Controlling the Functionalizations of Hexagonal Boron Nitride

Aug 15, 2011 - Using density functional theory calcualtions, we reveal a novel control on the functionalizations of hexagonal boron nitride (h-BN) str...
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LETTER pubs.acs.org/JPCL

Controlling the Functionalizations of Hexagonal Boron Nitride Structures by Carrier Doping Zhuhua Zhang* and Wanlin Guo* Key Laboratory of Intelligent Nano Materials and Devices of Ministry of Education and Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

bS Supporting Information ABSTRACT: Using density functional theory calcualtions, we reveal a novel control on the functionalizations of hexagonal boron nitride (h-BN) structures by carrier doping. When the system is electron-doped, adatoms (e.g., H or F atoms) will exclusively bond with B atoms, resulting in possible magnetization of the system, whereas hole doping favors the adatoms to form insulating orthodimer structures on the BN structures. This behavior is caused by a peculiar chemical bond formed between the N and adatoms, whose strength significantly depends on the carrier type and level. Moreover, the adatoms’ diffusion on these BN structures can be steered along a designable path by the carrier doping, still attributted to the carrier-dependent bond stability. This carrier control of functionalizations is robust via adatom concentration and the physical conditions of BN structures, thus offering an easy route to controllably anchor the properties of functionalized BN systems for desired applications. SECTION: Surfaces, Interfaces, Catalysis

H

exagonal boron nitride (h-BN), a structural analogue to graphite, has been attracting considerable research attention due to its novel properties and potential applications.1 3 Similar to carbon counterparts, h-BN can be rolled into BN nanotubes (BNNTs)4,5 and isolated to monolayered nanosheets.6 9 Because of the high thermal stability and outstanding chemical inertness,10 h-BN structures exhibit amazing prospects of fabricating nanodevices competent to operate in harsh environments. However, pristine h-BN structures are unsuitable for many functional applications due to their large insulating band gap. To circumvent this hurdle, the most popular method is to modify the electronic properties of h-BN structures by surface chemisorptions of certain elements.11 In the past decade, extensive theoretical and experimental studies have shown that the electronic properties of BNNTs and BN sheets can be improved by fluorination,12 14 hydrogenation,15 17 or other covalent functionalizations.18 24 In particular, recent theoretical researches predict that fluorinated or hydrogenated BNNT can even be ferromagnetic.25,26 Despite these useful findings, a critical issue emerges that the properties of the functionalized BN structures correlate closely with the adatoms’ pattern,12,14,27 which is often formed in a random way on a host structure depending on processes, and thereby is extremely difficult to predict. This results in poor properties of the functionalized BN systems and even inefficiency in the functions.12 To facilitate the development of devices based on functionalization, it is imperative to explore a facile route capable of efficiently controlling how the adatoms distribute on the BN structures. Nevertheless, fixing the desired pattern of external r 2011 American Chemical Society

atomic species on a host material is still among the most difficult in semiconducting electronics. In this study, we reveal by first-principles calculations that fluorinating or hydrogenating BN sheets or nanotubes can be well controlled by carrier doping. With electron doping, the adatoms become exclusive to uniformly bond with the B atoms of h-BN structures, which can change the system into a magnetic metal. In contrast, with hole doping, the adatoms prefer to form orthodimer structures that retain the system to be insulating. Meanwhile, such carrier doping can also efficiently control the adatoms’ diffusion on BN structures by tuning its energy barrier. Our findings open an exciting possibility to precisely control the reaction sites and kinetics on BN sheets and nanotubes and represent an important step toward versatile BN-based nanodevices. The calculations in this work were performed within the density functional theory framework as put into practice in the VASP code.28,29 We used the projector augmented wave method30 for the core region and the local spin density approximation (LSDA) for the exchange-correlation potential. We have also verified our results by testing generalized gradient approximation (GGA) calculations with PBE functional. In the planewave expansion, the kinetic energy cutoff was set to 530 eV. The BN sheet was modeled with a 4  4 supercell and the BNNT was modeled with a supercell containing two primitive tube cells. Carrier doping to the BN systems is simulated by adjusting the Received: July 13, 2011 Accepted: August 10, 2011 Published: August 15, 2011 2168

