Abstract
Temperature dependence of the Young’s modulus of cylindrical single-wall nanotubes with zigzag and armchair chiralities and consolidated-wall nanotubes has been studied by the molecular mechanics method with the use of the atom–atom potential. The nanotubes have been obtained by rolling up of crystal layers (111) of TiO2 with fluorite structure. Calculations have been performed for isothermal conditions on the basis of calculating the Helmholtz free energy of the system. The dependence of the Helmholtz free energy of nanotubes on the period has been calculated in the quasi-harmonic approximation as a result of calculation of phonon frequencies. It has been shown that the temperature dependence of the stiffness of nanotubes is determined by their chirality, and some nanotubes exibit anomalous behavior of both the Young’s modulus and the period of unit cell with variation in temperature.
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M. T. Byrne, J. E. McCarthy, M. Bent, R. Blake, Y. K. Gun’ko, E. Horvath, Z. Konya, A. Kukovecz, I. Kiricsi, and J. N. Coleman, J. Mater. Chem. 17, 2351 (2007).
P. J. F. Harris, Int. Mater. Rev. 49, 31 (2004).
R. Tenne, Front. Phys. 9, 370 (2014).
S. Kaur, M. Gallei, and E. Ionescu, in Organic–Inorganic Hybrid Nanomaterials, Ed. by S. Kalia and Y. Haldorai (Springer-Verlag, Cham, Switzerland, 2015).
A. W. Tan, B. Pingguan-Murphy, R. Ahmad, and S. A. Akbar, Ceram. Int. 38, 4421 (2012).
L. S. Santos, N. T. C. Oliveira, C. M. Lepienski, C. E. B. Marino, and N. K Kuromoto, Rev. Mater. 19, 33 (2014).
A. W. Miles and S. Gheduzzi, Surgery 30, 86 (2012).
T. Shokuhfar, G. K. Arumugam, P. A. Heiden, R. S. Yassar, and C. Friedrich, ACS Nano 3, 3098 (2009).
G. A. Crawford, N. Chawla, K. Das, S. Bose, and A. Bandyopadhyay, Acta Biomater. 3, 359 (2007).
G. A. Crawford, N. Chawla, and J. E. Houston, J. Mech. Behav. Biomed. Mater. 2, 580 (2009).
K. Fischer and S. G. Mayr, Adv. Mater. (Weinheim) 23, 3838 (2011).
I. Kaplan-Ashiri, S. R. Cohen, K. Gartsman, R. Rosentsveig, G. Seifert, and R. Tenne, J. Mater. Res. 19, 454 (2004).
A. V. Bandura, R. A. Evarestov, and S. I. Lukyanov, Phys. Chem. Chem. Phys. 16, 14781 (2014).
J. P. Lu, Phys. Rev. Lett. 79, 1297 (1997).
J. P. Lu, Phys. Chem. Solids 58, 1649 (1997).
Y. Jin and F. G. Yuan, Compos. Sci. Technol. 63, 1507 (2003).
P. M. Agrawal, B. S. Sudalayandi, L. M. Raff, and R. Komanduri, Comput. Mater. Sci. 38, 271 (2006).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 7: Theory of Elasticity (Nauka, Moscow, 1987; Butterworth–Heinemann, Oxford, 1995).
T. Lorenz, D. Teich, J.-O. Joswig, and G. Seifert, J. Phys. Chem. C 116, 11714 (2012).
M. Griebel, J. Hamaekers, and F. Heber, Comput. Mater. Sci. 45, 1097 (2009).
E. W. Bucholz and S. B. Sinnott, J. Appl. Phys. 112, 123510 (2012).
Y. Jin and F. G. Yuan, Compos. Sci. Technol. 63, 1507 (2003).
G. Dereli and C. Ozdogan, Phys. Rev. B: Condens. Matter 67, 35416 (2003).
G. Gao, T. Cagin, and W. A. Goddard III, Nanotechnology 9, 184 (1998).
A. Sears and R. C. Batra, Phys. Rev. B: Condens. Matter 69, 235 406 (2004).
Y. J. Guo, PhD Dissertation (California Institute of Technology, Pasadena, California, United States, 1992).
I. Kaplan-Ashiri, S. R. Cohen, K. Gartsman, R. Rosentsveig, G. Seifert, and R. Tenne, J. Mater. Res. 19, 454 (2004).
I. Kaplan-Ashiri, S. R. Cohen, K. Gartsman, V. Ivanovskaya, T. Heine, G. Seifert, I. Wiesel, H. D. Wagner, and R. Tenne, Proc. Natl. Acad. Sci. 103, 523 (2006).
