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Structural Trends Among Nanotubes of Group 13-15 Binary Hydrides Jukka T. Tanskanen,* Mikko Linnolahti, Antti J. Karttunen, and Tapani A. Pakkanen Department of Chemistry, UniVersity of Joensuu, P.O. Box 111, FI-80101 Joensuu, Finland ReceiVed: March 30, 2009; ReVised Manuscript ReceiVed: April 30, 2009
Structural characteristics of perhydrogenated single-walled group 13 nitride, phosphide, and arsenide nanotubes have been determined by quantum chemical calculations. Partial endo-hydrogenation is energetically beneficial for nanotubes beyond 1 nm in diameter, until which full exo-hydrogenation is relevant. The molecular structures of the partially endo-hydrogenated nanotubes are derived by rolling perhydrogenated group 13-15 monolayer sheets into cylinders. The structural principles of the resulting nanotubes are strongly influenced by electrostatic interactions between polarized surface hydrogen species. Generally, a low degree of polarization results in the preference for structures analogous to the (111) sheet of the diamond-like crystal, with a high degree of polarization resulting in the preference for the corresponding (110) structures. Introduction Carbon and boron nitride (BN), being isoelectronic, typically show similar structural characteristics. The BN counterpart of graphite is hexagonal BN (h-BN) having sp2-hybridized atoms, whereas the counterpart of diamond is cubic BN (c-BN) with sp3-hybridization, i.e., with tetrahedrally coordinated atoms. The structural analogy between carbon and BN also applies at the nanoscale. Taking nanotubes as an example, carbon nanotubes (CNTs)1 and boron nitride nanotubes (BNNTs)2 can be considered as cylinders rolled up from the monolayer sheets of the isostructural graphite and h-BN, respectively. Regardless of the similarities between CNTs and BNNTs, their structural characteristics significantly differ after treatment with hydrogen.3 The experimentally known perhydrogenated single-walled CNTs are structurally analogous to the perhydrogenated graphene sheet,4,5 i.e., graphane,6,7 which has been recently synthesized.8 In contrast, BN-analogue of graphane, i.e., perhydrogenated monolayer sheet of h-BN, has not been synthesized and, according to theoretical predictions, is unlikely to exist due to preference of the monolayer sheet to bend.9 The origin of the effect is in polarization of hydrogens, and it is thereby relevant for group 13-15 binary hydrides in general.10,11 Due to the different structural characteristics of the monolayer sheets, also the nanotubes of the group 13-15 binary hydrides, when considered being rolled up from the sheets, are expected to show different structural characteristics. There is a wealth of experimental information on the tubular nanostructures of group 13-15 binary compounds, among which BN is the only one having been experimentally shown to form well-characterized single- and multiwalled nanotubes analogous to CNTs.1,2,12 The prepared heavier group 13-15 nanotubes typically have zinc blend or wurtzite lattices13 with tube walls up to hundreds of nanometers thick.14-16 Besides BN, tubular nanostructures of group 13 nitrides (AlN,17 GaN,18-20 and InN21) and group 13 phosphides (GaP22 and InP23,24) are experimentally known. Group 13 arsenide nanotubes have not been reported. The theroretical study reported herein aims at determining the structural principles of the perhydrogenated single-walled nanotubes of group 13-15 binary compounds. The stabilities * To whom correspondence should be addressed. E-mail: jukka.tanskanen@ joensuu.fi. Fax: (+358) 13-251-3336.