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Figure 1. Carrier-controllable fluorination on an h-BN sheet. (a) Atomic configurations of four different adsorption structures for two F atoms on a 4  4 h-BN sheet, which are ortho- and paradimer as well as the NN1 and NN3, respectively. (b) Energy differences between NN1 and orthodimer sheets, as well as between NN3 and orthodimer sheets as functions of carrier density, m. The orthodimer sheet becomes the NN1 sheet when m < 3.7  1013 cm 2.

charge neutrality level with a uniform jellium countercharge. Dipole correction to the total energy is considered in the calculations.31 The distances between two adjacent BN sheets or nanotubes were held to at least 12 Å to eliminate interactions between them. The Brillouin-zone integration was sampled by up to 20 special k points. The structures were fully relaxed using the conjugate gradient method until the force on each atom was less than 0.01 eV/Å. The minimum energy path (MEP) was mapped out using the climbing image-nudged elastic-band method.32,33 Fluorination Configuration Control. First, we use the monolayer h-BN sheet as a prototype system for demonstration of the carrier control of fluorination. In an h-BN sheet, an N atom is negatively charged while a B atom is positively charged. A single F atom will exclusively bond with the B atoms and is unstable when bonding with N atoms due to their high Pauli electro-negativities that cause a strong repulsion between them, in line with previous calculations.13,14 Concomitant with this adsorption, localized hole states are created on N atoms around the fluorinated B atom,25 and hence, the reaction activity of these N atoms is remarkably enhanced, making them also favorable to chemisorb an additional F atom. Consequently, there are a number of possible structures for two F atoms to be chemisorbed on an hBN sheet. These structures can be categorized into two groups. The first one is the dimer group, in which the two F atoms are located on a B atom and a N atom of the BN sheet, respectively. Here, we only find two stable dimer structures, denoted as orthodimer and paradimer, respectively, as shown in Figure 1a. Another group is the NN group, in which the sheet has both of the F atoms on B atoms. We denote the sheet with two F atoms on two nearest-neighbor B atoms as the NN1 sheet and the sheet with two F atoms on two third-nearest-neighbor B atoms as the NN3 sheet (see Figure 1a). We also examine the NN2 (secondnearest-neighbor) sheet and find that its energy and properties are well between those of the NN1 and NN3 sheets, thus it is not addressed here for brevity. It is shown that all the sheets belonging to the dimer group are electrically insulating, while all the sheets in the NN group are metallic and magnetic, with the magnetic moment being inversely proportional to the distance between two F atoms.25 For example, the NN, NN2, and NN3 sheets have magnetic moments of 1.5, 1.0, and 0.2 μB, respectively. On the other hand, as the paradimer sheet is less stable than the orthodimer sheet by up to 0.4 eV/supercell, we focus on

