© The Institution of Engineering and Technology
This Letter presents an analytical formulation for predicting the radial breathing mode (RBM) frequency of boron nitride nanotubes (BNNTs) with arbitrary chirality. Accurate material properties of the BNNTs are usually not available and the values of the material properties have certain amount of scatter, and some level of uncertainty. In the present investigation, the convex modelling is utilised to consider the bounded uncertain material properties in calculating the RBM frequency of the BNNTs. The results are compared with available data in the literature. Present study may provide useful information on the RBM frequency of the BNNTs with arbitrary chirality in practical applications.
References
-
-
1)
-
25. Ghavanloo, E., Fazelzadeh, S.A.: ‘Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect’, Appl. Math. Model., 2012, 36, pp. 4988–5000 (doi: 10.1016/j.apm.2011.12.036).
-
2)
-
2. Jeon, G.S., Mahan, G.D.: ‘Lattice vibrations of a single-wall boron nitride nanotube’, Phys. Rev. B, 2009, 79, pp. 085424 (doi: 10.1103/PhysRevB.79.085424).
-
3)
-
19. Wang, X., Wang, L., Elishakoff, I., et al: ‘Probability and convexity concepts are not antagonistic’, Acta Mech.2011, 219, pp. 45–64 (doi: 10.1007/s00707-010-0440-4).
-
4)
-
9. Sanchez-Portal, D., Hernandez, E.: ‘Vibrational properties of single-wall nanotubes and monolayers of hexagonal BN’, Phys. Rev. B, 2002, 66, pp. 235415 (doi: 10.1103/PhysRevB.66.235415).
-
5)
-
5. Rao, A.M., Richter, E., Bandow, S., et al: ‘Diameter-selective Raman scattering from vibrational modes in carbon nanotubes’, Science, 1997, 275, pp. 187–191 (doi: 10.1126/science.275.5297.187).
-
6)
-
7. Wirtz, L., Rubio, A., de la Concha, R.A., et al: ‘Ab initio calculations of the lattice dynamics of boron nitride nanotubes’, Phys. Rev. B, 2003, 68, pp. 045425 (doi: 10.1103/PhysRevB.68.045425).
-
7)
-
23. Ansari, R., Mirnezhad, M., Sahmani, S.: ‘Prediction of chirality- and size-dependent elastic properties of single-walled boron nitride nanotubes based on an accurate molecular mechanics model’, Superlattice. Microst., 2015, 80, pp. 196–205 (doi: 10.1016/j.spmi.2014.12.033).
-
8)
-
6. Ghavanloo, E., Fazelzadeh, S.A., Rafii-Tabar, H.: ‘Analysis of radial breathing-mode of nanostructures with various morphologies: a critical review’, Int. Mater. Rev., 2015, 60, pp. 312–329 (doi: 10.1179/1743280415Y.0000000002).
-
9)
-
10. Xiang, H.J., Yang, J., Hou, J.G., et al: ‘First-principles study of small-radius single-walled BN nanotubes’, Phys. Rev. B, 2003, 68, pp. 035427 (doi: 10.1103/PhysRevB.68.035427).
-
10)
-
8. Erba, A., Ferrabone, M., Baima, J., et al: ‘The vibration properties of the (n,0) boron nitride nanotubes from ab initio quantum chemical simulations’, J. Chem. Phys., 2013, 138, pp. 054906 (doi: 10.1063/1.4788831).
-
11)
-
22. Oku, T.: ‘Atomic structures and properties of boron nitride nanomaterials’, in Méndez-Vilas, A., Díaz, J. (Eds.), Microscopy: science, technology, applications and education, 2010, pp. 1630–1641.
-
12)
-
13. Chowdhury, R., Wang, C.Y., Adhikari, S., et al: ‘Vibration and symmetry-breaking of boron nitride nanotubes’, Nanotechnology, 2010, 21, pp. 365702 (doi: 10.1088/0957-4484/21/36/365702).
-
13)
-
11. Aydin, M.: ‘Vibrational and electronic properties of single-walled and double-walled boron nitride nanotubes’, Vib. Spectrosc., 2013, 66, pp. 30–42 (doi: 10.1016/j.vibspec.2013.01.011).
-
14)
-
4. Chopra, N.G., Luyken, R.J., Cherrey, K., et al: ‘Boron nitride nanotubes’, Science, 1995, 269, pp. 966–967 (doi: 10.1126/science.269.5226.966).
-
15)
-
21. Kudin, K.N., Scuseria, G.E., Yakobson, B.I.: ‘C2F, BN, and C nanoshell elasticity from ab initio computations’, Phys. Rev. B, 2001, 64, pp. 235406–235416 (doi: 10.1103/PhysRevB.64.235406).
-
16)
-
20. Ghavanloo, E., Fazelzadeh, S.A.: ‘Effect of temperature change on the radial breathing mode frequency of single-walled carbon nanotubes’, Nano, 2013, 8, pp. 1350057 (doi: 10.1142/S1793292013500574).
-
17)
-
14. Velasco, V.R., Muñoz, M.C.: ‘Vibrations in cylindrical shells with transverse elastic isotropy: application to III–V nitride nanotubes’, Surf. Sci., 2009, 603, pp. 2950–2957 (doi: 10.1016/j.susc.2009.07.046).
-
18)
-
15. Jiang, L., Guo, W.: ‘A molecular mechanics study on size-dependent elastic properties of single-walled boron nitride nanotubes’, J. Mech. Phys. Solids, 2011, 59, pp. 1204–1213 (doi: 10.1016/j.jmps.2011.03.008).
-
19)
-
3. Blasé, X., Rubio, A., Louie, S., et al: ‘Stability and band gap constancy of boron nitride nanotubes’, Europhys. Lett., 1994, 28, pp. 335–340 (doi: 10.1209/0295-5075/28/5/007).
-
20)
-
17. Radebe, I.S., Adali, S.: ‘Buckling and sensitivity analysis of nonlocal orthotropic nanoplates with uncertain material properties’, Compos. B, 2014, 56, pp. 840–846 (doi: 10.1016/j.compositesb.2013.08.054).
-
21)
-
12. Kumar, D., Verma, V., Dharamvir, K., et al: ‘Phonon dispersions in h-boron nitride sheet and radial breathing modes in boron nitride nanotubes’, Nanosci. Nanotech. Lett., 2014, 6, (7), pp. 606–611 (doi: 10.1166/nnl.2014.1829).
-
22)
-
24. Akdim, B., Pachter, R., Duan, X.F., et al: ‘Comparative theoretical study of single-wall carbon and boron-nitride nanotubes’, Phys. Rev. B, 2003, 67, pp. 245404 (doi: 10.1103/PhysRevB.67.245404).
-
23)
-
1. Dresselhaus, M.S., Lin, Y.M., Rabin, O., et al: ‘Nanowires and nanotubes’, Mater. Sci. Eng. C, 2003, 23, pp. 129–140 (doi: 10.1016/S0928-4931(02)00240-0).
-
24)
-
16. Kim, T.U., Shin, J.W.: ‘Crack analysis of piezoelectric material considering bounded uncertain material properties’, KSAS Int. J., 2003, 4, pp. 9–16.
-
25)
-
18. Ben-Haim, Y., Elishakoff, I.: ‘Convex models of uncertainty in applied mechanics’ (Elsevier, Amsterdam, 1990).
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