alongside with electronic characteristics of the nanotubes are systematically investigated by periodic B3LYP calculations. The focus is on the binary hydrides corresponding to the first three rows in the periodic table, i.e., BN, AlN, GaN, BP, AlP, GaP, BAs, AlAs, and GaAs. Computational Details Infinitely long nanotubes were fully optimized by periodic B3LYP25 calculations. The calculations were carried out by the CRYSTAL0626 quantum chemistry software. Line group symmetries27 were utilized in the calculations to enable the treatment of nanotubes several nanometers in diameter.28 Basis sets were adopted from a preceding study on perhydrogenated group 13-15 monolayers,10 and are as follows: modified 6-21G* for B and N,29 modified 86-21G* for Al,30 modified 85-21G* for P,31 modified 86-4111d41G* for Ga,30b,32,33 standard def-SVP for As,33 and standard 6-31G** for H. Default optimization convergence thresholds and an extra large integration grid were utilized in the calculations. Density of states-plots (DOS) were calculated for [AlNH2]n monolayers and six Legendre polynomials were used for the expansion of the DOS plots. Results and Discussion The recently reported perhydrogenated group 13-15 monolayer sheets are structurally analogous to the perhydrogenated (110) and (111) slabs of group 13-15 diamond-like crystals. With the exceptions of BN, AlAs, and GaAs, reaction between hydrogen and pristine monolayer to form the respective perhydrogenated monolayer is exothermic.10 Rolling of the monolayer sheets into a cylinder produces corresponding nanotubes, whereas the sheets themselves can be considered as nanotubes of infinite diameter. Hence, a brief summary of the previously described structural characteristics of the respective monolayer sheets is given below. The preference for either (110) or (111) monolayer structures is related to the electronegativity differences between the heteroatoms, which in turn determine the degree of the polarization of the hydrogen species in the binary hydrides. Generally, the compounds with a large electronegativity difference between the constituent heteroatoms, such as the group 13 nitrides, prefer the (110) sheets. This is due to electrostatic attractive H-H
10.1021/jp9028563 CCC: $40.75 2009 American Chemical Society Published on Web 05/12/2009
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Figure 1. Perhydrogenated (110) monolayer sheet of group 13-15 diamond-like crystal (top), corresponding zigzag (24,0) nanotube (middle), and corresponding armchair (18,18) nanotube.
interactions taking place on the (110) surfaces, the H-H interactions being repulsive on the (111) surface. When the differences in the electronegativities are small, particularly in the cases of BP and BAs, the (111) structures are energetically favored.10 Structural Characteristics of the Nanotubes. Rolling the perhydrogenated group 13-15 (110) monolayer sheets produces distinct families of nanotubes, each having half of the hydrogens inside (endo-hydrogens) and half of the hydrogens outside (exohydrogens). Instead, the perhydrogenated group 13-15 nanotubes similarly derived from the (111) sheets, each have two structural alternatives: (1) group 13 elements exo-hydrogenated and group 15 elements endo-hydrogenated, and (2) group 13 elements endo-hydrogenated and group 15 elements exohydrogenated.9 All the described structures were included in the study, and were systematically studied up to about 6 nm in diameter. Single-walled fully exo-hydrogenated nanotubes were included for comparison. Using the naming conventions of CNTs,34,35 the nanotubes have either zigzag (n,0), armchair (n,n), or chiral (n,m) orientations, of which zigzag and armchair nanotubes were studied. The monolayers and representatives of the studied nanotubes are illustrated in Figures 1 and 2. The perhydrogenated group 13-15 (110) and (111) monolayer sheets, together with the corresponding nanotubes, are composed of XYH2 units, where X ) B, Al, or Ga and Y ) N, P, or As. Accordingly, their relative energies are determined by dividing the total energies of the systems by the number of XYH2 units in the respective unit cells. The energies of the nanotubes relative to the (111) monolayer sheets are illustrated in Figures 3, 5, and 6. It should be noted that the monolayer sheets are energetically favored over the corresponding benzene analogues, i.e., X3Y3H6, the energetic differences being the smallest for BN, 26.5 kJ/mol per BNH2, and the largest for AlN, 138.8 kJ/mol per AlNH2. In the following, nitrides, phosphides, and arsenides are separately analyzed and discussed. Nitrides. The energies of the perhydrogenated single-walled group 13 nitride nanotubes, relative to the respective perhydrogenated (111) sheets, are shown in Figure 3. Concerning the (111) nanotubes with two structural alternatives as described above, only the energies of the preferred isomers are shown. In
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Figure 2. Perhydrogenated (111) monolayer sheet of group 13-15 diamond-like crystal (top), corresponding zigzag (24,0) nanotube (middle), and corresponding armchair (18,18) nanotube. Shown are the isomers with group 13 elements exo-hydrogenated and group 15 elements endo-hydrogenated.
