An ab initio study of the size-dependent mechanical behavior of single-walled AlN nanotubes

Accepted Manuscript An ab Initio study of the size-dependent mechanical behavior of single-walled AlN nanotubes Jun-Hua Hao, Yu-Fang Wang, Yu-Hua Yin, Run Jiang, Yun-Feng Wang, Qing-Hua Jin PII:

S1293-2558(15)00111-9

DOI:

10.1016/j.solidstatesciences.2015.05.001

Reference:

SSSCIE 5127

To appear in:

Solid State Sciences

Received Date: 3 August 2014 Revised Date:

28 April 2015

Accepted Date: 10 May 2015

Please cite this article as: J.-H. Hao, Y.-F. Wang, Y.-H. Yin, R. Jiang, Y.-F. Wang, Q.-H. Jin, An ab Initio study of the size-dependent mechanical behavior of single-walled AlN nanotubes, Solid State Sciences (2015), doi: 10.1016/j.solidstatesciences.2015.05.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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An ab Initio Study of the Size-dependent Mechanical Behavior of single-walled AlN nanotubes Jun-Hua Haoa,*, Yu-Fang Wangb, Yu-Hua Yinb, Run Jiangb, Yun-Feng Wanga, Qing-Hua Jinb Department of Physics, Tianjin University Ren′ai College, Tianjin 301636, People’s Republic of China b

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a

School of Physics, Nankai University, Tianjin 300071, People’s Republic of China

Employing ab-initio electronic structure calculations combined with the

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linear combination of atomic orbitals (LCAO) we have investigated a size

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dependence of mechanical behavior in single-walled AlN nanotubes with armchair and zigzag forms. A simple procedure of nanotubes construction based on the wurtzite (0 0 1) slab with monolayer rolling and subsequent cylindrical coordinate system introduction is suggested. The present

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calculations indicate that the Young’s modulus and electronic band gap of these tubes are increased monotonically as the radius increases, but

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decreases with the Al-N bond length. In addition, the amount of charge transfer calculated by the Mulliken's population analysis is introduced to

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explain clearly the strength of bonding between Al and N atoms in single-walled AlN nanotubes. Keywords: Ab initio calculations; Nanostructures; Mechanical properties

* Corresponding author. Tel: + 86-22-68579990-9596 E-mail: [email protected]; [email protected] (J. H. Hao)

1. Introduction 1

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Presently, III-V semiconductor nanostructures materials [1, 2] have attracted more attentions as they are expected to play an important role in the development of future nanoscale technologies. Currently, Aluminum

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nitride nanostructures (needles [3], platelets [4], nanowires [5-7], nanoribbons [8], and nanotubes [9,10]) have aroused considerable interest because of their novel properties as well as extreme different

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functionality compared to their bulk counterparts, such as enhanced field

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emission, high thermal conductivity, good dielectric properties, large electrical resistivity, large optical band gap, low thermal expansion coefficient. Most of all, AlN nanostructures have higher reactivity than carbon nanotubes or BN nannotubes due to their great polarity, which

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make AlN nanostructures be suitable for advanced nanoscale electronic and optoelectronic device applications. AlN nanostructures are not only used for field emitters in flat panel displays, potential hydrogen storage

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media [11] and integration compatibility with silicon substrates but also

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make them to be excellent candidates for actuators, sensors, and nano-electromechanical systems [12, 13]. So the knowledge of the structure and properties of AlN nanostructures are required. AlN nanotubes with diameters of 30–80 nm have been successfully

synthesized via direct nitriding of aluminum powder [14-16], theoretical calculations on single-walled AlN nanotubes have indicated that these tubular structures are stable and have unique electronic properties [17-19]. 2

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Although AlN nanotubes have been extensively investigated over the past years, to the best of our knowledge, there are few first principle simulations about the elastic properties by a consideration of AlN

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nanotubes with different sizes and structures. In this paper, we evaluated the strain energy required in order to wrap up an AlN graphitic sheet into a singled-walled AlN nanotube based

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on density functional theory (DFT) calculations. We found that the

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energy cost to form an AlN nanotube from its sheet structure is lower than that required to form carbon, GaN, and BN nanotubes from their corresponding graphitic materials. The electronic structures of armchair and zigzag AlN nanotubes with different radius have also been obtained

