Since the early times that carbon nanotube (CNT) was discovered by Iijima , the physical, chemical, and structural properties and applications of this material are investigated extensively [2–4]. The properties of CNTs are mostly dependent on the tubular diameter, doped atoms in the structure and chirality, which make their synthesis for the specific purposes difficult. Many studies are carried out in the investigation of stable structures of non-carbon-based nanotubes, among them boron-nitride nanotubes (BNNTs) have a great importance . The stable tubular structure of BNNT was initially found by calculations  and later was successfully synthesised . After this time, a large growing number of experimental and theoretical studies, specifically ab initio calculations on carbon-, silicon-, and germanium-substituted BN nanotubes are performed on the electronic structures of the BNNTs [8–11]. CNTs have conducting properties, but BNNTs because of a large band gap are electrical insulators . Decorating BNNTs with some elements can change their conductivity and reactivity. The results show that C, Si, and Ge replacements can induce spontaneous magnetisation with different deformation in the nanotube .
Now, nuclear magnetic resonance (NMR) spectroscopy [14, 15] is the best technique to study the electronic structure properties of materials. Doping of chiral BNNTs by C, Si, and Ge atoms changes their properties and so the interactions of the nanotube and foreign atoms or molecules. (Fig. 1). In this work, we studied the electronic structure properties, including bond lengths, bond angles, dipole moments (μ), energies, band gaps, and NMR parameters in the C-, Si-, Ge-doped chiral BNNTs structures.
2 Computational Methods
All calculations were performed using Gaussian 98 computational package (Gaussian INC, Wallingford, CT, USA)  with density functional theory (DFT) method using Becke’s three-parameter hybrid-exchange functions with the correlation functions of Lee, Yang, Parr (B3LYP) [17, 18] using 6-31G (d) basis set . Previously, it is found that the calculated NMR parameters at the B3LYP and B3PW91 levels have a good agreement with the experiment . It is shown that B3LYP gives reasonable and even accurate band gap values for nanotubes , and hence, this function is chosen for band gap calculations.
In this study, we considered a pristine (6,3) chiral BNNTs of diameter 6.6 Å and 10.1 Å length. This BNNT model consists of 42 boron, 42 nitrogen, and 18 hydrogens (B42N42H18) B and N sites of this BNNT are doped by C, Si, Ge (Fig. 1).
Consider the following seven models, namely pristine (Fig. 1a), or with a B or N atom doped by C, that is, the B–C–B or N–C–N model (Fig. 1b, c), doped by a Si atom, that is, the B–Si–B or N–Si–N model (Fig. 1d, e), doped by a Ge atom, that is, the B–Ge–B or N–Ge–N model (Fig. 1f, g). We investigated the influence of the C, Si, and Ge doping on the properties of the (6,3) chiral BNNTs. The hydrogenated models of the pristine (6,3) chiral BNNTs and the three atoms doped models of BNNTs consisted of 102 atoms with the formulas of B42N42H18 (pristine), CB41N42H18 and CB42N41H18 (B–C–B or N–C–N model), SiB41N42H18 and SiB42N41H18 (B–Si–B or N–Si–N model), GeB41N42H18 and GeB42N41H18 (B–Ge–B or N–Ge–N model). The calculated CS tensors in the principal axis system (PAS) with the order of σ33>σ22>σ11  for C, Si, and Ge doping for the investigated models of the (6,3) chiral BNNTs were converted into measurable NMR parameters [isotropic chemical shielding (CSI) and anisotropic chemical shielding (CSA) parameters] using (1) and (2) , summarised in Tables 3–6.
For nuclear quadrupole resonance (NQR) parameters, computational calculations do not directly detect experimentally measurable NQR parameters, nuclear quadrupole coupling constant (CQ), and asymmetry parameter (ηQ). Therefore, (3) and (4) are used to convert the calculated electric field gradient (EFG) tensors in the principal axis system (PAS) with the order of |qzz|>|qyy|>|qxx| to their proportional experimental parameters; CQ is the interaction energy of nuclear electric quadrupole moment (eQ) with the EFG tensors at the sites of quadrupole nuclei (nuclei with nuclear spin angular momentum greater than >1/2), but the asymmetry parameter (ηQ) is a measure of the EFG tensors, which describes the deviation from tubular symmetry at the sites of quadrupole nuclei. The standard Q value [Q (11B)=40.59 mb] reported by Pyykkö  is used in (3). The NQR parameters of 11B nuclei for the investigated models of the (6,3) BNNTs are summarised in Table 7.