every case, including the phosphides and arsenides discussed below, those with group 13 elements exo-hydrogenated and group 15 elements endo-hydrogenated, are preferred in energy. Full exo-hydrogenation (red curves) is relevant for tubes below 1 nm in diameter, the lowest energies among the fully exo-hydrogenated nanotubes being obtained for zigzag (3,0) and armchair (2,2). This is in agreement with previous studies on tubular nanostructures of group 13-15 binary compounds.36,37 The (3,0) tubes benefit from the electrostatic attractions between surface hydrogens and are hence favored over the (2,2) ones. The electronegativity differences between the heteroatoms decrease in the order AlN > GaN > BN. As a consequence, the electrostatic H-H interactions are the most favorable for AlN (3,0), which is energetically slightly favored over the reference (110) sheet (dashed line). The studied fully exo-hydrogenated group 13 nitride nanotubes have large band gaps, around 7.8-9 eV for BN, 7.5-8.5 eV for AlN, and 6.2-7.5 eV for GaN. Beyond zigzag (3,0) and armchair (2,2), the fully exohydrogenated nanotubes become destabilized as a function of tube diameter. This is due to the decreasing curvature of the tubes, resulting in increasing distortion from the optimal sp3 hybridization. As a consequence, partially endo-hydrogenated (110) and (111) nanotubes become preferred for diameters beyond 1 nm, (Figure 3, green and blue curves) structurally and energetically approaching the corresponding sheets as a function of diameter. Generally, the band gaps of the (110) and (111) nanotubes are of the same magnitude as the gaps of the corresponding monolayers. The gaps decrease upon moving from boron to gallium due to increasing metallic character of the group 13 atoms, and approach the values calculated for the monolayer sheets as a function of the tube diameter. In the case of BN, the gaps vary at small diameters and rapidly converge toward the gaps of the corresponding monolayers as a function of tube diameter. This finding is in agreement with previous work on the band gaps of pristine BNNTs.38 Generally, the (110) nanotubes are favored over the (111) nanotubes. This is due to the attractive electrostatic H-H interactions taking place on the (110) surfaces. The armchair
Perhydrogenated Group 13-15 Nanotubes
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Figure 4. DOS plots for the perhydrogenated (110) and (111) sheets of diamond-like AlN. Contributions from Al, N, and H are illustrated in red, blue, and green, respectively. The plots have been shifted to give the Fermi energy as zero.
Figure 3. Energies (∆E) of the perhydrogenated single-walled group 13 nitride nanotubes relative to the perhydrogenated (111) sheets of the diamond-like group 13 nitrides.
(110) nanotubes are favored over the zigzag ones. The (110) zigzag nanotubes are destabilized with respect to the (110) armchair nanotubes due to short distances between the nearest BH-BH, AlH-AlH, GaH-GaH, and NH-NH hydrogen species inside the zigzag tubes.3 The hydrogens bound to group 13 elements, with negative partial charges and hence increased spatial requirements, mainly contribute to the repulsion. The attractive electrostatic H-H interactions have been previously demonstrated for perhydrogenated BNNTs, together with for group 13-15 monolayer sheets, on the basis of natural population analyses, charge-density maps, and DOS plots.3,10 For further illustration, DOS plots for the [AlNH2]n monolayers, having highly polarized surface hydrogens, are shown in Figure 4. Here, the contributions from H atoms are of particular significance. For (110) sheet, with attractive H-H interactions, the H contribution is significant in the valence regime, while for (111) no such contributions are present in the valence regime. The perhydrogenated armchair (110) AlNNTs with diameters larger than approximately 3.7 nm become favored over the (110) monolayer, suggesting the (110) AlNNTs to have a preferred diameter, beyond which the relative energies of the tubes start to converge toward the (110) sheet. The preference for the
Figure 5. Energies (∆E) of the perhydrogenated single-walled group 13 phosphide nanotubes relative to the perhydrogenated (111) sheets of the diamond-like group 13 phosphides.