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by using DFT calculations. All the AlN nanotubes are predicted to be semiconductors with band gaps ranging from 5.37 to 7.78 eV. Their energy band gap slightly depends on the chirality, but significantly on the

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radius for the tubes of small radius. The zigzag and armchair nanotubes

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are both semiconductors with direct and indirect band gap, respectively. Contrary to the cases of carbon nanotubes, the band gap of AlN nanotubes increases with the increasing radius of the tubes and saturates at a value corresponding to the calculated band gap of an AlN hexagonal sheet. The existence of a direct gap in zigzag nanotubes is rather important, because it suggests that such nanostructures may exhibit a strong electroluminescence, which has never been observed for their bulk 3

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materials [20]. This paper is structured as follows: in section 2 we describe our computational details. In section 3 we discuss structures and energetic

And section 4 contains the main conclusions. 2. Theoretical background

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properties, the radius and chirality dependence of the elastic constants.

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Aluminum nitride is the only stable compound in the group III

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nitrides and exists in only one crystal structure (wurtzite, hexagonal), which is described by the P63mc space group. Calculations were performed with the CRYSTAL06 periodic ab initio code [21], which using the formalism of localized Gaussian-type atomic orbitals and the

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nanotubes construction based on the two dimensional wurtzite (001) layer rolling and subsequent cylindrical coordinate system introduction is adopted.

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Here we have considered two types of single-walled aluminum

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nitride nanotubes (SWAlNNTs), namely, armchair and zigzag, as shown in figure 1. The original structures of armchair type (n, n) and zigzag type (n, 0) SWAlNNTs are constructed by rolling up an AlN graphitic sheet. The exchange-correlation potential is according to the generalized gradient approximation (GGA) corrections in the form of PWGGA (Perdew–Wang generalized gradient approximation) [22-25] which has been applied to variety of problems in clusters, surfaces and solids. The 4

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all-valence basis sets for Al (8s511sp1d) [26] and N (81s31p1d) [27] GTFs were optimized elsewhere that have been used, therefore we only slightly have re-optimized their diffuse exponents of valence s, p and d

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orbitals in bulk wurtzite calculations with exchange-correlation DFT functional PWGGA. For accuracy, we have used the reciprocal space integration with the suitable shrinking factors for the Monkhorst–Pack

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and Gilat nets: 8×8×8, the level of accuracy in evaluating the Coulomb

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and Hartree–Fock exchange series is controlled by five parameters, for which the 8 8 8 8 16 values were used. The SCF convergence on energy was set to 10-8 Eh (1Eh = 27.2114eV).

The bulk wurtzite atomic and electronic structure was reproduced as

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a = 3.083 Å (3.11), c = 4.850 Å (4.98), u = 0.384 Å (0.382), and the band gap Eg = 6.48 eV (6.2 eV) which are in fair agreement with the experiments [28, 29] (in brackets the experimental values are given). Our

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calculations were performed for (n, 0) zigzag (n ranging from 4 to 23)

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and (n, n) armchair (n from 4 to 23) AlN nanotubes as a function of n with radius (R) ranging between 2.08 and 19.37 Å. 3 Results and discussion For the optimized SWAlNNTs, Al and N atoms shift inward and

outward along the tube’s radius so that all of the Al and N atoms are located at two different coaxial cylindrical surfaces (see Fig. 1) whose radius are denoted as RAl and RN. 5

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RAl and RN are not equal in the same nanotube but very close, so a common radius has been defined as equation (1) to compare the properties of AlN nanotubes with different sizes and structures. RAl + R N 2

(1)

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R=

The total energy of the optimized tubes was calculated as

E tot (unit cell of AlN model) nAlN

(2)

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E=

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where Etot is the calculated total energy per molecule or unit cell and nAlN is the number of AlN pairs per unit cell. Figure 2 shows the size dependence of the total energy for fully relaxed SWAlNNTs. It is seen that a strong size effect is evident for both types of tubes. By comparison

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of total energies, SWAlNNT of zigzag form is found to be more stable than that of armchair form. The total energies of armchair and zigzag NTs decrease monotonically with increased radius and tend to the AlN

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graphitic sheet when the radius is infinite, in good agreement with a

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previous study [25, 30]. The above results can be elucidated by the curvature effects of tube that is, the strain energy becomes lower with decreased curvature (i.e. increased radius) so that the total energy of the rolled-up AlN nanotubes is gradually close to that of the AlN graphitic sheet. To characterize the mechanical properties, the Young’s modulus (Y) as one of the most important constant must to be considered. The 6

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Young’s modulus has been calculated from the second derivative of the total energy E with respect to the strain ε at the equilibrium volume V0 [31, 32].

