Theoretical Study of Boron Nitride Nanotubes with Defects in Nitrogen

College of Liberal Arts, Jeonju UniVersity, Hyoja-dong, Wansan-ku, Chonju,. Chonbuk 560-759, Republic of Korea. ReceiVed: NoVember 30, 2005; In Final ...
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J. Phys. Chem. B 2006, 110, 4621-4628

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Theoretical Study of Boron Nitride Nanotubes with Defects in Nitrogen-Rich Synthesis Hong Seok Kang* College of Liberal Arts, Jeonju UniVersity, Hyoja-dong, Wansan-ku, Chonju, Chonbuk 560-759, Republic of Korea ReceiVed: NoVember 30, 2005; In Final Form: January 14, 2006

On the basis of calculations using the density functional theory, it is shown that BNNT synthesis could produce tubes deprived of one (B1 hole) or two (B2 hole) boron atoms under the condition where nitrogen atoms exist in excess throughout this study. The relative populations of various isomers of defective tubes will depend on the chirality of the tube. Interestingly, calculations show that B2 holes are much more favored than B1 holes, particularly in armchair tubes. Electronic properties are modified in such a way that the band gap is decreased through the introduction of defect states inside the gap. Magnetic properties will also be dependent on the chirality. The majority of armchair tubes with B2 holes will be nonmagnetic, while the majority of zigzag tubes with defects will exhibit magnetism. Contrary to the case of defect-free BNNT, the defective tubes are expected to be easily subject to reduction by accommodating excess electrons in the presence of Li atoms. In addition, the defect sites will show a higher affinity toward hydrogenation than the defect-free sites.

1. Introduction Because of the diverse electronic properties of carbon nanotubes (CNTs) depending upon the chirality1 and the difficulty of separating tubes of a desired electronic property from others, boron nitride nanotubes (BNNTs) have been considered as possible alternatives for them. In fact, BNNTs are wide gap semiconductors with band gaps nearly independent of diameter and chirality.2 Additionally, the electric polarization effect, due to the existence of two different kinds of atoms, may have optoelectronic applications.3 Furthermore, the large gap also provides BNNTs with excellent chemical stability. For example, the oxidative resistance of BNNTs is much more pronounced than that of CNTs.4 This chemical stability makes BNNTs potentially useful as nanoinsulating covers for embedded materials.5 However, this also implies that chemical functionalization is much more difficult for BNNTs than for CNTs. According to the author’s knowledge, there have been few reports regarding the functionalization of BNNTs other than in the area of fluorination.6 In view of the growing number of chemical derivatizations of CNTs and their applications to a variety of electronic devices, this can be a serious drawback. Since this problem is definitely related to the electronic structure of BNNT, it will be very useful if we can produce a well-defined method of modifying the electronic and chemical properties of BNNT. One possible way of doing this is to introduce defects. One of the most commonly observed defects is the (5,7,7,5) defect introduced by the Stone-Wales transformation under tensile strain. It was experimentally identified7 and found to be more stable than the (4,8,8,4) defect,8 even though it brings in unfavorable N-N bonds. A recent experimental and theoretical work proposed even fourfold and eightfold ring structures in kinks and bends.9 A radial deformation of BNNTs can change their band gaps, making them useful for optical devices.10 A theoretical study showed that vacancies, antisites, and substitutional impurities of BNNTs are also capable of changing their electronic structure.11 * [email protected].

On the basis of theoretical calculations, this work is devoted to the study of the nature of defects that can be formed in the synthetic condition where nitrogen atoms exist in excess while boron atoms are deficient. In reality, high N contents (B/N = 0.75) were experimentally found inside nanocages obtained from a BNNT synthesis utilizing a CNT template12 and BNNTs synthesized via a thermal chemical vapor deposition of B/B2O3 under the NH3 flow.13 In addition, this particular condition is easily satisfied in the synthetic method which uses laser heating of BN compounds in a diamond anvil cell due to the application of high nitrogen pressure.14 Another chemical vapor deposition process can also supply excess amounts of nitrogen in which the B-N-O precusor is pyrolized under an N2/NH3 atmosphere.15 In this work, we will make a systematic investigation of this kind of defects in (5,5) BNNT as well as (10,0) BNNT. In addition, we consider not only B1 holes but also B2 holes, i.e., the defect where two boron atoms are removed per supercell. We will show that B2 holes can be observed much more frequently than B1 holes from an energetic consideration. We will also show that electronic, chemical, and magnetic properties are modified by implementing defects in BNNTs of various chiralities. Furthermore, we will show that defect sites are easily hydrogenated. This is important in view of recent experimental findings that BNNTs can be used for hydrogen storage.16 In fact, collapsed BNNTs are found to exhibit a hydrogen uptake capacity (4.2 wt %) that is higher than any CNTs.16 An even higher uptake capacity (7.4%) is reached for graphite nanostructures prepared by mechanical alloying.17 This is mostly due to the adsorption of atomic or molecular hydrogens on the edges with dangling bonds and thus suggests that defect sites are useful for hydrogen storage. 2. Theoretical Methods Our total energy calculations are based on the solution of the Kohn-Sham (KS) equation within the generalized gradient approximation (GGA) of Perdew, Berke, and Ernzerhof (PBE).18 Calculations were done on an IBM-p690 parallel supercomputer

