Tuning the electronic properties of boron nitride nanotube by mechanical uni-axial deformation: a DFT study
© Ju et al; licensee Springer. 2011
Received: 14 July 2010
Accepted: 21 February 2011
Published: 21 February 2011
The effect of uni-axial strain on the electronic properties of (8,0) zigzag and (5,5) armchair boron nitride nanotubes (BNNT) is addressed by density functional theory calculation. The stress-strain profiles indicate that these two BNNTS of differing types display very similar mechanical properties, but there are variations in HOMO-LUMO gaps at different strains, indicating that the electronic properties of BNNTs not only depend on uni-axial strain, but on BNNT type. The variations in nanotube geometries, partial density of states of B and N atoms, B and N charges are also discussed for (8,0) and (5,5) BNNTs at different strains.
In nanoscale materials, especially for nanotubes, numerous special properties depend on their ultra-small sizes. Carbon nanotubes (CNTs), discovered by Iijima in 1991 , have been a very promising one-dimensional material in nanoscience. Theoretical calculations and experimental measurements on carbon nanotubes have shown many exceptional properties that make CNTs promising for several proposed applications, such as high Young's modulus and electronic properties [1–6]. Boron nitride nanotubes (BNNTs) were theoretically predicted in 1994 and were synthesized experimentally in the following year . BNNTs are a structural analogy to CNTs that instead alternate boron and nitride atoms to replace the carbon atoms in the hexagonal structure. Although CNTs and BNNTs have similar structures, their properties are quite different. For example, electronic properties of CNT are distinctly different from those of BNNTs because of the large ionicity of B-N bonds . Another difference is that BNNTs have a much better resistance to oxidation in high temperature systems than CNTs . Moreover, the BNNT is independent of the chirality and diameter and is a semiconductor with a wide band gap .
As BNNTs have many special mechanical, thermal, electrical, and chemical properties and have a large number of potential applications, such as in composite materials, hydrogen storage, and force sensors [10–13], many scientists have studied the properties of BNNTs and related material [2, 14–18]. The hydrogen storage attracted much attention in recent years especially. Ma et al.  found that the structure of BNNTs is better able to store hydrogen at high temperature than CNTs, such that BNNTs can store 1.8 to 2.6 wt% at 10 MPa. In theoretical studies, Cheng et al. obtained that capability of hydrogen storage in single-walled boron nitride nanotube arrays (SWBNNTA) can be increased with the increase of distance between BNNTs. Zhao and Ding  indicated that several gas molecules (H2, O2, and H2O) dissociate and chemisorb on BNNT edges, and the adsorption of these molecules induces a charge transfer. Yuan and Liew  reported that boron nitride impurities will cause a decrease in Young's moduli of SWCNTs. Moreover, the effect of these impurities in zigzag SWCNTs is more significant because of the linking characteristics of an increase in electrons. Mpourmpakis and Froudakis  discovered that BNNTs are preferable to CNTs for hydrogen storage because of the ionic character of BNNTs bonds which can increase the binding energy of hydrogen. In addition, some methods have been shown to improve the efficiency of storage. An increase in the diameter of BNNT can increase the efficiency of hydrogen storage . Further, Tang et al.  improved the concentration of hydrogen storage to 4.6 wt% by bending the BNNTs. BNNTs also have many great physical and chemical properties. Zhi et al.  found that MWBNNTs have the ability to form covalent bonds with ammonia and can act as a solute in an organic solution. Chen et al.  obtained the result that field-emission current density of an Au-decorated boron nitride nanotube (Au-BNNT) is significant enhanced in contrast to pure BNNTs. Chen et al.  used ball milling-annealing to synthesize BNNTs and found that the average resistivity of that is 7.1 ± 0.9 × 1012 Ω. Chopra and Zettl  observed that the BNNT has the highest elastic modulus of 700-900 GPa in one-dimensional fibers.