AlNNTs over the monolayer sheet at large diameters is associated with the H-H interactions, as well. Closely related,
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Figure 7. Structural preferences of the group 13-15 perhydrogenated nanotubes as a function of the tube diameter. The binary compounds are listed in the order of increasing electronegativity difference44 (∆χ) between the heteroatoms. Carbon is included as a reference.
Figure 6. Energies (∆E) of the perhydrogenated single-walled group 13 arsenide nanotubes relative to the perhydrogenated (111) sheets of the diamond-like group 13 arsenides.
it has been previously demonstrated that perhydrogenated sheetlike AlnNnHm molecules are not planar but prefer to bend.10 However, single-walled nanotubes having diameters of several nanometers probably collapse in conditions other than vacuum, as has been demonstrated for CNTs.39-41 The cylindrical shapes of the nanotubes might be preserved by multilayering, which is energetically beneficial for perhydrogenated BNNTs.3 The (111) isomers with all group 13 elements exo-hydrogenated and all nitrogen species endo-hydrogenated are favored over the isomers with all nitrogens exo-hydrogenated and all group 15 elements endo-hydrogenated. This is due to larger spatial requirements of the hydrogens with negative partial charges, i.e. those bound to group 13 elements, the distance between adjacent endo-hydrogens being shorter than between adjacent exo-hydrogens. Due to the variations in the spatial requirements of the hydrogens, controlled by the electronegativities of the constituent heteroatoms, the preferred group 13 nitride (111) nanotubes have broad minima in relative energies, and preferred diameters at around 3.5 nm for BN, 1.8 nm for AlN, and 1.9 nm for GaN (see Figure 3, green curves). Phosphides. The relative energies of the perhydrogenated single-walled group 13 phosphide nanotubes are illustrated in Figure 5. In analogy with group 13 nitrides, full exo-hydrogenation applies for group 13 phospide nanotubes with small diameters, the zigzag (3,0) and armchair (2,2) being energetically
the most favorable exo-hydrogenated nanotubes. The fully exohydrogenated group 13 phosphide nanotubes have band gaps of 5.0-6.1 eV for BP, 5.1-6.1 eV for AlP, and 4.3-5.6 eV for GaP. The partially endo-hydrogenated (110) and (111) nanotubes become preferred at diameters beyond 1 nm. The (111) BPNTs are energetically favored at diameters above 1 nm, whereas in the cases of the AlPNTs and GaPNTs the armchair (110) nanotubes become energetically favored over the (111) nanotubes at diameters of 2.5 and 3.2 nm, respectively. The band gaps of the (110) and (111) nanotubes approach the values calculated for the corresponding monolayer sheets as a function of the tube diameter, the gaps decreasing upon moving from boron to gallium. The electronegativity difference between B and P is small and hence the stabilization of the (110) structures by the electrostatic attractive H-H interactions is not significant. Accordingly, BPNTs prefer the (111) structures, zigzag and armchair tubes being energetically equal. Note that group 14 elemental hydrides with unpolarized bonds prefer the (111) structures, as well.42,43 In the cases of AlP and GaP, the electronegativity differences between the heteroatoms are larger than in BP, but also considerably smaller than for the group 13 nitrides. This results in weaker electrostatic attractive H-H interactions for the phosphides in comparison with the nitrides. As a consequence, the differences in relative energies between (110) and (111) structures are clearly smaller for AlPNTs and GaPNTs than for the group 13 nitrides, and thus the trends less apparent. Arsenides. In analogy with the group 13 phosphides, the electronegativity difference between B and As is small while the differences are larger for AlAs and GaAs. Accordingly, the structural characteristics of the group 13 arsenide nanotubes are similar to the studied phosphides. This is