Tuning the electronic properties of boron nitride nanotube by mechanical uniaxial deformation: a DFT study
 ShinPon Ju^{1}Email author,
 YaoChun Wang^{1} and
 TingWei Lien^{1}
DOI: 10.1186/1556276X6160
© Ju et al; licensee Springer. 2011
Received: 14 July 2010
Accepted: 21 February 2011
Published: 21 February 2011
Abstract
The effect of uniaxial 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 stressstrain profiles indicate that these two BNNTS of differing types display very similar mechanical properties, but there are variations in HOMOLUMO gaps at different strains, indicating that the electronic properties of BNNTs not only depend on uniaxial 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.
Introduction
In nanoscale materials, especially for nanotubes, numerous special properties depend on their ultrasmall sizes. Carbon nanotubes (CNTs), discovered by Iijima in 1991 [1], have been a very promising onedimensional 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 [7]. 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 BN bonds [2]. Another difference is that BNNTs have a much better resistance to oxidation in high temperature systems than CNTs [8]. Moreover, the BNNT is independent of the chirality and diameter and is a semiconductor with a wide band gap [9].
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. [16] 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 singlewalled boron nitride nanotube arrays (SWBNNTA) can be increased with the increase of distance between BNNTs. Zhao and Ding [11] indicated that several gas molecules (H_{2}, O_{2}, and H_{2}O) dissociate and chemisorb on BNNT edges, and the adsorption of these molecules induces a charge transfer. Yuan and Liew [18] 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 [19] 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 [20]. Further, Tang et al. [21] 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. [14] 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. [15] obtained the result that fieldemission current density of an Audecorated boron nitride nanotube (AuBNNT) is significant enhanced in contrast to pure BNNTs. Chen et al. [22] used ball millingannealing to synthesize BNNTs and found that the average resistivity of that is 7.1 ± 0.9 × 10^{12} Ω. Chopra and Zettl [2] observed that the BNNT has the highest elastic modulus of 700900 GPa in onedimensional fibers.
Recent studies have shown that applying strain to a onedimensional material will affect its electrical property. Shiri et al. discovered that the band gap of silicon nanowire (SiNW) can be affected under uniaxial tensile strain. They also found that the strain induced directtoindirect transition in the band gap of SiNW with different diameters [23]. Tombler et al. used theoretical and experimental approaches to study the effect of singlewalled 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 [24]. For the theoretical studies, Li et al. [25] demonstrated that the transport property of CNT with double vacancy is reduced under external force. The stressstrain curve of armchair CNTs shows a stepbystep increasing behavior, and the CC bond length varies significantly at specific strain during the tensile process. Those changes are more apparent for the smallersized armchair CNT. Wang reported a structural transformation from zigzag (Ztype) to an unusual type of fourfoldcoordinated (Htype) and to armchair (Atype) structure in the ultrathin SiCNTs under uniaxial compression [26]. Wu et al. [27] found that the radial deformation of BNNT significantly affects the H_{2} adsorption energy on BNNT. They presented the relationship between the H_{2} adsorption energy at different adsorption sites and the extent of radial deformation of BNNT.
In experimental part, Kaniber et al. [28] utilized the piezoelectric device to apply different uniaxial 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 uniaxial strains, they found that the electronic properties of CNT can be affected by the uniaxial 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) singlewall BNNTs under different uniaxial loadings. The HOMOLUMO 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.
Simulation model
Diameter, bond length, and binding energy for different BNNTs
Nanotube and stoichiometry  Tube diameter  Bond length distribution (Å)  Binding energy (eV/each atom)  