Recent studies have shown that applying strain to a one-dimensional material will affect its electrical property. Shiri et al. discovered that the band gap of silicon nanowire (SiNW) can be affected under uni-axial tensile strain. They also found that the strain induced direct-to-indirect transition in the band gap of SiNW with different diameters . Tombler et al. used theoretical and experimental approaches to study the effect of single-walled carbon nanotubes (SWNTs) with deformation on its electrical conductance. They found the electrical conductance of SWNT is obviously reduced as compared to SWCNT without deformation . For the theoretical studies, Li et al.  demonstrated that the transport property of CNT with double vacancy is reduced under external force. The stress-strain curve of armchair CNTs shows a step-by-step increasing behavior, and the C-C bond length varies significantly at specific strain during the tensile process. Those changes are more apparent for the smaller-sized armchair CNT. Wang reported a structural transformation from zigzag (Z-type) to an unusual type of fourfold-coordinated (H-type) and to armchair (A-type) structure in the ultrathin SiCNTs under uni-axial compression . Wu et al.  found that the radial deformation of BNNT significantly affects the H2 adsorption energy on BNNT. They presented the relationship between the H2 adsorption energy at different adsorption sites and the extent of radial deformation of BNNT.
In experimental part, Kaniber et al.  utilized the piezoelectric device to apply different uni-axial strains to CNT. They mounted the CNT on two Au pads (source and drain) of a piezoelectric stack. When different voltages were applied to the piezoelectric device, the axial length of CNT can be adjusted. For CNT with different uni-axial strains, they found that the electronic properties of CNT can be affected by the uni-axial mechanical deformation. From this experiment and references [23–28] it is obvious that besides the size and shape of nanomaterials, the electronic properties can be further adjusted by applying the mechanical deformation. Since BNNTs have some material properties superior to CNT, it is worth understanding how to adjust the electronic properties of BNNT by the mechanical deformation for further applications, such as hydrogen storage for fuel cell. Therefore, this study utilizes DFT to investigate armchair (5,5) and zigzag (8,0) single-wall BNNTs under different uni-axial loadings. The HOMO-LUMO gap, radial bucking variety, and bond length are adopted to discuss the relationship between the mechanical deformation and electronic properties for the two different chiralities.
Diameter, bond length, and binding energy for different BNNTs
Nanotube and stoichiometry
Bond length distribution (Å)
Binding energy (eV/each atom)
Results and discussion
where m is the mass of atom i; and are the velocity components of atom i in the m- and n-directions, respectively; v i is the volume assigned around atom i; N s is the number of particles contained within region S, where S is defined as the region of atomic interaction; r is the position of atom i; and is the internal force acting on atom i.
where a i is the average radius of atom i and r ij is the distance between atom i and its neighboring atom j.
where is the length of the BNNT in the axial direction following elongation and l z ( o ) is the initial length, which the axial stress is zero after a complete geometry optimization by DFT. The stress-strain relationship of the BNNT can then be obtained from Equations 1 and 3.
The lengths of both (8,0) and (5,5) BNNTs after the relaxation by the DFT method are defined as the referenced lengths at strain of 0, where the axial stresses are 0 after calculation by Equation 1. As we focus on the electronic properties of the intact BNNTs at different strains without bond breakage, the maximal strains shown in Figure 2 before significant necking and some bond breakage are 21.5 and 27% for (8,0) and (5,5) BNNTs, respectively; the corresponding maximal stresses are about 0.526 and 0.511 TPa. For the stress-strain profiles, it is apparent that the stresses increase with an increase in strain in both cases. The profiles of HOMU-LUMO gaps, where the gap value for the (8,0) BNNT remains at a constant of 3.7 eV, are close to the reference value  from strain 0 to 5%, and then displays a parabolic decrease when the strain increases from 5 to 12.5%. As the strain is larger than 12.5%, the gap decreases linearly with the increase of strain. For (5,5) BNNT, the HOMO-LUMO gap is 4.65 eV at strain 0, which is close to the reference value , the gap linearly decreases with the increase of strain until the strain reaches 20%. When the strain is larger than 20%, the profile displays a parabolic decrease. Although the stress-strain profiles of (8,0) and (5,5) BNNTs seem very similar, the variations of HOMO-LUMO gaps at different strains are clearly different. Accordingly, Figure 2 clearly demonstrates that the mechanical deformations of BNNTs significantly influence their electronic properties, with the electronic properties of different chirality BNNTs displaying different responses to the strains. Further, different levels of strain may produce either linear or non-linear electronic property profiles.