R. P. Stoffel, C. Wessel, M.-W. Lumey, and R. Dronskowski, Angew. Chem., Int. Ed. Engl. 49, 5242 (2010).
K. Lagarec and S. Desgreniers, Solid State Commun. 94, 519 (1995).
J. Wang, L. Wang, L. Maa, J. Zhao, B. Wang, and G. Wang, Physica E (Amsterdam) 41, 838 (2009).
R. A. Evarestov, A. V. Bandura, M. V. Losev, S. Piskunov, and Yu. F. Zhukovskii, Physica E (Amsterdam) 43, 266 (2010).
R. A. Evarestov, Yu. F. Zhukovskii, A. V. Bandura, and S. Piskunov, J. Phys. Chem. C 114, 21061 (2010).
J. D. Gale, Z. Kristallogr. 220, 552 (2005).
A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatova, Theory of Lattice Dynamics in the Harmonic Approximation (Academic, New York, 1971).
A. Hallil, R. Tétot, F. Berthier, I. Braems, and J. Creuze, Phys. Rev. B: Condens. Matter 73, 165406 (2006).
C. M. Freeman, J. M. Newsam, S. M. Levinea, and C. R. A. Catlow, J. Mater. Chem. 3, 531 (1993).
M. O. Zacate, R. W. Grimes, and K. Scrivener, J. Mater. Sci. 35, 3727 (2000).
M. Mostoller and J. C. Wang, Phys. Rev. B: Condens. Matter 32, 6773 (1985).
M. Matsui and M. Akaogi, Mol. Simul. 6, 239 (1991).
D.-W. Kim, N. Enomoto, Z. Nakagawa, and K. Kawamura, J. Am. Ceram. Soc. 79, 1095 (1996).
V. Swamy and J. D. Gale, Phys. Rev. B: Condens. Matter 62, 5406 (2000).
X. J. Han, L. Bergqvist, P. H. Dederichs, H. Müller- Krumbhaar, J. K. Christie, S. Scandolo, and P. Tangney, Phys. Rev. B: Condens. Matter 81, 134108 (2010).
S. M. Woodley, P. D. Battle, J. D. Gale, and C. R. A. Catlow, Phys. Chem. Chem. Phys. 1, 2535 (1999).
T. Liang, Y. K. Shin, Y.-T. Cheng, D. E. Yilmaz, K. G. Vishnu, O. Verners, C. Zou, S. R. Phillpot, S. B. Sinnott, and A. C. T. van Duin, Annu. Rev. Mater. Res. 43, 109 (2013).
R. D. Shannon, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 32, 751 (1976).
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1987).
M. Horn, C. F. Schwerdtfeger, and E. P. Z. Meagher, Z. Kristallogr., Kristallgeom., Kristallphys., Kristallchem. 136, 273 (1972).
K. V. Krishna Rao, S. V. Nagender Naidu, and L. Iyengar, J. Am. Ceram. Soc. 53, 124 (1970).
J. K. Burdett, T. Hughbanks, G. J. Miller, J. W. Richardson, and J. V. Smith, J. Am. Chem. Soc. 109, 363 (1987).
J. B. Wachtman, W. E. Tefft, and D. G. Lam, J. Res. Natl. Stand., Sec. A. 66, 465 (1962).
S. P. Albu, A. Ghicov, S. Aldabergenova, P. Drechsel, D. LeClere, G. E. Thompson, J. M. Macak, and P. Schmuki, Adv. Mater. (Weinheim) 20, 4135 (2008).
N. Liu, H. Mirabolghasemi, K. Lee, S. P. Albu, A. Tighineanu, M. Altomareab, and P. Schmuki, Faraday Discuss. 164, 107 (2013).
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Original Russian Text © S.I. Lukyanov, A.V. Bandura, R.A. Evarestov, 2015, published in Fizika Tverdogo Tela, 2015, Vol. 57, No. 12, pp. 2391–2399.
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Lukyanov, S.I., Bandura, A.V. & Evarestov, R.A. Temperature dependence of Young’s modulus of titanium dioxide (TIO2) nanotubes: Molecular mechanics modeling. Phys. Solid State 57, 2464–2472 (2015). https://doi.org/10.1134/S1063783415120239
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DOI: https://doi.org/10.1134/S1063783415120239