10.1021/jp056941l CCC: $33.50 © 2006 American Chemical Society Published on Web 02/18/2006

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TABLE 1: Various Parameters of B1-(5,5) BNNT and B1-(10,0) BNNT chiral index

(5,5)

(10,0)

∆Ed[B1] (eV)a µ (µB)b gap (eV)c ∆E[Li doping] (eV)d

0.40 1 0.95 -3.14

0.30 1 0.78 -3.71

a Energy change of the process [80 atoms of BNNT] + N f [79 atoms of BNNT with a B1 hole] + 2/80 [80 atoms of BNNT]. b Magnetic moment. c Band gap. d Energy change of the process B1BNNT + Li f [B1-BNNT]-Li.

with the Vienna ab initio Simulation Package (VASP)19 using the projected augmented wave (PAW) method20 with a large cutoff energy (400 eV). To optimize the structures, atoms were relaxed in the direction of the Hellmann-Feynman force using the conjugate gradient method, until the convergence criteria of 0.03 eV/Å is satisfied per atom. All of the valence electrons, as well as the 1s2 electrons of Li, are explicitly treated in the KS equation. All calculations were done with explicit consideration of spin polarization. A BNNT is represented by a supercell with 80 atoms (40 nitrogen and 40 boron atoms) for (5,5) and (10,0) tubes. Tube length is optimized by considering total energy as a function of the length. As a result, we find that the length, which is the size of the supercell along its X direction, is 10.1 and 8.7 Å for (5,5) and (10,0) BNNTs, respectively. Large vacuum space is allowed in the other two directions so that the nearest-neighbor distances between atoms in two supercells are larger than 7.00 Å. In the main body of the calculation, appropriate defects are introduced as described in the next section. k-space sampling is done with two points in the irreducible region of the first Brillouin zone along the tube axis (X). 3. Results We will first focus on a (5,5) BNNT with a B1 hole (B1BNNT) per supercell, where one boron atom is removed from the tube in a supercell. For the study of the B1 hole, we have calculated the energy change, ∆Ed[B1; (5,5)80], of the process [80 atoms of BNNT] + N f [79 atoms of BNNT with a B1 hole] + 2/80 [80 atoms of BNNT].21 This process corresponds to the participation of the boron atom, which does not take any part in the formation of a pristine tube, in the formation of a defect-free BNNT together with one of the atomic nitrogens which exist in excess. As shown in Table 1, the small positive value (0.40 eV) of ∆Ed(B1) indicates that the formation of a B1 hole is indeed energetically as favorable as that of the defectfree BNNT when nitrogen atoms exist in excess. Therefore, we can expect that the product of BNNT synthesis includes not only defect-free armchair BNNTs but also their correspondents with B1 holes. As shown in Figure 1, our structure optimization shows the formation of a (5,9) pair, i.e., a pair of five- and nine-membered rings, each exhibiting aromaticity due to its six or ten π electrons. N18 and N25 come closer to each other and form a bond between themselves, as manifested in the interatomic distance (1.51 Å) between them after geometry optimization. The bond length corresponds to a N-N single bond,22 and indeed, our analysis using the Gaussian 03 program23 with PBEPBE/6-31G(d) shows that the Wiberg bond index (WBI)24 between them is 0.98.25 In comparison to the geometry of the unrelaxed tube, there is a severe deformation in the geometry of the tube. Specifically, N4 protrudes from the circumference of the tube, while N18 and N25 subside in the tube. This phenomenon seems to be related to the reduction of an electron-

Figure 1. Optimized structure of B1-(5,5) BNNT in a supercell viewed along Z (a) and X (b) axes.