3 Results and Discussion
3.1 Structures of the (6,3) Chiral BNNTs
The structural properties consisting of the B–N bond lengths, bond angles, dipole moments (μ), energies, and band gaps for the investigated models of the (6,3) chiral BNNTs are given in Tables 1 and 2. R1, R2, and R3 are B–X–B and N–X–N bond lengths (doped atom and its neighbours). α, β, and γ are B–X–B and N–X–N angles. There are six forms of C-, Si-, Ge-doped chiral BNNTs for the (6,3) chiral model.
These calculations indicated that the average of the (X=C, Si, Ge) bond lengths of the B–X–B and N–X–N models is larger than those the pristine models. The reason seems to be increasing of atomic radius going from carbon to Ge.
The bond angles produce some structural deformations that are responsible for deformation in structure by changing the doped atom size respect to carbon. For the B–X–B and N–X–N (X=C, Si, Ge) models, the diameter values are larger than those the pristine models. It has worth to be noted that the significant changes of geometries are just for those atoms placed in the nearest neighborhood of X atom and those of other atoms almost remained unchanged.
3.2 Energy Band Structure and Density of States
The total densities of states (DOS) of these tubes are presented in Figure 2. As can be observed from Figure 2, the calculated HOMO-LUMO gap (band gap) of the (6,3) chiral BNNTs is 6.2 (eV) and the calculated band gaps of the C-, Si-, Ge-doped models molecular orbitals are 3.5, 5.8, 5.0, 5.0, 5.5, and 5.0 (eV), respectively (Tab. 2). The results indicate that the HOMO-LUMO gap for pristine model is wide, implies that it is a semicounductor, but doping enhances its counductivity. Doping of C, Si, and Ge in these tubes causes significant changes in the gaps of the DOS plots. In comparison with the pristine model, the band gaps of these models are reduced that increase their electrical conductance. These results indicated that the doping of C, Si, Ge atom by B, N atoms B–X–B and N–X–N model (X=C, Si, Ge) has more influence on the band gap of the chiral BNNTs (Tab. 2). By increasing atomic number and size polarisability increases that enhances dipole moment. Dipole moments (μ) of the C-, Si-, Ge-doped chiral BNNTs structures (Fig. 1) indicate slightly changes with respect to the pristine model. High dipole moment of investigated structures can enhance the adsorption properties via electrostatic interaction. Because dipole–dipole interaction with charged or polar species increases chemisorption or physisorption energy . Therefore, we can say Ge–N doped has a larger interaction and so larger adsorption energy.
3.3 NMR Parameters of the (6,3) Chiral BNNTs
The NMR parameters for the investigated models of the (6,3) chiral BNNTs are tabulated in Tables 3–6. In the pristine model of the (6,3) chiral BNNTs, there are 42 B atoms and 42 N atoms in the considered model, and the NMR parameters are separated into five layers and six columns, which means that the CS parameters for the atoms of each layer and column have equivalent chemical environment and electrostatic properties. In Figure 1b–g, the B and N atoms has been replaced by the C, Si, Ge atoms.
The calculated results in Table 3 indicate that doping C, Si, and Ge slightly changes the NMR parameters of the various B and N atoms in (Fig. 1b–g) of the Si, Ge, C doped(6,3) chiral SWBNNTs except for the N25 and N27 atoms for which the changes are significant. Because among the atoms of (Fig. 1b–e) B–X model (X=C, Si, Ge), the N25 and N27 atoms are the nearest neighbours of the C, Si, and Ge atoms; hence, both the CSI and CSA parameters show the most significant changes due to the C, Si, Ge doping. Also, changes in the CSI parameters of the N10 and N12 atoms, which are the next nearest neighbors of the C, Si, Ge atoms, are also notable. There are differences between the properties of the electronic structures of C, Si, Ge atoms.
