992, 97, 4084–4093. (33) Wang, S. Y.; Yu, J. Z.; Mizuseki, H.; Yan, J. A.; Kawazoe, Y.; Wang, C. Y. J. Chem. Phys. 2004, 120, 8463–8468. (34) Wang, S. Y.; Duan, W.; Zhao, D. L.; Wang, C. Y. Phys. Rev. B 2002, 65, 165424–165429. (35) Castro, M.; Liu, S. R.; Zhai, H. J.; Wang, L. S. J. Chem. Phys. 2003, 118, 2116–2123. (36) Lekka, Ch. E.; Evangelakis, G. A. Surf. Sci. 2001, 473, 39–49. (37) Lekka, Ch. E.; Papageorgiou, D. G.; Evangelakis, G. A. Surf. Sci. 2002, 518, 111–125. (38) Papageorgiou, D. G.; Lekka, Ch. E.; Evangelakis, G. A. Appl. Surf. Sci. 2003, 219, 64–73. (39) McRae, E. G.; Buck, T. M.; Malic, R. A.; Wallace, W. E.; Sanchez, J. M. Surf. Sci. 1990, 238, L481–L485. (40) McRae, E. G.; Malic, R. A. Phys. Rev. B 1990, 42, 1509–1517. (41) Over, H.; Gilarowski, G.; Niehus, H. Surf. Sci. 1991, 381, L619–L622. (42) Jonsson, H.; Mills, G.; Jacobsen, K. W. In Classical and Quantum Dynamics in Condensed Phase Simulations; Berne, B. J., Ciccotti, G., Coker, D. F., Eds.; World Scientific: River Edge, NJ, 1998; p 385. (43) Doverstal, M.; Karlsson, L.; Lindgren, B.; Sassenberg, U. Chem. Phys. Lett. 1997, 270, 273–277. (44) Russon, L. M.; Heidecke, S. A.; Birke, M. K.; Conceicao, J.; Morse, M. D.; Armentrout, P. B. J. Chem. Phys. 1994, 100, 4747–4755. (45) Dag, S.; Durgum, E.; Ciraci, S. Phys. Rev. B 2004, 69 (R), 121407–121410. (46) Dag, S.; Ciraci, S. Phys. Rev. B 2005, 71, 165414–165419.

15181


TiN Decoration of Single-Wall Carbon Nanotubes and Graphene by

Recommend Documents