 ∂2E  ×  2   ∂ε ε = 0

(3)

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1  ∂2E  1 Y = ×  2  = V0  ∂ε  ε =0 2πR0 L0δ

where δ indicates the thickness of the nanotube wall, and R0 and L0 are

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the radius and the length (per unit cell) of the unstrained nanotube. For a

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carbon nanotube with its monatomic wall, the value of δ is quite ambiguous. However, in order to compare the calculated Young’s moduli for carbon nanotubes with experimental values, δ is often chosen as the van der Waals distance in the graphitic lattice (

3.3 Å) [33]. For AlN

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nanotubes, the thickness of the wall (δ = 4.1 Å) [34] can be used. This value is approximately by considering the van der Waals radius of Al and N.

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For various types of SWAlNNTs, the dependencies of the modulus

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on tube radius are displayed in Figure 3a. For clarify, we also plot a couple of energy-strain curves (Figure 3b) for SWAlNNTsto demonstrate the evolution of the energy with the deformation. Clearly, for a given radius, the Young’s modulus of armchair tube is slightly larger than that of zigzag one. For both types of tubes, the elastic modulus depends on their radius [35-38], similar to that of SWCNTs [39]. However, as aforementioned, the structure of SWAlNNTs is analogous to that of 7

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SWCNTs. No surface stiffening effect occurs in these tubes. Since the Young’s modulus characterizes the strength of the forces between atoms that varies with the type of their bonding in a given

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material, it is relatively sensitive to the change of interatomic distance. Therefore, the Young’s modulus should be expected to be closely associated with the bond length of this material. To explore the origin of

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size dependence of the elastic modulus of SWAlNNT, we have calculated

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Al-N bond lengths in these tubes. Note that the Al-N bond lengths inside each AlN nanotube are not equal but their differences are small, whereas for the AlN graphitic sheet, all of the Al-N bond lengths are equal to 1.764 Å. Therefore, the average bond length is introduced to characterize

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the bonding strength between Al and N atoms in the SWAlNNTs. Figure 4 shows the radius dependence of the average Al-N bond length. Experimental Al-N bond lengths are available in refs [40] and [41] and

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are in good agreement with the present calculated parameters. It is seen

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from this figure that strong size effects are also evident for both types of SWAlNNTs. Their bond lengths are decreased with increased radius, showing a strengthening bond in the tubes with larger radius. Furthermore, the bond length of the armchair tube is clearly larger than that of zigzag tube. Both bond lengths have values greater than the value of bond length of AlN sheet, and display a monotonic variation and approach the sheet values as radius increases. The larger the radius, the 8

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more the structure of the nanotube becomes close to that of sheet so that the Al-N bond length is decreased with the enlarged tube radius. In particular, we note that the zigzag SWAlNNTs have the average

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dihedral angles lying between 90° and 164.3° and the armchair have the dihedral angles between 132.5° and 171.8° compared to the corresponding value 179.9° in the near-planar AlN sheet.

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It can be seen that the figures 3 and 4 that the elastic moduli of the

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AlN tubes are chirality-dependent. Young’s modulus of AlN armchair tubes are greater than the counterpart of zigzag tubes, which are agree with the conclusions in the literatures [42,43]. The in-plane elastic properties of the monolayer grapheme are proved to be anisotropic based

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on the interatomic potential energy and continuum mechanics [44]. The anisotropic elastic property is caused by the angle variation of the Al-N bond. The same conclusions can be found for the carbon nanotubes [45,

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46]. The Young’s moduli of the AlN zigzag tubes are increased with the

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increasing of the diameters. However, the Young’s moduli of the armchair tubes are not very sensitively to the radius or bond lengths. This finding has further demonstrated that the elastic modulus is closely associated with the interatomic bonding strength. To trace the origin of bonding strength, a detailed investigation of electronic distribution is urgent for quantitative description of interatomic interactions in the SWAlNNTs. A key approach is the study of the charge transfer taking 9