electron repulsion between a spin-unpaired sp2 electron of N4 with σ or π electrons between N18 and N25. To mention the magnetic property of the tube, the tube has a magnetic moment of 1 µB. Spin density is mainly concentrated on an undercoordinated nitrogen atom (N4) and perpendicular to the π electrons of the system. Interestingly, our band structure calculation shows that the tube is not a metal with a half-filled band, but a magnetic semiconductor with a band gap of 0.95 eV.26 (See also Table 1.) Considering that the defect-free (5,5) BNNT is an insulator with a band gap of 4.44 eV, the formation of a B1 hole is a useful way of modifying its electronic and magnetic properties. In view of the presence of an unpaired electron and the small band gap, we can also expect that the B1-BNNT could be easily reduced to a negative ion by accommodating one excess electron. In fact, the energy change (-3.14 eV) of the Li-doping reaction, B1-(5,5) BNNT + Li f [B1-(5,5) BNNT]-1-Li+1, is much more negative than the corresponding datum (-0.04 eV) involving the defect-free (5,5) BNNT. (See Table 1.) Moreover, this reaction does not require any activation barrier to surmount. In this reaction, there is a complete charge transfer from Li to the host tube, particularly to N4, converting the system to nonmagnetic. In short, the formation of a B1 hole drastically enhances the chemical reactivity of (5,5) BNNT with respect to reduction. We will next consider B2-(5,5) BNNT, i.e., (5,5) BNNT with two boron atoms removed. There are three isomers in the

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Figure 2. Eighty atoms of (5,5) BNNT in a supercell. Sites of boron atoms which can be removed are labeled with letters A-D.

TABLE 2: Various Parameters of B2-(5,5) BNNT and B2-(10,0) BNNT chiral index isomer

(5,5)

(10,0)

isomer isomer isomer 1 2 3

isomer isomer isomer 1 2 3

∆Ed[B2] (eV)a -3.74 µ (µB)b 0 gap (eV)c 3.09 ∆Eh(3)d -8.92

-3.69 0.70 -0.49 -1.19 0.52 0 2 0 2 2 3.31 0.95 2.10 0.69 0.78 -7.91 -12.24 -11.34 -7.76 -12.68

a Energy change of the process [80 atoms of BNNT] + 2N f [78 atoms of BNNT with a B1 hole] + 4/80 [80 atoms of BNNT]. b Magnetic moment. c Band gap. d Energy change of the process B2-BNNT + 3H2 f B2-BNNT-6H.

tube. In isomers 1 and 2, boron atoms in sites (A, B) and (A, C) are removed, respectively, in Figure 2. In isomer 3, two boron atoms, A and D, are absent on the opposite sides of the circumference of the tube. Table 2 shows that the energy changes ∆Ed[B2; (5,5)80] of the process [80 atoms of BNNT] + 2N f [78 atoms of BNNT with a B2 hole] + 4/80 [80 atoms of BNNT] are -3.74, -3.69, and 0.07 eV for isomers 1-3. In the presence of an excess amount of nitrogen atoms, therefore, all three B2 isomers can be produced at least as favorably as a defect-free BNNT. More importantly, isomers 1 and 2 should be produced as dominant products among all members of B2(5,5) BNNTs under a nitrogen-rich condition. Furthermore, B2 holes should be observed much more frequently than B1 holes. Therefore, all discussions for B2-BNNT will concentrate on these particular two isomers unless specified. As shown in Figures 3 and 4, their drastic stabilization can also be understood in terms of the formation of single bonds between pairs of adjacent nitrogen atoms, resulting in (5,8,5)-membered rings. In isomer 1, (N4, N18), (N4, N25), and (N7, N8) distances are 1.46, 1.46, and 1.49 Å, respectively.27 Similarly, (N11, N18), (N17, N18), and (N4, N25) distances are 1.48, 1.46, and 1.50 Å in isomer 2. Consequently, there are complete spin-pairings with zero net magnetic moments in the two isomers. In a sense, this can be considered an antiferromagnetic coupling of spins from two B1 holes. (In isomer 3, on the contrary, two isolated (6π,10π) systems are formed, resulting in a magnetic semiconductor with µ ) 2 µB. Therefore, separate B1 holes couple ferromagnetically to produce a large magnetic moment due to the locality of defect states.) There are deformations in the geometry of the B2-(5,5) BNNTs. Specifically, nitrogen atoms involved in the formation of eight-membered rings tend to subside in the tube. Interestingly, there are (6π,10π,6π) aromatic systems involving (5,8,5)membered rings. However, there are also antiaromatic rings involving (N4, N18, N25) and (N4, N8, N25) in isomers 1 and

Figure 3. Optimized structure of isomer 1 of B2-(5,5) BNNT in a supercell viewed along Z (a) and X (b) axes.