where r B and r N represent the radii of the B and N cylinders. If the value of radial buckling approaches zero, the B and N atoms will be located on the cylindrical surface of the BNNT, while a positive value indicates that the BNNT consists of two cylindrical surfaces with N atoms situated on the outer surface . At strain of 0, the values of radial buckling are about 0.02 and 0.074 for (8,0) and (5,5) BNNTs, indicating the radial buckling is less significant for a zigzag BNNT. In Figure 5, the radial buckling of the (5,5) BNNT dramatically decreases with an increase in strain, indicating that the B and N atoms are gradually forced to the same cylindrical surface when the (5,5) armchair BNNT is subjected to an increasing uni-axial external stress. However, for the (8,0) zigzag BNNT, the value of radial buckling remains at an almost constant 0.02 when the strain continuously increases.
Figure 8a,b,c,d shows the PDOS of s and p orbitals of B63 and N61 atoms as well as the summation of those orbitals for the (5,5) BNNT. At strain of 0, there is almost no contribution to the total DOS from 2s orbitals of B63 and N61 around the Fermi level. The N61 2p orbital contributes more to the DOS of occupied states near the Fermi level, and grabs electron from nearby B atoms. Consequently, N atoms have negative charges and B atoms possess positive charges, as was shown in Figure 6. For the empty states, the total DOS strength mainly comes from the B63 2p electrons and to a lesser degree the N61 2p electron. As the strain increases to 8, 17, and 25%, the occupied states undergo a slight right-shift toward the Fermi level and the unoccupied states left-shift, resulting in a decrease of the HOMO-LUMO gap, which can be seen from Figure 2b. During the tensional process, the unoccupied state is not split into two states.
In Figure 10a, the distribution of positive iso-value around the B63 atom indicates that the extra electron will accumulate between the B-N bond after the B and N atoms form the (5,5) BNNT at strain of 0. The BO values of two slanted B-N bonds are slightly smaller than that of the B-N bond normal to the axial direction, indicating that the slanted bond strength is slightly weaker than that of the bond normal to the axial direction. The summation of three BO values decreases from 3.23 to 3.079 as the strain continuously increases from 0 to 25%, but the BO value of the normal bond gradually increases from 1.110 to 1.289, indicating the bonding strength of the normal bond will slightly increase under the larger strain. However, the BO values of two slanted bonds become smaller at larger strains. As the strain increases from 0 to 25%, the distributions of electron differences along the slanted bonds become narrow, whereas that of the normal bond turns out to be wider, indicating that the electron accumulation along the slanted bonds will become more significant when the BNNT is under larger strain.
This study utilizes DFT calculation to address the influence of axial tensions on the electronic properties of (8,0) zigzag and (5,5) armchair BNNTs. Although the stress-strain profiles indicate the mechanical properties of these two BNNTs are very similar, the variations of electronic properties at different uni-axial strains are drastically different. At strain lower than 5%, the HOMO-LUMO gap of (8,0) BNNT remains at a constant value, but decreases at a larger strain. For the (5,5) BNNT, the gap monotonically decreases when the strain becomes larger. The changes in nanotube geometries, PDOS of B and N atoms, B and N charges also indicate the uni-axial deformation definitely influences the electronic properties of (8,0) and (5,5) BNNTs.
Au-decorated boron nitride nanotube
boron nitride nanotubes
density functional theory
density functional semi-core pseudo-potentials
generalized gradient approximation
partial density of states
single-walled boron nitride nanotube arrays
single-walled carbon nanotubes.
The authors would like to thank the (1) National Science Council of Taiwan, under Grant No. NSC98-2221-E-110-022-MY3, (2) National Center for High-performance Computing, Taiwan, and (3) National Center for Theoretical Sciences, Taiwan, for supporting this study.
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