Type I  Type II  
BNNT (4,4)  5.657  1.461  1.456  6.361 
5.49^{a}  1.440^{b}  1.444^{b}  
BNNT (5,5)  7.043  1.457  1.455  6.422 
6.87^{a}  1.439^{b}  1.442^{b}  
BNNT (6,6)  8.43  1.462  1.458  6.457 
8.23^{a}  1.439^{b}  1.440^{b}  
BNNT (7,7)  9.49  1.462  1.459  6.476 
9.59^{a}  1.438^{b}  1.439^{b}  
BNNT (8,8)  11.21  1.459  1.457  6.490 
10.95^{a}  1.439^{b}  1.439^{b}  
BNNT (4,0)  3.556  1.499  1.439  6.187 
3.35^{a}  1.476^{b}  1.423^{b}  
BNNT (5,0)  4.191  1.473  1.442  6.371 
4.08^{a}  1.460^{b}  1.429^{b}  
BNNT (8,0)  6.263  1.460  1.454  6.606 
6.37^{a}  1.445^{b}  1.434^{b} 
Results and discussion
where m is the mass of atom i; ${v}_{i}^{m}$ and ${v}_{i}^{n}$ are the velocity components of atom i in the m and ndirections, 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 ${F}_{i}^{\text{Int}}$ 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 $\overline{{l}_{z(t)}}$ 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 stressstrain 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 stressstrain profiles, it is apparent that the stresses increase with an increase in strain in both cases. The profiles of HOMULUMO gaps, where the gap value for the (8,0) BNNT remains at a constant of 3.7 eV, are close to the reference value [34] 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 HOMOLUMO gap is 4.65 eV at strain 0, which is close to the reference value [35], 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 stressstrain profiles of (8,0) and (5,5) BNNTs seem very similar, the variations of HOMOLUMO 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 nonlinear 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 [36]. 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 uniaxial 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 rightshift toward the Fermi level and the unoccupied states leftshift, resulting in a decrease of the HOMOLUMO 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 isovalue around the B63 atom indicates that the extra electron will accumulate between the BN bond after the B and N atoms form the (5,5) BNNT at strain of 0. The BO values of two slanted BN bonds are slightly smaller than that of the BN 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.
Conclusion
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 stressstrain profiles indicate the mechanical properties of these two BNNTs are very similar, the variations of electronic properties at different uniaxial strains are drastically different. At strain lower than 5%, the HOMOLUMO 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 uniaxial deformation definitely influences the electronic properties of (8,0) and (5,5) BNNTs.
Abbreviations
 AuBNNT:

Audecorated boron nitride nanotube
 BNNT:

boron nitride nanotubes
 CNTs:

carbon nanotubes
 DFT:

density functional theory
 DSPP:

density functional semicore pseudopotentials
 GGA:

generalized gradient approximation
 PDOS:

partial density of states
 PW91:

PerdewWang 1991
 SWBNNTA:

singlewalled boron nitride nanotube arrays
 SWNTs:

singlewalled carbon nanotubes.
Declarations
Acknowledgements
The authors would like to thank the (1) National Science Council of Taiwan, under Grant No. NSC982221E110022MY3, (2) National Center for Highperformance Computing, Taiwan, and (3) National Center for Theoretical Sciences, Taiwan, for supporting this study.
Authors’ Affiliations
References
 Iijima S: Helical microtubules of graphitic carbon. Nature 1991, 354: 56. 10.1038/354056a0View ArticleGoogle Scholar
 Chopra NG, Zettl A: Measurement of the elastic modulus of a multiwall boron nitride nanotube. Solid State Commun 1998, 105: 297. 10.1016/S00381098(97)101259View ArticleGoogle Scholar
 Salvetat JP, Bonard JM, Thomson NH, Kulik AJ, Forro L, Benoit W, Zuppiroli L: Mechanical properties of carbon nanotubes. Appl Phys A 1999, 69: 255. 10.1007/s003390050999View ArticleGoogle Scholar
 Odom TW, Huang JL, Kim P, Lieber CM: Atomic structure and electronic properties of singlewalled carbon nanotubes. Nature 1998, 391: 62. 10.1038/34145View ArticleGoogle Scholar
 Bockrath M, Cobden DH, Mceuen PL, Chopra NG, Zettl A, Thess A, Smalley RE: Singleelectron transport in ropes of carbon nanotubes. Science 1997, 275: 1922. 10.1126/science.275.5308.1922View ArticleGoogle Scholar
 Ruoff RS, Lorents DC: Mechanical and thermalproperties of carbon nanotubes. Carbon 1995, 33: 925. 10.1016/00086223(95)000215View ArticleGoogle Scholar
 Bengu E, Marks LD: Singlewalled BN nanostructures. Phys Rev Lett 2001, 86: 2385. 10.1103/PhysRevLett.86.2385View ArticleGoogle Scholar
 Moon WH, Hwang HJ: Moleculardynamics simulation of structure and thermal behaviour of boron nitride nanotubes. Nanotechnology 2004, 15: 431. 10.1088/09574484/15/5/005View ArticleGoogle Scholar
 Blase X, Rubio A, Louie SG, Cohen ML: Stability and bandgap constancy of boronnitride nanotubes. Europhys Lett 1994, 28: 335. 10.1209/02955075/28/5/007View ArticleGoogle Scholar
 Song J, Huang Y, Jiang H, Hwang KC, Yu MF: Deformation and bifurcation analysis of boronnitride nanotubes. Int J Mech Sci 2006, 48: 1197. 10.1016/j.ijmecsci.2006.06.006View ArticleGoogle Scholar
 Zhao JX, Ding YH: The effects of O2 and H2O adsorbates on fieldemission properties of an (8,0) boron nitride nanotube: a density functional theory study. Nanotechnology 2009, 20: 085704. 10.1088/09574484/20/8/085704View ArticleGoogle Scholar
 Golberg D, Bando Y, Tang CC, Zhi CY: Boron nitride nanotubes. Adv Mater 2007, 19: 2413. 10.1002/adma.200700179View ArticleGoogle Scholar
 Enyashin AN, Ivanovskii AL: Mechanical and electronic properties of a C/BN nanocable under tensile deformation. Nanotechnology 2005, 16: 1304. 10.1088/09574484/16/8/054View ArticleGoogle Scholar
 Zhi CY, Bando Y, Tang CC, Huang Q, Golberg D: Boron nitride nanotubes: functionalization and composites. J Mater Chem 2008, 18: 3900. 10.1039/b804575eView ArticleGoogle Scholar
 Chen H, Zhang HZ, Fu L, Chen Y, Williams JS, Yu C, Yu DP: Nano Audecorated boron nitride nanotubes: Conductance modification and fieldemission enhancement. Appl Phys Lett 2008, 92: 243105. 10.1063/1.2943653View ArticleGoogle Scholar
 Ma RZ, Bando Y, Zhu HW, Sato T, Xu CL, Wu DH: Hydrogen uptake in boron nitride nanotubes at room temperature. J Am Chem Soc 2002, 124: 7672. 10.1021/ja026030eView ArticleGoogle Scholar
 Rajeswaran M, Blanton TN, Zumbulyadis N, Giesen DJ, ConesaMoratilla C, Misture ST, Stephens PW, Huq A: Threedimensional structure determination of N(ptolyl)dodecylsulfonamide from powder diffraction data and validation of structure using solidstate NMR spectroscopy. J Am Chem Soc 2002, 124: 14450. 10.1021/ja027978bView ArticleGoogle Scholar
 Yuan JH, Liew K: Effects of boron nitride impurities on the elastic properties of carbon nanotubes. Nanotechnology 2008, 19: 445703. 10.1088/09574484/19/44/445703View ArticleGoogle Scholar
 Mpourmpakis G, Froudakis GE: Why boron nitride nanotubes are preferable to carbon nanotubes for hydrogen storage?: An ab initio theoretical study. Catal Today 2007, 120: 341. 10.1016/j.cattod.2006.09.023View ArticleGoogle Scholar