demonstrated in Figure 6, illustrating the relative energies of the perhydrogenated single-walled group 13 arsenide nanotubes (see Figure 5 for comparison with the phosphides). Among the fully exo-hydrogenated nanotubes, zigzag (3,0) and armchair (2,2) are preferred in energy. The band gaps of the studied fully exo-hydrogenated group 13 arsenide nanotubes lie close to the semiconducting regime, around 4.2-5.7, 4.3-5.4, and 3.6-4.9 eV for BAs, AlAs, and GaAs, respectively. The (111) nanotubes are energetically favored at diameters above 1 nm for BAs, while for AlAs and GaAs the (111) structures are preferred up to diameters of 3.6 and 4.7 nm, respectively. For larger diameters the armchair (110) nanotubes become preferred for AlP and GaP. The band gaps
Perhydrogenated Group 13-15 Nanotubes of the group 13 arsenide (110) and (111) nanotubes converge toward the values calculated for the corresponding monolayer sheets. Comparison of the Nitrides, Phosphides, and Arsenides. In sum, the perhydrogenated nanotubes of group 13-15 binary compounds prefer full exo-hydrogenation at diameters below 1 nm, beyond which partially endo-hydrogenated structures, either (111) or (110) type, become preferred. The structural preferences of the nanotubes are controlled by the electronegativity differences between the group 13 and group 15 atoms, which is illustrated in Figure 7. The corresponding perhydrogenated carbon nanotubes are included for comparison, representing a case where the electronegativity difference is zero. Conclusions We have investigated the structural characteristics of perhydrogenated single-walled nanotubes of group 13-15 binary compounds. Both fully exo-hydrogenated and partially endohydrogenated nanotubes were included in the study. The molecular structures of the partially endo-hydrogenated nanotubes were derived by rolling hydrogen-saturated (110) and (111) slabs of diamond-like binary compounds into cylinders. Full exo-hydrogenation applies for group 13-15 nanotubes with diameters up to around 1 nm, beyond which the partially endo-hydrogenated structures become energetically preferred. The structures and stabilities of the perhydrogenated nanotubes are influenced by electrostatic interactions between polarized surface hydrogen species. The polarization originates from the partially ionic nature of the bonds in the group 13-15 binary compounds, the degree of polarization determining the type of nanotube, (110) or (111), to be energetically preferred at a specified diameter (see Figure 7). For binary compounds with highly polarized bonds, (110) structures are generally preferred, which is due to stabilizing interactions between the surface hydrogens. Instead, low degree of polarization results in the preference for (111) structures. The described structural characteristics are expected to help in the experimental characterization of novel nanotubes of group 13-15 binary compounds. Acknowledgment. Funding from the Finnish Funding Agency for Technology and Innovation (Tekes BNN-project) and the University of Eastern Finland is gratefully acknowledged. References and Notes (1) Iijima, S. Nature 1991, 354, 56. (2) Chopra, N. G.; Luyken, R. J.; Cherrey, K.; Crespi, V. H.; Cohen, M. L.; Louie, S. G.; Zettl, A. Science 1995, 269, 966. (3) Tanskanen, J. T.; Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. ChemPhysChem 2008, 9, 2390. (4) Tanskanen, J. T.; Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. Chem. Phys. 2007, 340, 120. (5) Nikitin, A.; Li, X.; Zhang, Z.; Ogasawara, H.; Dai, H.; Nilsson, A. Nano Lett. 2008, 8, 162. (6) Sofo, J. O.; Chaudhari, A. S.; Barber, G. D. Phys. ReV. B 2007, 75, 153401. (7) Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. ChemPhysChem 2006, 7, 1661. (8) Elias, D. C.; Nair, R. R.; Mohiuddin, T. M. G.; Morozov, S. V.; Blake, P.; Halsall, M. P.; Ferrari, A. C.; Boukhvalov, D. W.; Katsnelson, M. I.; Geim, A. K.; Novoselov, K. S. Science 2009, 323, 610.
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