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studying the orthodimer, NN1, and NN3 sheets in the following discussion. Among the three structures, the orthodimer sheet is less stable than the NN1 and NN3 sheets by 0.086 eV/supercell and 0.149 eV/supercell, respectively, consistent with existing results of F adsorption on BNNTs14 and in contrast to the H adsorption on graphite.34 In what follows, we propose a strategy to tune the energy difference between the sheets of dimer and NN groups using carrier doping with the view that the local charge states can significantly affect the formation of the F N bond, so that the fluorination pattern can be amenable for control. The level of doped carriers per h-BN area is expressed as m (cm 2), and the positive and negative values represent hole and electron doping, respectively. Figure 1b shows the energy differences between the NN1 and orthodimer sheets, ENN1 Eortho, as well as between the NN3 and orthodimer sheets, ENN3 Eortho, as functions of m. Since the NN1 and NN3 sheets have close levels of energies and similar properties under different m, the following focuses on comparing the NN1 sheet with the orthodimer sheet. It is shown that ENN1 Eortho decreases rapidly with more negative carrier density, indicating that the stability of NN1 sheet quickly enhances compared to that of the orthodimer sheet. Especially, when m e 3.7  1013 cm 2, which corresponds to half electrons added to the large supercell, the F N bond in the orthodimer sheet is spontaneously broken, and the orthodimer sheet evolves into the NN1 sheet, evident by the fact that they have the same energy. These results indicate that a selfassembly fluorination with uniform B atoms appears when the system is doped with electrons. On the other hand, ENN1 Eortho linearly increases with increasing hole density. In particular, when m is over 3.7  1013 cm 2, the orthodimer sheet becomes the most energetically stable structure, while the NN3 sheet gradually becomes the most unfavorable. Therefore, the F atoms prefer to bind on a pair of joint B and N atoms alternately, forming an orthodimer upon hole doping. Since the properties of the orthodimer sheet are strikingly different from those of NN group sheets, such carrier-tunable chemisorption promises potential applications. To see how the fluorination is controlled by carriers, we examine the electronic structures of the three sheets by showing their total spin-unpolarized density of states in Figure 2a. Both the NN1 and NN3 sheets are metals with partially filled bonding states around the Fermi level, which are from the pz orbitals of N atoms around the fluorinated B atoms. In this case, doped electrons will preferentially fill these states and give a large energy gain from this bond-state filling (see Figure 2c). In contrast, the orthodimer sheet is insulating, similar to the pristine BN sheet, but within the band gap there is a deep, localized state, contributed by the F N antibonding state. The doped electrons in the orthodimer sheet will therefore occupy the localized state and reside on the N and the joint F atoms (see Figure 2d). This electron filling significantly enhances the repulsion between the F and N atoms and hence stretches the F N bond (Figure 2b). The enhanced repulsion is corroborated by an analysis of the electron localization functions, which shows that as more electrons are doped, the F N bond in the orthodimer sheet increasingly weakens as its length increases (see insets of Figure 2b). This significantly reduces the orthodimer sheet’s stability. As the poorer stability of the orthodimer sheet is induced mostly from the elongated F N bond, the change in ENN1 Eortho is more remarkable at lower electron doping levels. The situation is changed for hole doping. Figure 2a shows that the valence band-top energy in the orthodimer sheet is higher than that of the NN1 and NN3 sheets, which is also found in spinpolarized density of states. Moreover, the electronic states 2169

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Figure 2. Mechanism for carrier-tunable fluorination on h-BN. (a) Total density of states (DOS) for the NN, NN3, and orthodimer sheets. The numbers in the label are the respective Fermi levels EF of these sheets, as indicated by the vertical lines. (b) Bond lengths of F B and F N bonds in the NN1 and orthodimer sheets as functions of carrier density, m. Insets in panel b are the calculated electron localization functions of the orthodimer sheet under the indicated carrier densities by arrows. (c,d) Isosurface ( 4 10 3 e/Å3) plots of carrier distribution within the NN1 (c) and the orthodimer (d) sheets at m = 2.2  1013 cm 2, with yellow and purple isosurfaces representing accumulation and depletion regions, respectively.

around the valence band top of the NN1 and NN3 sheets are partially filled, which further lowers the energy of their highest occupied level. Therefore, when hole doping is carried out, the markedly higher one-electron energy in the orthodimer sheet can make its total energy lower than that of the NN1 sheet. Since the hole-induced energy changes are almost all from this difference, the change in ENN1 Eortho with doped hole density is nearly linear and less pronounced than in the case of electron doping. Exactly, both the highest occupied and lowest unoccupied levels in the NN3 sheet are lowest in energy among the three sheets, which accounts for its lowest stability at high hole density and its highest stability at electron doping levels. In contrast to the case of electron doping, the changes in all F B and F N bond lengths are tiny in the hole-doping region, thus making a trivial contribution to relative stability. To show how robust this carrier-tunable behavior is, we added more F atoms within the same supercell to increase the fluorination concentration. For three F atoms in the supercell, the results show that they prefer to form an orthodimer structure plus a singly fluorinated B atom nearby upon the hole doping, leaving a N atom in the vicinity of the singly fluorinated B atom as a radical site for fixing a subsequent F atom, whereas under electron doping, the three F atoms are still energetically highly favorable to uniformly bond with three B atoms, and the self-assembly transition also occurs when m < 8.9  1013 cm 2. Having more F atoms in the supercell will not change any conclusions on the trend and mechanism of carrier-controllable chemisorption, featuring a very robust phenomenon. Fluorine Diffusion Control. Next, we turn to examine the diffusion of F atoms on the h-BN sheet. The diffusion barrier for an isolated chemisorbed F atom is calculated to be 1.08 eV, smaller than the desorption barrier of 1.96 eV. A similar situation is also found for two chemisorbed F atoms, for which the desorption barriers are 2.0 eV higher. This implies that the chemisorbed F atoms will diffuse rather than desorb upon

