1568
J. Phys. Chem. B 1998, 102, 1568-1570
First-Principles Simulations of Endohedral Bromine in BC3 Nanotubes R. A. Jishi Department of Physics and Astronomy, California State UniVersity, Los Angeles, California 90032
C. T. White and J. W. Mintmire* Chemistry DiVision, NaVal Research Laboratory, Washington, D.C. 20375-5342 ReceiVed: September 16, 1997; In Final Form: December 19, 1997
Using first-principles calculations, we investigate the stability of composite systems consisting of BC3 nanotubes with a linear chain of bromine atoms inside. For the BC3 (n,n) nanotubes considered here (n ) 2, 3, 4), we find that the binding energy per bromine atom exceeds its corresponding value in solid, liquid-phase, or gas-phase bromine. Charge transfer from the BC3 nanotube to the bromine chain results in hole pockets in the valence σ bands of the BC3 wall.
The synthesis of carbon nanotubes1-4 and the subsequent filling of their hollow cores with different types of materials5-14 have opened the way for potential applications in nanoelectronics. External doping of carbon nanotubes with K and Br has recently been shown to induce conductivity enhancements in these materials.15 In addition to carbon nanotubes, other types of nanotubes such as BN,16,17 BC3,18 BC2N,18,19 and MOS220 have been synthesized. The boron-containing nanotubes are predicted to behave as semiconductors over a large range of diameters and chiralities21-24 and might thus constitute a suitable class of materials for nanoelectronics technology. In particular, the potential filling or doping of these nanotubes with different kinds of materials might provide a mechanism for controlling their electronic properties. Dujardin et al.12 have suggested that materials with low surface tension in the liquid state will be readily incorporated inside carbon nanotubes.12 Such materials should also fill other kinds of nanotubes, although no experimental data are yet available on such filling processes. In this paper we undertake a theoretical study of the filling of BC3 nanotubes with bromine. The structure of BC3 nanotubes can be understood with reference to Figure 1, which shows the proposed honeycomb structure for the two-dimensional (2D) BC3 sheet,25 in which the B-C nearest-neighbor distance is 0.155 nm and the C-C nearest-neighbor distance is 0.142 nm. The 2D lattice is hexagonal with fundamental lattice vectors R1 and R2, with the resulting translational lattice vectors of the form nR1 + mR2. As in the carbon nanotubes, the proper boundary conditions around the cylinder can only be satisfied if one of these Bravais lattice vectors maps to a circumference around the cylinder.1,26 Thus by rolling the sheet so that two points on the sheet separated by a lattice vector (n, m) coincide, we obtain the nanotube denoted by BC3(n, m). Other workers have previously carried out first-principles calculations for the BC3(2, 2) nanotube, as well as tight-binding calculations for BC3(n, n) nanotubes with n ) 3, 4, and 5.24 These earlier calculations indicate that the BC3 nanotubes are narrow-gap semiconductors with a band gap of about 0.2 eV. The low-lying conduction bands have π and π* character, while the uppermost valence bands have σ character. This earlier * Corresponding author.
Figure 1. Honeycomb structure of the BC3 sheet with primitive translational lattice vectors R1 and R2.