2, respectively. Considering that a 14π aromatic system is formed in isomer 1 when the N4-N25 bond is broken, we can conclude that stabilization from an N-N bond formation does more than compensate for the destabilization due to the formation of antiaromaticity. For this, we recall that the aromaticity of borazine is much weaker than that of benzene due to the polarity of B-N bonds.28 As shown in Table 2, band gaps (3.09 and 3.31 eV for isomers I and 2) are smaller than that of the defect-free (5,5) BNNT, coming to the optical region. Similarly to the case of B1-(5,5) BNNT, Figure 5 shows that this is due to the introduction of acceptor-like defect states inside the band gap, corresponding to π* orbitals of N-N bonds. Namely, two bands just below the Fermi level represent localized orbitals for the N7-N8 and N18-N4-N25 bonds of isomer 1 in ascending order. (Again, the formation of B2 holes is an effective way of modifying the electronic structure of armchair BNNTs.) The observed nature of localized π* states inside the band gap suggests that the (5,8,5)-membered rings could be much more reactive than nondefective sites. Indeed, our calculation shows that the doping of a Li atom on top of the eight-membered ring of isomer 1 is highly exothermic and experiences no activation barrier. In fact, the energy change (-2.87 eV) of the process B2-(5,5) BNNT + Li f B2-(5,5) BNNT-Li is comparable to that of the corresponding process involving B1-(5,5) BNNT.

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Figure 4. Optimized structure of isomer 2 of B2-(5,5) BNNT in a supercell viewed along Z (a) and X (b) axes. Figure 6. Hydrogenated isomers 1 (a), 2 (b), and 3 (c) of B2-(5,5) BNNTs in a supercell.

Figure 5. Band structure of isomer 1 of B2-(5,5) BNNT (right) in comparison to that of a defect-free (5,5 BNNT (left). For each of them, the Fermi energy is separately set to energy zero.

The reaction is accompanied by breaking the N7-N8 bond in Figure 3a, resulting in (5,11)-membered rings. In other words, the eight- and five-membered rings involving N7 and N8 merge into an eleven-membered ring after breaking the bond. In fact, the N7-N8 distance changes from 1.49 to 2.49 Å upon Li-doping. Our separate analysis shows that the strong binding of the Li atom can also be ascribed to the electrostatic interaction between Li+ and the negatively charged elevenmembered ring after the transfer of an electron from the 2s(Li) state to the ring.

It will be informative to investigate a hydrogenation process of B2-(5,5) BNNT + nH2 f B2-(5,5) BNNT-2nH to elucidate the fragility of the N-N bond. Thus, this paragraph will delve into the hydrogenation of 2n defect sites with n hydrogen molecules. For isomer 1, the energy [∆Eh(2) ) -6.47 eV] of the hydrogenation with two hydrogen molecules indicates that four nitrogen atoms (N4, N7, N8, and N25) are easily hydrogenated when hydrogen molecules are located ∼0.8 Å above them, resulting in the breaking of N4-N25, N7-N8, and H-H bonds. A similar argument holds for isomer 2. ∆Eh(2) for hydrogenation at sites N4, N17, N18, and N25 is -5.97 eV. Further hydrogenation is also energetically favorable. For example, two more hydrogen atoms can bind to N4 and N18 in isomer 1. In fact, Table 2 shows that the energies [∆Eh(3)] of hydrogenation with all three hydrogen molecules are -8.92 and -7.91 eV for isomers 1 and 2, respectively. (Figure 6 shows the hydrogenated isomers.) Therefore, the average energies of hydrogenation per H2 molecule are -2.97 and -2.63 eV for dominant isomers (isomers 1 and 2). Although these values are about half of the hydrogenation energy (-5.31 eV)

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Figure 7. Optimized structure of B1-(10,0) BNNT in a supercell viewed along the Z axis.