Comparison of the calculated NMR parameters in (Fig. 1b–g) indicates that the properties of the electronic structure of the Ge doped (6,3) chiral SWBNNTs are more influenced than those of the Si–N model, where the N atom is doped by the Si atom. We studied the electronic energies of the models. The changes in the NMR parameter due to the C, Si, and Ge doping are more significant for the N–Si, N–Ge, N–C models with the pristine model.
3.4 NQR Parameters
The 11B NQR parameters (ηQ and CQ) in the geometrically optimised SWBNNT models were calculated from the EFG tensors. The results are tabulated in Table 7. From the results, it is observed that the calculated NQR parameters are not similar for various nuclei; therefore, the electrostatic environment of BNNT is not equivalent in length in all BNNT models. Since, in contrast with CNTs, the ends of BNNTs are different, the NQR values decrease from each end to the opposite end of the chiral model. It was proved before that the end nuclei in the SW-BNNTs are crucial to their growth and also field emission properties [25, 26]. Since no experimental NQR data for BNNTs are available in the literature, the tables do not include any reference experimental data for the calculated results. B17 and B46 in all models have the largest CQ that states greater orientation of the EFG tensor eigenvalues along the z-axis of the electronic distribution at the sites of the 11B17 and 11B46 nuclei. The electrostatic environments of atom B17 and B46 are stronger than in the other layers along the length of the tube. The largest change in CQ is due to B46, located in the layer of doped atoms, because doping changes the geometrical parameters and hence the electronic behaviour of atoms.
The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in the pristine, and C–X (X=B, N) models are plotted in Figure 3. For the pristine model, HOMO and LUMO are uniformly distributed throughout the B–N bonds, whereas, in the C–X model (X=B, N) models, HOMO and LUMO are highly localised at the doped regions (Fig. 3). In comparison with the pristine model, band gaps of the C-, Si-, and Ge-doped models increased their electrical conductance.
Molecular electrostatic potential (MEP) surfaces of the studied structures are given in Figure 4. The electrostatic potential can be thought of as a measure of how positive or negative the molecule is at P. The MEP is related to electron density and indicates electrophilic or nucleophilic properties of sites. The electrostatic energy plays a strong role in the intramolecular energy. The electrostatic energy is unimportant for non-polar systems such as hydrocarbons and is therefore often completely neglected. It can be concluded that doping of Ge and Si significantly changed charge distribution of BNNTs. The dipole moments in the Table 2 confirms dipole moments relate to MEP. In this study, MEP relates to NMR shieldings, because it changes intra and intermolecular interactions.
We studied the electronic structure properties including bond lengths, bond angles, dipole moments (μ), energies, band gaps, the NMR parameter of the six C-, Si-, Ge-doped SWBNNTs models by means of DFT calculations. The calculated results indicated that the average Ge–B bond lengths of the Ge–N model are larger than those the pristine and the C–B, C–N, Si–B, Si–N and Ge–B models: Ge–N>Si–N>Ge–B>Si–B>C–N>Pure>C–B.
The values of dipole moments (μ) of the six C-, Si-, Ge-doped SWBNNTs are Ge–N>Si–N>Ge–B>C–N>Pure>Si–B>C–B. In comparison with the pristine model, the band gaps of the six C-, Si-, Ge-doped models are reduced and their electrical conductance increased as: C–B>Si–B=Si–N=Ge–N>Ge–B>C–N. The NMR values for the B and N atoms directly bound to the C, Si, and Ge in the C-, Si-, and Ge-doped models are significantly changed. Comparison of the calculated NMR parameters in the X–B and X–N (X=C, Si, Ge) models shows that the properties of the electronic structure of the X–B-doped (6,3) Chiral SWBNNTs are more influenced than X–N model in Figure 1b–g. The electronic sites of the B and N atoms in X–N model have greater effects than X–B model in Figure 1 in the C-, Ge-, and Si-doping processes.
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Published Online: 2015-09-08
Published in Print: 2015-10-01