work24 speculated that the introduction of halogen atoms into the nanotubes, possibly induced by capillary effects,12 would introduce holes into the valence bands resulting in a large conductivity. In this work we consider, from a theoretical point of view, the effects of filling BC3 nanotubes with bromine. In particular, we consider the conditions for the stability and electronic structure of the composite system Br-BC3(n, n), consisting of a BC3 nanotube with a Br chain along the nanotube axis. The calculations were carried out using a first-principles, allelectron, self-consistent local-density functional method in which the total energy and electronic structure are obtained using local Gaussian-type orbitals within a one-dimensional band structure approach.27,28 As in the carbon nanotubes,29 the BC3 nanotubes generally have a screw symmetry operation that permits the use of a smaller unit cell size than that needed using translational symmetry. We can define the screw operation S(h, φ) in terms of a translation h units down the z-axis in conjunction with a right-handed rotation φ about the z-axis. Because the symmetry group generated by the screw operation S is isomorphic with the one-dimensional translation group, Bloch’s theorem can be
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Endohedral Bromine in BC3 Nanotubes
J. Phys. Chem. B, Vol. 102, No. 9, 1998 1569 TABLE 1: Binding Energies per Bromine Atom in Pure Bromine and Br-BC3(n, n) Composite Systemsa system Br (solid) Br (chain) Br-BC3 (2, 2) Br-BC3 (3, 3) Br-BC3 (4, 4)
diameter (nm)
Eb (eV)
0.567 0.851 1.135
1.22 1.14 0.68 1.47 1.12
a The binding energy for the solid bromine system is the experimental value of the binding energy per bromine atom in solid bromine (ref 35); the binding energy for the chain bromine system is the calculated binding energy per atom in an isolated linear chain of bromine atoms at the same spacing as the composite systems.
Figure 2. Strain energy per BC3 stoichiometric unit (solid line) and the band gap (dashed line) in BC3 nanotubes as a function of nanotube diameter. The solid line for the strain energy is inversely proportional to the square of the diameter, while the dashed line for the band gaps is only a guide for the eye.
generalized so that the one-electron wave functions will transform under S according to
Smψi(r; κ) ) eiκmψi(r; κ)
(1)
where the quantity κ is a dimensionless quantity that is conventionally restricted to a range of -π < κ e π, a central Brillouin zone. For the BC3(n, n) nanotubes, this helical operation will be given by h ) 0.257 nm and a helical twist angle of pπ/n, where p is any odd integer. Using this helical symmetry for the (n, n) nanotubes, we can define a unit cell that contains 8n atoms; this is half the size of the conventional translational unit cell. By exploiting this helical symmetry, our method of calculation makes it feasible to carry out the calculations reported here. We have used 7s3p basis sets for carbon and boron, each basis set consisting of seven uncontracted s and three uncontracted p-type Gaussian orbitals; for bromine we used a similar quality 13s9p5d uncontracted basis set. The calculated strain energy per BC3 unit cell for the BC3(n, n) nanotubes (n ) 2, 3, 4) is plotted in Figure 2. The strain energy per unit cell for these nanotubes is found to vary inversely with the square of the nanotube diameter, consistent with earlier first-principles and empirical results for carbon nanotubes and with firstprinciples calculations for the (3, 0), (4, 0), and (2, 2) nanotubes. These nanotubes are found to be narrow-gap semiconductors with energy gaps that increase with increasing diameter, as shown in Figure 2. We have constructed a composite Br-BC3(n, n) system using a linear chain of evenly spaced bromine atoms aligned along the nanotube axis. Choosing a lattice constant for the Br chain to be 0.257 nm allows us to retain the helical symmetry of the nanotube; this distance is only slightly longer than our calculated equilibrium separation in the bromine dimer of 0.247 nm. Consequently the helical unit cell of the composite system consists of one bromine atom, 2n boron atoms, and 6n carbon atoms. For an isolated linear chain of bromine atoms with a lattice spacing of 0.257 nm, our calculations yield a binding energy of 1.14 eV per bromine atom relative to atomic bromine. For the composite systems studied, the binding energy per bromine atom of the composite was calculated as the difference of the total energy per helical unit cell of the composite system minus the sum of the total energies of the helical unit cell of BC3(n, n) and an isolated bromine atom. The results shown in Table 1 indicate that the composite system Br-BC3(3, 3) is
Figure 3. Calculated electronic band structures for (a) Br-BC3(3, 3) composite system, (b) BC3(3, 3) nanotube, and (c) linear chain of bromine atoms. The levels have been shifted so that the Fermi level of the BC3(3, 3) nanotube is zero; in all three systems the dotted line denotes the Fermi energy.