on graphite edges,17 they are still large enough to make the B2 holes useful for hydrogen storage. Even in the system when BNNTs are mechanically milled to generate dangling bonds, B2 holes will make an extra contribution to the hydrogen storage capacity. Meanwhile, isomer 3 has two isolated B1 holes. One of them is shown in Figure 1, where three N atoms (N4, N18, and N25) are reactive sites. We find that hydrogenation energy ∆Eh(3) is -12.24 eV, suggesting that isomer 3 could be much more reactive than other isomers. Although we have not made an explicit calculation, we should be able to expect that ∆Eh(1.5) for the hydrogenation of B1-(5,5) BNNT is about half of this value. For comparison, we investigate the hydrogenation of B2(5,5) BNNT as well as that of the defect-free (5,5) BNNT with one hydrogen molecule. We find that ∆Eh(1) for the N4-N25 bond of isomer 1 shown in Figure 3 is -1.73 eV. In the defectfree tube, the corresponding reaction energy is 0.89 eV for a pair of B-N atoms adjacent to each other along the direction perpendicular to the tube axis. Comparison of these two values shows that the N-N bond in the defective tube is more likely to be hydrogenated than the B-N bond in the defectfree tube. This time, we will look into B1-(10,0) BNNT, i.e., (10,0) BNNT with a B1 hole. Table 1 shows that its ∆Ed[B1; (10,0)80] is 0.30 eV, indicating that it is almost as favorable to form a B1 hole in (10,0) BNNT as in (5,5) BNNT. In the product of BNNT synthesis, there would approximately be the same amount of B1-(10,0) tubes as the defect-free (10,0) tube. As shown in Figure 7, there is formation of a N13-N14 single bond with a bond length of 1.47 Å, which results in a (5,9) pair and the change of magnetic moment from 0 to 1 µB. (The (5,9) defect in (10,0) BNNT was also considered by Schmidt et al. in ref 11.) In fact, the author’s separate analysis of spin density shows that the density is concentrated on N3, but not on N13 nor on N14, being oriented perpendicular to the π electrons of the system in accordance with the sp2 hybridization of N3. There is no appreciable deformation in the geometry other than the protrusion of N3 and N23 from the circumference of the tube by approximately 1.18 and 0.92 Å, respectively. Because of the introduction of localized defect states just below and above the Fermi level,29 the system is again a magnetic semiconductor with a band gap (0.78 eV) comparable to that (0.95 eV) of B1-(5,5) BNNT. (See Table 1.) Therefore, the system should be much more chemically reactive toward a reduction reaction. As a matter of fact, a large negative energy change (-3.71 eV) of the Li-doping reaction indicates this. (See also Table 1.)

Figure 8. Eighty atoms of (10,0) BNNT in a supercell. Sites of boron atoms which can be removed are labeled with letters A-D. In isomer 2 of B2-(5,5) BNNT to be described later, a nitrogen atom at the site E migrates to site C at which a boron atom is removed.

Here, we discuss the formation of B2-(10,0) BNNT, i.e., (10,0) BNNT with two boron atoms removed. We have also considered three isomers in Figure 8. In isomers 1 and 2, boron atoms in sites (A, B) and (A, C) are removed. In isomer 3, boron atoms (A, D), existing far from each other on the opposite sides of the circumference of the tube, are absent. Table 2 shows that the calculated values of the energy change ∆Ed[B2; (10,0)80] involving (10,0) BNNT are -0.49, -1.19, and 0.52 eV with magnetic moments of 0, 2, and 2 µB for isomers 1-3. Therefore, all isomers can be produced in amounts comparable to that of the defect-free tube. Particularly, isomer 2 should be produced as a major product. However, comparison of the energy change with ∆Ed[B2; (5,5)80] shows that the relative ease of a B2 hole formation is less pronounced than the (5,5) BNNT. Similarly to the case of B2-(5,5) BNNT, Figure 9a shows that there are three N-N single bonds in isomer 1, which lead to the formation of (5,8,5)-membered rings. As a result, the isomer is nonmagnetic. Bond lengths of N2-N12, N3-N13, and N13-N14 bonds are 1.66, 1.60, and 1.44 Å, respectively. Again, this can be related to the introduction of π* bands of the bonds inside the band gap, which are also responsible for the decrease in the band gap (2.10 eV) compared to that of the defect-free tube.30 Meanwhile, Figure 9b shows that there are no N-N bonds and thus no five-membered rings in isomer 2. In reality, there are three undercoordinated nitrogen atoms (N3, N13, and N14) and one undercoordinated boron atom (B12), resulting in the net magnetic moment of µ ) 2 µB. Calculation with the Gaussian 03 program shows that the N-N distances and Wiberg bond indices are (1.38 Å, 1.18) and (1.40 Å, 1.08) for N13N22 and N13-N23 bonds, respectively. N3-N14 (2.45 Å) and N13-N14 (2.97 Å) distances do not allow bonding between corresponding atoms. Regarding the discussion of magnetic properties of this system, the geometrical feature does not allow N-N bond formations, resulting in the ferromagnetic coupling of spins from two B1 holes. It is worth making a note that the magnetic property of B2-BNNT depends on its chiralty. Namely, the major isomer of B2-BNNT is magnetic for the (10,0) tube, while being nonmagnetic for the (5,5) tube. It is also interesting to note that N13, which was originally bonded to a boron atom (B12) between N2 and N12, migrates toward N22 and N23 by a distance approximately equal to the bond

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Figure 11. Another possible conformation of isomer 2 of B2-(10,0) BNNT in a supercell considered in this work.