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place upon formation of SWAlNNTs. To obtain the amount of the charge transfer

q, we have adopted

an improved algorithm, Mulliken's population analysis [47], on the q

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charge density grids. Upon formation of the tube, the charge transfer

from Al atoms to N ones within the tubes is nearly the same as in the single-wall ZnO nanotubes [32]. Figure 5 shows the radius dependence of

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the charge transfer. The amount of charge transferred to the N atom is

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increased remarkably as the tube radius becomes larger. An increased amount of charge transfer indicates the enhancing ionic interactions between Al and N atoms. Due to the importance of ionic interactions in SWAlNNTs, the stronger bonding strength between Al and N atoms will

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lead to shorter bond length accordingly with the increased tube radius. We also investigated the radius dependence of the band gap for armchair and zigzag AlN nanotubes. The evolution of the band gap as a

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function of radius of the tubes is given in Figure 6. In the calculations of

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SWCNTs, all the armchair tubes are metallic, whereas the zigzag tubes oscillate between the metals and small- to medium-gap semiconductors. However, the band gap increases regularly for both of AlN nanotubes with R increasing, and moves to the energy gap for the unrolled optimized graphitic sheet of AlN (7.84eV). This is quite similar to the result found for hexagonal AlN where the band gap decreases as the external pressure increases [48]. This may be related to the strain in the 10

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AlN nanotubes which affects the hybridizations of Al and N and in turn modifies the band gap of the tube. The strain energy in the AlN nanotube increases, and consequently the band gap shrinks as the nanotube radius

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becomes smaller. The sensitivity of energy band gap to the strain suggests the potential application of AlN nanotubes as interesting piezoelectric materials.

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Zhukovskii et al [25] have calculated the structural and electronic

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properties of (6,6), (10,0), (36,36) and (64,0) single-walled AlN nanotubes. They have used the non-local PWGGA exchange-correlation functional. Based on their calculated results they concluded that the larger the diameter of the AlN tubes, the smaller the width of its band gap, the

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strengths of its bonds and the charge separations in them. It is not consist with our calculations. It should be mentioned that the diameters of (36, 36) or (64, 0) tubes are very large, which is about 6 nm. The nanotube with

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large diameter may be collapsed. The conditions for the collapse have

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been investigated both theoretical and experimentally. M. He et al have determined the threshold diameter for SWNT to collapse was about 5.1nm [49] on the basis of the electron diffraction characterizations. Also, the collapse and stability of single-walled and multi-walled carbon nanotubes via atomistic simulations have been studied [50]. The diameters and chirality have strong influence on the collapsed structure, leading to flat, warped and twisted tubes. Also, the information about the 11

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band gap provided by the reference [25] are not enough, the dependent of the band gap on the diameters cannot be obtained correctly. 4. Conclusions

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In summary, we have theoretically investigated the elasticity of SWAlNNTs with armchair and zigzag forms by using first-principles calculations based on DFT. It is demonstrated that the Young’s modules

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for both types of SWAlNNTs are increased as the tube radius increase.

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But, we also found that it is inversely proportional to the Al-N bond length. Such size-dependent elastic modulus mainly arises from the Al-N bonding strength in these tubes. The Mulliken's population analysis of charge transfer shows that the amount of transferred charge is generally

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increased with enlarged radius, resulting in the strengthening bond between Al and N atoms. We have investigated the band gap of SWAlNNTs systemically as well, and found the band gap increases with

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the increasing radius of the tubes. The zigzag and armchair nanotubes are

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both semiconductors with direct band gap and indirect band gap, respectively, and the band gaps ranging from 5.37 to 7.78 eV. Acknowledgments

The authors gratefully acknowledge the financial support of the

National Natural Science Foundation of China with grant No. 60878025 and grant No. 20904026. The authors also would like to acknowledge the help of Dr. Shaoxin Feng. 12

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References [1] K. Rezouali, M.A. Belkhir, Acta Physica Polonica A 113 (2008) 713-722.

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[2] K. Rezouali, M.A. Belkhir, J.B. Bai, Physica. E 41(2008) 254-257. [3] Q. Zhao, J. Xu, X.Y. Xu, Z. Wang, D.P. Yu, Appl. Phys. Lett. 85 (2004) 5331-5333.