Figure 3. Carrier-controllable fluorine diffusion on an h-BN sheet layer. (a) Calculated MEPs for an F atom diffusing from the NN1 sheet to the orthodimer sheet under different carrier densities, m. The numbers on the right side are respective carrier densities in units of 1013 cm 2. Insets I and II illustrate the isosurface plots of carrier density distributions in the transition states TS of MEP at m = 0.7  1013 cm 2 and 8.9  1013 cm 2, respectively. The isosurface values are 0.004 and 0.01 e/Å3, respectively. (b) Calculated MEPs for an F atom diffusing from the NN1 sheet to the paradimer sheet and finally to the NN2 sheet under different carrier densities, hurdled by two transition states TS1 and TS2.

heating. Therefore gaining insight into the kinetics control of fluorination is also beneficial to applications. It is of great interest that the F diffusion is highly tunable by adjusting carrier density as well. Figure 3a presents the MEP for an F atom diffusing from the NN1 to the orthodimer phase under different m. In the 2170

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The Journal of Physical Chemistry Letters neutral case, the F atom hits a barrier at 0.59 eV in the MEP and 0.51 eV in the reverse path, both smaller than the desorption barrier of 2.07 eV, which renders the NN1 and orthodimer sheets into two bistable structures. Previous GGA calculations have obtained barriers of 0.47 and 0.73 eV for carbon35 and oxygen36 atoms diffusing on graphene, respectively, close to the barriers obtained here. These comparisons, to some extent, validate our LSDA results. When doping electrons, the energy barrier from the NN1 sheet to the orthodimer sheet increases but rapidly decreases in the reverse path, making the NN1-to-orthodimer path the more favorable reaction. At m = 3.7  1013 cm 2, the energy barrier in the MEP from the NN1 sheet to the orthodimer sheet even disappears, and the orthodimer sheet is dynamically not allowed under such carrier density. By contrast, hole doping reduces the NN1-to-orthodimer energy barrier and increases the reverse energy barrier, rendering the orthodimer-to-NN1 reaction to gradually become unfavorable. At m = 8.9  1013 cm 2, the NN1-to-orthodimer energy barrier decreases to 0.46 eV, remarkably lower than the energy barrier of 0.6 eV for the orthodimer-to-NN1 path. This effect also enhances with increasing m, and the NN1 sheet becomes dynamically unlikely at sufficiently high hole density. In particular, the orthodimer-toNN1 barrier is up to 0.27 eV higher than the NN1-to-orthodimer barrier when m = 14.8  1013 cm 2, which allows the filtering of the NN1 sheet by an annealing process. To understand the carrier-tunable diffusion, we plot the distributions of doped carriers in the transition states at m = 0.7 and 8.9  1013 cm 2, as illustrated by insets I and II in Figure 3a, respectively. In both transition states, the diffused F atom occupies a bridge site over a B N bond and bonds with both the underlying B and N atoms. In this case, the doped electrons are found to mostly reside on the diffused F atoms and on the destined N atom in the transition state at m = 0.7  1013 cm 2, thus enhancing the repulsion between the two atoms. This rapidly raises the energies of the transition and final states relative to the NN1 sheet, and hence increases the NN1-to-orthodimer energy barrier. By contrast, at m = 8.9  1013 cm 2, the joint F and N atoms partially contribute depleted electrons, so the repulsion between them is alleviated, because both the F and N atoms are originally negatively charged. The alleviated repulsion lowers the energy of the transition state and reduces the barrier of diffusion from the NN1 to the orthodimer sheet. Nevertheless, the energy of the orthodimer sheet is reduced more rapidly than the transition state because more depleted electrons are contributed by the F N bond in the orthodimer sheet. This causes a slight increase in the orthodimer-to-NN1 barrier. In order to achieve a full understanding of fluorine diffusion on the h-BN sheet, we further calculate the MEP for an F atom diffusing from the NN1 sheet to the NN2 sheet, with the paradimer sheet as the intermediate state. The results are shown in Figure 3b. We find that the influence of carriers on the barrier is essentially maintained for a F atom diffusing from the NN1 sheet to the NN2 sheet. At the neutral case, the barrier throughout the entire MEP is 0.7 eV, which is reduced to 0.51 eV at m = 8.9  1013 cm 2 while increased to 0.96 eV at m = 2.2  1013 cm 2, consistent with the trend shown in Figure 3a. These results agree to support that the F atoms more easily diffuse upon hole doping but are pinned more tightly upon electron doping, in stark contrast to the carrier dependence for oxygen diffusion on graphene.36 We can estimate the diffusion coefficient using the equation D = νd02 exp( ε/kBT)/4,37 where ε is the diffusion barrier, ν is the attempt frequency, d0 is an elementary length for