Figure 9. Optimized structures of isomers 1 (a) and 2 (b) of B2(10,0) BNNT in a supercell. X axis is the tube axis.

conformation of isomer 2 discussed above. Therefore, the migration of N13 plays an important role in stabilizing isomer 2 more than any other factors such as N-N bonds. We have also studied hydrogenation of B2-(10,0) BNNTs at defective sites. Our calculation shows that ∆Eh(2), the energies of hydrogenation with two hydrogen molecules (-8.61 and -6.71 eV) for isomers 1 and 2, are comparable to those of B2-(5,5) BNNTs. In this process, we assume that hydrogenation occurs at N2-N12 and N3-N13 bonds in isomer 1, while it occurs at undercoordinated atoms (N3, N13, N14, and B12) in isomer 2. Further hydrogenation with one more hydrogen molecule is energetically favorable too, and Table 2 shows that ∆Eh(3) values are -11.34 and -7.76 eV for isomers 1 and 2. (See Figure 12 for hexahydrogenated isomers 1-3.) Isomer 3 also exhibits a very high affinity toward hydrogenation, as indicated by its ∆Eh(3) (-12.68 eV). For isomers 1 and 2, the average hydrogenation energy per H2 molecule is at least half of that on graphite zigzag edges,17 also indicating the possible application of B2 holes in hydrogen storage. 4. Conclusion

Figure 10. Band structure of isomer 2 of B2-(10,0) BNNT for spinup (left) and -down (right) states.

length of one B-N bond and forms bonds with them. In Figure 8, this migration corresponds to that of a nitrogen atom in position E to C, whose boron atom was removed. As shown in Figure 10, our band structure analysis shows that it is not a metal but a magnetic semiconductor with a band gap of 0.69 eV.31 (See also Table 2.) This is again related to the introduction of localized defect states (n ) 157-159) inside the band gap. Spin polarization is largely due to the filling of n ) 157 and 158 for spin-up states. The structure of isomer 3 is equivalent to a defective tube with two isolated B1 holes, where we also observe ferromagnetic coupling of spins from two B1 holes. It is possible that there are other conformations for each of isomers 1-3 with energies comparable to or lower than those considered above. This would be particularly true for isomer 2, since the introduction of N-N bonds can stabilize the entire structure of the tube. To investigate this possibility, we have calculated the energy of a conformation shown in Figure 11. However, it was found that the conformation is less stable by 0.91 eV. Even though it has an N13-N22 bond, it is less stable than the

In this work, we have shown that the BNNT synthesis could produce a mixture of defect-free tubes and tubes with B1 or B2 holes in the synthetic condition where nitrogen atoms exist in excess. The relative population of each of those B1 or B2 holes will depend on the chirality of the tube. Importantly, our calculation shows that B2 holes are much more favored than B1 holes, particularly in armchair tubes. Although there have been some studies which have showed the possibility of forming B1 holes in CNTs at the postsynthetic stage,32 the important role played by B2 holes has never been elucidated before, even for CNTs. More importantly, the defects investigated in this work are different from those generated by the energetic bombardment of electrons or ions32 on CNTs in that they can be generated at the time of synthesis. (This does not preclude the possibility of forming the holes in the postsynthetic stage.) They are also different from (5,7,7,5) or (4,8,8,4) defects which form a set of five-, seven-, seven-, five-membered or four-, eight-, eight-, four-membered rings in that the holes can be generated in the absence of mechanical strain. Meanwhile, CNTs with holes commonly observed at the time of synthesis are those with pyridinelike local structures33 rather than those with B1 holes with undercoordinated carbon atoms. This can be understood if we note that hole formations are not energetically favorable in the CNT synthesis (unlike in the case of BNNT synthesis), since all carbon atoms will prefer to be involved in the formation of defect-free CNTs rather than CNTs with holes.