 Baumeier B, Kruger P, Pollmann J: Structural, elastic, and electronic properties of SiC, BN, and BeO nanotubes. Phys Rev B 2007, 76: 085407. 10.1103/PhysRevB.76.085407View ArticleGoogle Scholar
 Tang CC, Bando Y, Ding XX, Qi SR, Golberg D: Catalyzed collapse and enhanced hydrogen storage of BN nanotubes. J Am Chem Soc 2002, 124: 14550. 10.1021/ja028051eView ArticleGoogle Scholar
 Chen H, Chen Y, Liu Y, Fu L, Huang C, Llewellyn D: Over 1.0 mmlong boron nitride nanotubes. Chem Phys Lett 2008, 463: 130. 10.1016/j.cplett.2008.08.007View ArticleGoogle Scholar
 Shiri D, Kong Y, Buin A, Anantram MP: Strain induced change of bandgap and effective mass in silicon nanowires. Appl Phys Lett 2008, 93: 073114. 10.1063/1.2973208View ArticleGoogle Scholar
 Tombler TW, Zhou CW, Alexseyev L, Kong J, Dai HJ, Lei L, Jayanthi CS, Tang MJ, Wu SY: Reversible electromechanical characteristics of carbon nanotubes under localprobe manipulation. Nature 2000, 405: 769. 10.1038/35015519View ArticleGoogle Scholar
 Li Z, Wang CY, Ke SH, Yang W: Firstprinciples study for transport properties of defective carbon nanotubes with oxygen adsorption. Eur Phys J B 2009, 69: 375. 10.1140/epjb/e2009001792View ArticleGoogle Scholar
 Wang XQ, Wang BL, Zhao JJ, Wang GH: Structural transitions and electronic properties of the ultrathin SiC nanotubes under uniaxial compression. Chem Phys Lett 2008, 461: 280. 10.1016/j.cplett.2008.07.040View ArticleGoogle Scholar
 Wu XJ, Yang JL, Hou JG, Zhu QS: Deformationinduced site selectivity for hydrogen adsorption on boron nitride nanotubes. Phys Rev B 2004, 69: 153411. 10.1103/PhysRevB.69.153411View ArticleGoogle Scholar
 Kaniber SM, Song L, Kotthaus JP, Holleitner AW: Photocurrent properties of freely suspended carbon nanotubes under uniaxial strain. Appl Phys Lett 2009, 94: 261106. 10.1063/1.3159472View ArticleGoogle Scholar
 Delley B: Hardness conserving semilocal pseudopotentials. Phys Rev B 2002, 66: 155125. 10.1103/PhysRevB.66.155125View ArticleGoogle Scholar
 Perdew JP, Burke K, Ernzerhof M: Generalized gradient approximation made simple. Phys Rev Lett 1996, 77: 3865. 10.1103/PhysRevLett.77.3865View ArticleGoogle Scholar
 Perdew JP, Wang Y: Accurate and simple analytic representation of the electrongas correlationenergy. Phys Rev B 1992, 45: 13244. 10.1103/PhysRevB.45.13244View ArticleGoogle Scholar
 Chandra N, Namilae S, Shet C: Local elastic properties of carbon nanotubes in the presence of StoneWales defects. Phys Rev B 2004, 69: 094101. 10.1103/PhysRevB.69.094101View ArticleGoogle Scholar
 Srolovitz D, Maeda K, Vitek V, Egami T: Structural defects in amorphous solids statisticalanalysis of a computermodel. Philos Mag A 1981, 44: 847. 10.1080/01418618108239553View ArticleGoogle Scholar
 Zhang J, Loh KP, Yang SW, Wu P: Exohedral doping of singlewalled boron nitride nanotube by atomic chemisorption. Appl Phys Lett 2005, 87: 243105. 10.1063/1.2140876View ArticleGoogle Scholar
 Wu JB, Zhang WY: Tuning the magnetic and transport properties of boronnitride nanotubes via oxygendoping. Solid State Commun 2009, 149: 486. 10.1016/j.ssc.2008.12.030View ArticleGoogle Scholar
 Cox BJ, Hill JM: Geometric Model for Boron Nitride Nanotubes Incorporating Curvature. J Phys Chem C 2008, 112: 16248. 10.1021/jp803023qView ArticleGoogle Scholar
 Xu H, Zhang RQ, Zhang XH, Rosa AL, Frauenheim T: Structural and electronic properties of ZnO nanotubes from density functional calculations. Nanotechnology 2007, 18: 485713. 10.1088/09574484/18/48/485713View ArticleGoogle Scholar
 Nirmala V, Kolandaivel P: Structure and electronic properties of armchair boron nitride nanotubes. Theochem J Mol Struct 2007, 817: 137. 10.1016/j.theochem.2007.04.033View ArticleGoogle Scholar
 Mayer I: Bond orders and valences from abinito wavefunctions. Int J Quantum Chem 1986, 29: 477. 10.1002/qua.560290320View ArticleGoogle Scholar
 Jia JF, Wu HS, Jiao H: The structure and electronic property of BN nanotube. Physica B 2006, 381: 90. 10.1016/j.physb.2005.12.258View ArticleGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.