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Figure 4. Carrier-controllable fluorination on a (10,0) BNNT. (a) Atomic configurations of NN1, NN5, and orthodimer sheets for two F atoms chemisorbed on the tube. (b) Energy differences between the NN1 and orthodimer nanotubes as well as between the NN5 and orthodimer nanotubes as functions of carrier density, m. The orthodimer nanotube becomes the NN1 nanotube when m < 1.85  1013 cm 2, as evidenced by the zero energy difference between them.

diffusion, kB is the Boltzmann constant, and T is the absolute temperature. At T = 300 K, the estimated diffusion coefficient for F atom is increased by up to 5 orders of magnitude at m = 2.2  1013 cm 2 while it is decreased by 3 orders of magnitude at m = 8.9  1013 cm 2. These results implicate a feasible route to control the fluorination dynamics on h-BN structures. The Case in BNNTs. This carrier-tunable behavior is not unique to the BN sheet but also appears in BNNTs. We perform the same calculation for two F atoms chemisorbing on a (10,0) BNNT, and the corresponding structures are denoted as NN, NN5, and orthodimer nanotubes. The results show that the carrier controllable fluorination is robust to changes in BN curvature as shown in Figure 4, where the relative energetic changes are very similar to those shown in Figure 1b. The different behavior here is that the carrier-tunable fluorination is more sensitive than that on the planar BN sheet, and the selfassembly fluorination can be realized at desirably lower carrier concentrations. This is attributed to the smaller fluorination concentration in the tube and the larger tube wall area induced by the curvature. The study of F diffusion on the BNNT further confirms the carrier-tunable chemical behavior, despite the generally higher diffusion barrier than that on the planar BN sheet. Another distinct feature is that both the NN1 and NN5 nanotubes have robust magnetic ground states, in contrast to the insulating orthodimer nanotube and also different than the nearly nonmagnetic NN3 sheet. This is because the quantum confinement effect in BNNTs makes the near-gap electronic states more localized, so that all NN group nanotubes own spontaneous magnetic ordering.25 Therefore, the carrier-driven structural transition offers the exciting prospect of switching the magnetism in fluorinated BNNTs. The Case for Hydrogenation. At this point, it is important to see whether similar controls on chemisorption still hold for hydrogen, since hydrogenation is also a routine method to modify hBN structure’s properties. To clarify this point, we use a 4  4 BN supercell plus two H atoms and perform the same calculations as above, with the results presented in Figure 5. We also denote the corresponding hydrogenated h-BN sheet as NN1 and orthodimer sheets, and they are the most stable structures in their respective groups. In this case, the orthodimer sheet is outstandingly more stable over the NN1 sheet by 2.54 eV/supercell in the neutral state. Even the paradimer sheet is 2.08 eV more stable than the 2171

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Figure 5. Carrier-controllable hydrogenation on the h-BN sheet. Energy differences between the NN1 and the orthodimer sheets as well as between the NN1 and the paradimer sheets are shown as functions of carrier density, m. The NN1 sheet is energetically unfavorable when m > 3.1  1013 cm 2.

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It is exciting that the F chemisorption on the bolstered BN sheet is even controllable by the bias-driven carrier doping (see Figure 6). This bias control of chemisorptions can therefore be remarkably augmented by adopting better gate structures. Alternately, carrier doping of h-BN can also be realized via tunneling electrons from the scanning tunneling microscope (STM) tip by exerting electric voltage pulse. Electron injection from the STM tip into the adsorbed CO2 molecules has been demonstrated to induce the dissociation of CO2.41 In summary, we present strong first-principles evidence of a carrier-controllable functionalization on BN nanosheets and nanotubes. Doping electrons make the adatoms uniformly locating on B atoms, while ,alternatively, doping the hole carrier favors the adatoms to form the orthodimer structure on the h-BN. Furthermore, carrier doping is also an efficient route to control the barrier of adatoms’ diffusion on these BN structures, rendering carrier-switchable reaction kinetics. Our findings provide a viable route to yield controllably functionalized BN materials and may provide new opportunities for exploiting h-BN to design versatile devices, including electric and magnetic switches, sensors, and other bistable elements.