Defective BNNTs from Nitrogen-Rich Synthesis

J. Phys. Chem. B, Vol. 110, No. 10, 2006 4627 as data storage, spin-FET (field effect transistor), and quautum computing.34 Furthermore, introduction of the holes will decrease the band gap of the system to the optical region, because of the appearance of localized defect states inside the band gap, serving as an effective way for modifying the electronic structure of BNNTs. This might also have applications in optoelectronics such as photovoltaic devices,35 photoconductors, and photodiodes. Upon the introduction of defects, chemical properties will also be modified. Contrary to the case of a defect-free BNNT, in the presence of Li atoms, those defective tubes are expected to be reduced by accommodating an excess electron without an experiencing activation barrier. In addition, hydrogenation with hydrogen molecules at defect sites is energetically highly exothermic, also manifesting the high reactivity of the sites. Practically, this may have implications in the hydrogen uptake of BNNTs through the hydrogenation of the tubes. The optimal uptake capacity will be achieved when the B2-BNNTs are subject to mechanical milling or heat treatment so that dangling bonds or other kinds of defects are also introduced. This is particularly interesting in view of the recent experimental findings that the high-temperature treatment of BNNTs16 or the mechanical alloying of graphite nanostructures17 enhances the hydrogen storage. Furthermore, the formation of B2 holes can allow small atoms and molecules to be easily inserted into BNNTs through large holes at defective sites. For example, our extensive calculation shows that the activation energy for the encapsulation of a hydrogen molecule in isomer 1 of B2-(5,5) BNNT through the eight-membered ring is at most 3.69 eV.36 In summary, defect formation is a useful way of modifying the electronic, magnetic, and chemical properties of BNNTs. Acknowledgment. We appreciate Jeonju University for financial support. We also would like to acknowledge the support from KISTI (Korea Institute of Science and Technology Information) under the 7th Strategic Supercomputing Applications Support Program. The use of the computing system of the Supercomputing Center is also greatly appreciated. References and Notes

Figure 12. Hydrogenated isomers 1 (a), 2 (b), and 3 (c) of B2-(10,0) BNNTs in a supercell.

In addition, the magnetic property of defective BNNTs will be dependent on their chiralities. The majority of B2 holes will not introduce magnetism in armchair tubes because of the spinpairing in N-N bonds, while the majority will show magnetism in zigzag tubes because such N-N bonds are not possible. According to our knowledge, this is the first report concerning the possible magnetism of BNNTs. We expect that this finding will stimulate the experimental investigations of magnetic properties of BNNTs. In addition, a large magnetic moment of (10,0) BNNTs with B2 defects, together with their high spin polarization near the Fermi level, can suggest that zigzag BNNTs are useful for a variety of areas of spin-based electronics such

(1) Harris, P. J. F. Carbon Nanotubes and Related Structures; Cambridge University Press: Cambridge, 1999. (2) Blase´, X.; Rubio, A.; Louie, S. G.; Cohen, M. L. Europhys. Lett. 1994, 28, 335. (3) Kral, P.; Mele, E. J.; Tomanek, D. Phys. ReV. Lett. 2000, 85, 1512. (4) Chen, Y.; Zou, J.; Campbell, S.; Caer, G. Appl. Phys. Lett. 2004, 84, 2430. (5) Rubio, A.; Miyamoto, Y.; Blase´, X.; Cohen, M. L.; Louie, S. G. Phys. ReV. B 1996, 53, 4023. (6) Tang, C.; Bando, Y.; Huang, Y.; Yue, S.; Gu, C.; Xu, F.; Goldberg, D. J. Am. Chem. Soc. 2005, 127, 6552. (7) Miyamoto, Y.; Rubio, A.; Berber, S.; Yoon, M.; Tomanek, D. Phys. ReV. B 2004, 59, 121413. (8) Bettinger, H. F.; Dumitrica, T.; Scuseria, G. E.; Yakobson, B. I. Phys. ReV. B 2002, 65, 041406. (9) (a) Bengu, E.; Marks, D. Phys. ReV. Lett. 2001, 86, 2385. (b) Moon, W. H.; Hwang, H. J. Phys. Lett. A 2004, 320, 446. (10) Kim, Y.-H.; Chang, K. J.; Louie, S. G. Phys. ReV. B 2001, 63, 205408. (11) Schmidt, T. M.; Baierle, R. J.; Piquini, P.; Fazzio, A. Phys. ReV. B 2003, 67, 113407. (12) Goldberg, D.; Bando, Y.; Sato, T.; Grobert, N.; Reyes-Reyes, M.; Terrones, H.; Terrones, M. J. Chem. Phys. 2002, 116, 8523. (13) Choi, H. C.; Bae, S. Y.; Jang, W. S.; Park, J.; Song, H. J.; Shin, H.-J. J. Phys. Chem. B 2005, 109, 7007. (14) Goldberg, D.; Bando, Y.; Eremets, M.; Takemura, K.; Kurashima, K.; Yusa, A. Appl. Phys. Lett. 1996, 69, 2045. (15) (a) Ishii, T.; Sato, T.; Sekikawa, Y.; Iwata, M. J. Cryst. Growth 1981, 52, 285. (b) Ma, R.; Bando, Y.; Sato, T. AdV. Mater. 2002, 14, 366.