stable with a binding energy per bromine atom that exceeds the corresponding value in solid bromine by a considerable amount. The Br-BC3(2, 2) system is unstable because of the small diameter of the nanotube, while the Br-BC3(4, 4) nanotube is unstable in the conformation that we considered because of the negligible interaction between the bromine atoms and the nanotube wall. This latter composite system might, however, be stable in an optimized geometry in which the bromine chain is displaced from the nanotube axis and the separation between bromine atoms is allowed to vary. The calculated electronic band structures for the most stable composite system Br-BC3(3, 3), for the BC3(3, 3) nanotube, and for the isolated bromine linear chain are depicted in Figure 3. The band structure for the bromine chain shows a wide σ band that crosses the Fermi energy, along with a doublydegenerate π band that contains a small pocket of holes. The band structure for BC3(3, 3) indicates that it is a semiconductor with an energy gap of 0.36 eV. We note that this apparently indirect gap results from using a helical unit cell that is half the size of the translational unit cell. The corresponding Brillouin zone for a unit cell using translational symmetry can be obtained from these results by folding the bands into a Brillouin zone half the size. Using translational symmetry then both the highest occupied and lowest unoccupied band states
1570 J. Phys. Chem. B, Vol. 102, No. 9, 1998 would occur at the Brillouin zone center, and the material would have a direct gap. As we have noted for carbon nanotubes,30 the optical absorption spectra using a polarized light source would be expected to be anisotropic with respect to the relative orientation of the nanotube axis and the direction of polarization. The band gap of 0.36 eV would be the threshold for optical absorption using light polarized perpendicular to the nanotube axis; for polarizations parallel to the nanotube axis the threshold should occur at an energy of 0.55 eV, corresponding to the gap at κ ) 0 in Figure 3b. The electronic band structure of Br-BC3(3, 3) shown in Figure 3a indicates that the bromine acts as an electron acceptor as revealed by the presence of hole pockets at the Brillouin zone center; comparison with Figure 3b shows that two bands containing holes can be identified with the BC3 nanotube bands. Using a Mulliken population analysis, about 0.13 electron charges are transfered to each bromine, which is comparable to the corresponding value of 0.11-0.17 in graphite-bromine intercalation compounds.31-34 The hole mass mh in the uppermost valence band is 0.35 m0, where m0 is the free electron mass. The evolution of the bromine-derived bands can be seen by inspection of Figure 3. The wider-bandwidth σ-type conduction band is not appreciably affected by the interaction with the BC3(3, 3) nanotube, while the π-like narrower band in Figure 3c is now completely below the Fermi energy in the composite, having donated all its holes to the BC3(3, 3) nanotube bands. We note that the band structure for the bromine linear chain was generated using the same helical symmetry used for the Br-BC3(3, 3) and BC3(3, 3) systems. For a linear chain of atoms, of course, translational symmetry could be used for the same unit cell size and would result in a band structure diagram where the π band ranging from roughly -1 to -3 eV would be flipped in the figure from left to right. We note that we have not attempted to optimize the geometry of the composite system by varying the separation between adjacent bromine atoms or by considering possible dimerization along the bromine chain. The separation between the bromine atoms is dictated by computational needs, for otherwise the unit cell of the composite system would contain an impracticably large number of atoms. The fact that the total energy of the Br-BC3(3, 3) composite is considerably lower than the sum of the energies of the nanotube and isolated Br2 molecules indicates that if any dimerization occurs along the Br axis, it will be weak. Strong dimerization would inhibit charge transfer between the chain and the nanotube wall; this in turn would raise the total energy of the composite system. A weak dimerization will occur if it leads to further reduction in the total energy and thus further increase in the stability of the composite system. Our conclusions concerning the stability and the existence of holes in the nanotube-derived bands would still hold. In summary, we have presented a theoretical study of composite systems consisting of a linear chain of bromine atoms inside BC3 nanotubes. We find that the system Br-BC3(3, 3) is stable with a binding energy per Br atom that exceeds the corresponding value in solid bromine. The electronic band structure of Br-BC3(3, 3) reveals the existence of free electrons along the bromine chain and free holes along the nanotube wall, leading to a potentially highly conductive composite system.
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