SC

[4] Y.B. Tang, H.T. Cong, H.M. Cheng, Appl. Phys. Lett. 89 (2006)

M AN U

093113-1-3.

[5] M. Lei, H. Yang, P.G. Li, W.H. Tang, J. Alloys Comp. 459 (2008) 338-342.

[6] J.A. Haber, P.C. Gibbons, W. E. Buhro, Chem. Mater. 10 (1998)

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4062-4071.

[7] K. Rezouali, M.A. Belkhir, J.B. Bai, J. Phys. Chem. C. 114(2010) 11352-11357.

EP

[8] X.J. Du, Z. Chen, J. Zhang, Zh.R. Ning, X.L. Fan, J. Alloys Comp.

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586 (2014) 176-179.

[9] M. T. Baei, A. A. Peyghan, Z. Baghari, Superlattices Microstruct. 53 (2013) 9-15.

[10] K. Rezouali, M.A. Belkhir, A. Houari, J.B. Bai, Computational Materials Science 45(2009) 305-309. [11] S. H. Lim, J. Lin, Chem. Phys. Lett. 466 (2008) 197-204. [12] A. N. Cleland, M. Pophristic, I. Ferguson, Appl. Phys. Lett. 79 (2001) 13

ACCEPTED MANUSCRIPT

2070-2072. [13] V. Cimalla, F. Niebelschütz, K. Tonisch, Ch. Foerster, K. Brueckner, I. Cimalla, T. Friedrich, J. Pezoldt, R. Stephan, M. Hein, O. Ambacher,

RI PT

Sens. Actuators B 126 (2007) 24-34. [14] Q. Wu, Z. Hu, X. Z. Wang, Y. N. Lu, X. Chen, H. Xu, Y. Chen, J. Am. Chem. Soc. 125 (2003) 10176-10177.

SC

[15] V. N. Tondare, C. Balasubramanian, S.V. Shende, D.S. Joag, V.P.

M AN U

Godbole, S.V. Bhoraskar, M. Bhadbhade, Appl. Phys. Lett. 80 (2002) 4813-4815.

[16] C. Balasubramanian, S. Bellucci, P. Castrucci, M. De Crescenzi, S. V. Bhoraskar, Chem. Phys. Lett. 383 (2004) 188-191.

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[17] D. Zhang, R.Q. Zhang, Chem. Phys. Lett. 371 (2003) 426-432. [18] M. Zhao, Y. Xia, D. Zhang, L. Mei, Phys. Rev. B 68 (2006) 235415-235418.

EP

[19] M. Zhao, Y. Xia, Z. Tan, X. Liu, F. Li, B. Huang, Y. Ji, D. Zhang, L.

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Mei, Chem. Phys. Lett. 389 (2004) 160-164. [20] R. Tenne, A. K. Zettl, in Carbon Nanotubes: Synthesis, Structure, Properties, and Applications, edited by M. S. Dresselhaus, G. Dresselhaus, P. Avouris (Springer, Berlin, 2001), p. 81. [21] R. Dovesi, V. R. Saunders, C. Roetti, R. Orlando, C. M. Zicovich-Wilson, F. Pascale, B. Civalleri, K. Doll, N. M. Harrison, I. J. Bush, Ph. D'Arco, M. Llunell, CRYSTAL06 User's Manual, 2007. 14

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http://www.crystal.unito.it [22] J. P. Perdew, Y. Wang, Phys. Rev. B 33 (1986) 8800-8802. [23] J. P. Perdew, Y. Wang, Phys. Rev. B 40 (1989) 3399.

RI PT

[24] J. P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244-13249. [25] Yu. F. Zhukovskii, A. I. Popov, C. Balasubramanian, S. Bellucci, J. Phys.: Condens. Matter 18 (2006) S2045-S2054.

SC

[26]M. Catti, G. Valerio, R. Dovesi, M. Causá, Phys. Rev. B 49 (1994)

M AN U

14179-14187.

[27] A. Gulans, R. A. Evarestov, I. Tale, C. C. Yang, Phys. Status Solidi C 2 (2005) 507-510.

[28] I. Vurgaftman, J. R. Meyer, J. Appl. Phys. 94 (2003) 3675-3696. Phys. Rev. B 48 (1993) 4335-4351.