4628 J. Phys. Chem. B, Vol. 110, No. 10, 2006 (16) (a) Ma, R.; Bando, Y.; Zhu, H.; Sato, T.; Xu, C.; Wu, D. J. Am. Chem. Soc. 2002, 124, 7672. (b) Tang, C.; Bando, Y.; Ding, X.; Qi, S.; Goldberg, D. J. Am. Chem. Soc. 2002, 124, 14550. (17) (a) Fukunaga, T.; Itoh, K.; Orimo, S.; Aoki, M.; Fujii, H. J. Alloy Compd. 2001, 327, 224. (b) Sha, X.; Jackson, B. J. Am. Chem. Soc. 2004, 126, 13095. (18) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (19) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, RC558. (20) Kresse, G.; Furthmuller, J. Phys. ReV. B 1996, 54, 11169. (21) We note that reactants exist as atomic species at high temperature (>1000 °C) usually achieved in synthetic condition. (22) Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry; HarperCollins: New York, 1993; p A-34. (23) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision B.05; Gaussian, Inc.: Pittsburgh, PA, 2003. (24) Wiberg, K, B. Tetrahedron 1968, 24, 1083. (25) This is clearly different from the argument given in ref 11, which states that the N18-N25 bond is a triple bond. An exchange-splitted oneelectron level inside the band gap is not a π orbital but a π* orbital between the N-N bond. Filling of its spin-up levels located below the Fermi level should contribute to the weakening of the bond. Our analysis shows that a similar argument holds for (10,0) BNNT. Without this, the N-N bond would be stronger.

Kang (26) This reflects the exchange splitting of the π* band appearing inside the band gap due to a strong localization of the electron density distribution. See also ref 25. (27) Our analysis using the Gaussian 03 program with PBEPBE/ 6-31G(d) shows that the Wiberg bond indices are 0.98, 0.99, and 0.99 for N7-N8, N4-N18, and N4-N25 bonds, respectively. k-space sampling was done using only Γ-point for this calculation. (28) Kiran, B.; Phukan, A. K.; Jemmis, E. D. Inorg. Chem. 2001, 40, 3615. (29) LUMO band represents a π* state of the N13-N14 bond. (30) One ()HOMO band) of the defect states corresponds a π* state of the N3-N13 bond, while another ()LUMO band) is a σ* state of the N2N12 bond. The band gap of this tube is the energy gap between the two bands. (31) For spin-up and -down, bands are filled up to n ) 158 and 156, respectively. (32) (a) Ajayan, P. M.; Ravikumar, V.; Charlier, J.-C. Phys. ReV. Lett. 1998, 81, 1437. (b) Zhu, Y.; Yi, T.; Zheng, B.; Cao, L. Appl. Surf. Sci. 1999, 137, 83. (c) Krasheninnikov, A. V.; Nordlund, K.; Sirvio, M.; Salonen, E.; Keinonen, J. Phys. ReV. B 2001, 63, 245405. (d) Rossato, J.; Baierle, R. J.; Fazzio, A.; Mota, R. Nano Lett. 2005, 5, 197. (33) Czerw, R.; Terrones, M.; Charlier, J.-C.; Blase´, X.; Foley, B.; Kamalakaran, R.; Grobert, N.; Terrones, H.; Tekleab, D.; Ajayan, P. M.; Blau, W.; Ruhle, M.; Caroll, D. L. Nano Lett. 2001, 1, 457. (34) Wolf, S. A.; Awschalom, D. D.; Burhman, R. A.; Daughton, J. M.; von Molnar, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Science 2001, 294, 1488. (35) As an example of the application of CNTs in the photovoltaic device, see Bhattacharyya, S.; Kymakis, E.; Amaratunga, G. A. J. Chem. Mater. 2004, 16, 4819. (36) In the calculation, a hydrogen molecule was assumed to approach the tube in a direction perpendicular to the plane of the eight-membered ring shown in Figure 3. The upper bound to the activation energy of hydrogen encapsulation was estimated from the curve of the total energy as a function of H2-tube distance, where the total energy at each distance was calculated from a constrained energy minimization. The correct activation barrier for the insertion should be smaller than the barrier calculated from this method.