’ ASSOCIATED CONTENT

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Figure 6. Bias control of fluorination on the h-BN sheet. (a) Atomic configurations of the NN1 and orthodimer structures for two F atoms on a bilayered 4  4 h-BN sheet. (b) Energy difference between the NN1 and orthodimer sheets as a function of the applied bias voltage. Negative electric field direction is shown by the big arrow in the inset.

NN1 sheet. This is ascribed to the low Pauli electronegativity of hydrogen so that the repulsive interaction between the H and N atoms is alleviated to allow the highly stable dimer structures. Doping holes in the system increases ENN1 Eortho and ENN1 Epara to further stabilize the orthodimer and paradimer sheets. In contrast to the case of fluorination, the NN1 sheet, which is magnetic, spontaneously evolves into the orthodimer sheet with an insulating property when the hole density is over 3.1  1013 cm 2. On the other side, ENN1 Eortho and ENN1 Epara are reduced rapidly with doping electrons and the NN1 sheet starts to become the ground state structure when m < 6.1  1013 cm 2 (see Figure 5). Another different behavior here is that the changes in ENN1 Eortho and ENN1 Epara are much more pronounced than those shown in Figure 1b for fluorination. The mechanism for this controllable hydrogenation is due to the carrier-dependent stability of the H N bond, which has higher bond energy than the F N bond and thus behaves more rigidly. Similar carrier-induced control is also observed in hydrogenated BNNTs. Finally, we should point out that the carrier densities we studied are desirably low compared to previous studies36,38 40 and the carrier doping is easily realized in reality, e.g., by using a field-effect transistor structure, electrochemical doping or other charge-transfer dopants. For example, a carrier density of 7.42  1013 cm 2 has been accessible with the most common gates.40 To further demonstrate this ease, we place the BN sheet on an hBN substrate and then apply a bias voltage to dope the BN sheet.

Supporting Information. The dependence of energy differences of different structures on carrier density for three and four F atoms on a 4  4 h-BN sheet; the dependence of energy differences of different structures on carrier density for two F atoms on a bilayered 4  4 h-BN sheet are collected; band structures of the NN1 and orhodimer structures. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (Z.Z.); [email protected] (W.G.).

’ ACKNOWLEDGMENT This work is supported by the 973 Program (2007CB936204), National NSF (10732040, 91023026), and Jiangsu Province NSF (BK2008042) of China. Z.Z. is also supported by the NUAA Research Initiative for New Staff (4015-YAH10043). ’ REFERENCES (1) Pauli, T. K.; Bhattacharya, P.; Bose, D. N. Characterization of Pulsed Laser Deposited Boron Nitride Thin Films on InP. Appl. Phys. Lett. 1990, 56, 2648–2650. (2) Dana, S. S. The Properties of Low Pressure Chemical Vapor Deposited Boron Nitride Thin Films. Mater. Sci. Forum 1990, 54 55, 229–260. (3) Golberg, D.; Bando, Y.; Huang, Y.; Terao, T.; Mitome, M.; Tang, C.; Zhi, C. Boron Nitride Nanotubes and Nanosheets. ACS Nano 2010, 4, 2979–2993. (4) Rubio, A.; Corkill, J. L.; Cohen, M. L. Theory of Graphitic Boron Nitride Nanotubes. Phys. Rev. B 1994, 49, 5081–5084. (5) Chopra, N. G.; Luyken, R. J.; Cherrey, K.; Crespi, V. H.; Cohen, M. L.; Louie, S. G.; Zettl, A. Boron Nitride Nanotubes. Science 1995, 269, 966–967. (6) Novoselov, K. S.; Geim, A. K.; Morozov, S. V. Two-Dimensional Atomic Crystals. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10451–10453. 2172

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