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[29] Y. N. Xu, W. Y. Ching

[30] M. W. Zhao, Y. Y. Xia, D. J. Zhang, L. M. Mei, Phys. Rev. B 68 (2003) 235415-1-4.

EP

[31] T. Lorenz, D. Teich, J. O. Joswig, G. Seifert J. Phys. Chem. C 116

AC C

( 2012) 11714-11721.

[32] Y. H. Wen, Y. Zhang, S. Q. Wu, Z. Z. Zhu, J. Appl. Phys. 109 (2011) 084325.

[33] A. N. Enyashin, S. Gemming, T. Heine, G. Seifert, L. Zhechkov, Phys. Chem. Chem. Phys. 8 (2006) 3320-3325. [34] S.S. Batsanov, Journal of Molecular Structure (Theochem) 468 (1999) 151–159. 15

ACCEPTED MANUSCRIPT

[35] G. Stan, C. V. Ciobanu, P. M. Parthangal, R. F. Cook, Nano Lett. 7 (2007) 3691-3697. [36] G. Stan, S. Krylyuk, A. V. Davydov, M. Vaudin, L. A. Bendersky, R.

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F. Cook, Appl. Phys. Lett. 92 (2008) 241908-1-3. [37] S. Cuenot, C. Frétigny, S. Demoustier-Champagne, B. Nysten, Phys. Rev. B 69 (2004) 165410-1-5.

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[38] C. Q. Chen, Y. Shi, Y. S. Zhang, J. Zhu, Y. J. Yan, Phys. Rev. Lett.

M AN U

96 (2006) 075505-1-4.

[39] V. N. Popov, V. E. Van Doren, M. Balkanski, Phys. Rev. B 61 (2000) 3078-3084.

[40] S. Hou, J. Zhang, Z. Shen, X. Zhao, Z. Xue, Physica E 27 (2005)

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45-50.

[41] D. Zhang, R. Q. Zhang, Chem. Phys. Lett. 371 (2003) 426-432. [42] F. Scarpa, S. Adhikari, A. S. Phani, Nanotechnology 20 (2009)

EP

065709-1-11.

AC C

[43] Y. Gao, P. Hao, Physica E 41 (2009) 1561-1566. [44] J. G. Guo, L. J. Zhou, Y. L. Kang, Journal of Nanoscience and Nanotechnoloty, 12 (2012) 3159-3164. [45] M. M. Shokrieh, R. Rafiee, Mater. Design 31(2010) 790-795. [46] T. Chang, H. Gao, J. Mech. Phys. Solids 51 (2003) 1059-1074. [47] R. S. Mulliken, J. Chem. Phys. 23 (1955) 1833-1840. [48] E. A. Pentaleri, V. A. Gubanov, C. Boekema, C. Y. Fong, Phys. 16

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Status Solidi B 203 (1997) 149-168. [49] M. He, J. Dong, K. Zhang, F. Ding, H. Jiang, A. Loiseau, J. Lehtonen, E. I. Kauppinen, ACS Nano 8 (2014) 9657-9663.

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EP

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M AN U

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Nanotechnology 18 (2007) 395703-1-7.

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[50] J. Xiao, B. Liu, Y. Huang, J. Zuo, K. C. Hwang, M. F. Yu,

17

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Figure Captions Figure 1.The optimized zigzag (left) and armchair (right) AlN nanotubes

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Figure 2. The total energy as a function of SWAlNNT radius. The dashed horizontal line denotes the total energy of the corresponding

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sheet.

Figure 3. a) The dependence of Young’s modulus of SWAlNNT on

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radius. The dashed horizontal line denotes the Al-N Young’s modulus of corresponding sheet. b) The energy-strain curves for zigzag (10, 0) and armchair (10, 10) SWAlNNTs.

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Figure 4. The average Al-N bond length of SWAlNNT as a function of radius. The dashed horizontal line denotes the Al-N bond length of

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corresponding sheet.

Figure 5. The amount of charge transfer from Al to N atom in

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SWAlNNTs with different radius. Figure 6. Dependence of band gap of armchair and zigzag AlN

nanotubes with different radius

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ACCEPTED MANUSCRIPT Highlights 1. The AlN nanotubes construction based on the two dimensional layer rolling is adopted. 2. The mechanical properties of the Young’s modulus constant in SWALNNTs have been considered

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3. The elastic properties of SWALNNTs are calculated with different sizes and structures.