Abstract
The formalism of line symmetry groups for one-periodic (1D) nanostructures with rotohelical symmetry has been applied for symmetry analysis of single-walled titania nanotubes (SW TiO2 NTs) formed by rolling up the stoichiometric two-periodic (2D) slabs of anatase structure. Either six- or twelve-layer (101) slabs have been cut from TiO2 crystal in a stable anatase phase. After structural optimization, the latter keeps the centered rectangular symmetry of initial slab slightly compressed along a direction coincided with large sides of elemental rectangles. We have considered two sets of SW TiO2 NTs with optimized six- and twelve-layer structures, which possess chiralities (−n, n) and (n, n) of anatase nanotubes. To analyze the structural and electronic properties of titania slabs and nanotubes, we have performed their ab initio LCAO calculations, using the hybrid Hartree-Fock/Kohn-Sham exchange-correlation functional PBE0. The band gaps (Δɛ gap) and strain energies (E strain) of six-layer nanotubes have been computed and analyzed as functions of NT diameter (D NT). As to models of 12-layer SW TiO2 NTs of both chiralities, their optimization results in structural exfoliation, i.e., the multi-walled structure should be rather formed in nanotubes with such a number of atomic layers.
[1] U. Diebold, Surf. Sci. Rep. 48, 53 (2003) http://dx.doi.org/10.1016/S0167-5729(02)00100-010.1016/S0167-5729(02)00100-0Search in Google Scholar
[2] J. Muscat, V. Swamy, N.M. Harrison, Phys. Rev. B 65, 224112 (2002) http://dx.doi.org/10.1103/PhysRevB.65.22411210.1103/PhysRevB.65.224112Search in Google Scholar
[3] W. Wang, O.K. Varghese, M. Paulose, C.A. Grimes, J. Mater. Res. 19, 417 (2004) http://dx.doi.org/10.1557/jmr.2004.19.2.41710.1557/jmr.2004.19.2.417Search in Google Scholar
[4] J. Zhao, X. Wang, T. Sun, L. Li, Nanotechnology 16, 2450 (2005) http://dx.doi.org/10.1088/0957-4484/16/10/07710.1088/0957-4484/16/10/077Search in Google Scholar PubMed
[5] T. Maiyalagan, B. Viswanathan, U.V. Varadaraju, Bull. Mater. Sci. 29, 705 (2006) Search in Google Scholar
[6] D.V. Bavykin, J.M. Friedrich, F.C. Walsh, Adv. Mater. 18, 2807 (2006) http://dx.doi.org/10.1002/adma.20050269610.1002/adma.200502696Search in Google Scholar
[7] N. Viriya-empikul, N. Sano, T. Charinpanitkul, T. Kikuchi, W. Tanthapanichakoon, Nanotechnology 19, 035601 (2008) http://dx.doi.org/10.1088/0957-4484/19/03/03560110.1088/0957-4484/19/03/035601Search in Google Scholar PubMed
[8] G. Mogilevsky, Q. Chen, A. Kleinhammes, Y. Wu, Chem. Phys. Lett. 460, 517 (2008) http://dx.doi.org/10.1016/j.cplett.2008.06.06310.1016/j.cplett.2008.06.063Search in Google Scholar
[9] R. Tenne, G. Seifert, Ann. Rev. Mater. Res. 39, 387 (2009) http://dx.doi.org/10.1146/annurev-matsci-082908-14542910.1146/annurev-matsci-082908-145429Search in Google Scholar
[10] S. Zhang et al., Phys. Rev. Lett. 91, 256103 (2003) http://dx.doi.org/10.1103/PhysRevLett.91.25610310.1103/PhysRevLett.91.256103Search in Google Scholar PubMed
[11] R. Ma, Y. Bando, T. Sasaki, Chem. Phys. Lett. 380, 577 (2003) http://dx.doi.org/10.1016/j.cplett.2003.09.06910.1016/j.cplett.2003.09.069Search in Google Scholar
[12] Y.Q. Wang, C.G. Hu, X.F. Duan, H.L Sun, Q.K. Hue, Chem. Phys. Lett. 365, 427 (2002) http://dx.doi.org/10.1016/S0009-2614(02)01502-610.1016/S0009-2614(02)01502-6Search in Google Scholar
[13] W. Hebenstreit, N. Ruzycki, G.S. Herman, Y. Gao, U. Diebold, Phys. Rev. B 62, R16334 (2000) http://dx.doi.org/10.1103/PhysRevB.62.R1633410.1103/PhysRevB.62.R16334Search in Google Scholar
[14] Z. Liu, Q. Zhang, L.C. Qin, Solid State Commun. 141, 168 (2007) http://dx.doi.org/10.1016/j.ssc.2006.09.05510.1016/j.ssc.2006.09.055Search in Google Scholar
[15] F. Lin et al., Chem. Phys. Lett. 475, 82 (2009) http://dx.doi.org/10.1016/j.cplett.2009.05.01810.1016/j.cplett.2009.05.018Search in Google Scholar
[16] A.V. Bandura, R.A. Evarestov, Surf. Sci. 603, L117 (2009) http://dx.doi.org/10.1016/j.susc.2009.07.04110.1016/j.susc.2009.07.041Search in Google Scholar
[17] A.N. Enyashin, G. Seifert, Phys. Status Solidi B 242, 1361 (2005) http://dx.doi.org/10.1002/pssb.20054002610.1002/pssb.200540026Search in Google Scholar
[18] A.N. Enyashin, A.L. Ivanovskii, J. Mol. Struct.: THEOCHEM 766, 15 (2006) http://dx.doi.org/10.1016/j.theochem.2006.03.02610.1016/j.theochem.2006.03.026Search in Google Scholar
[19] J. Wang et al., Physica E 41, 838 (2009) http://dx.doi.org/10.1016/j.physe.2008.12.01810.1016/j.physe.2008.12.018Search in Google Scholar
[20] D.J. Mowbray, J.I. Martinez, J.M. García Lastra, K.S. Thygesen, K.W. Jacobsen, J. Phys. Chem. C 113, 12301 (2009) http://dx.doi.org/10.1021/jp904672p10.1021/jp904672pSearch in Google Scholar
[21] T. He et al., J. Phys. Chem. C 113, 13610 (2009) http://dx.doi.org/10.1021/jp903224410.1021/jp9032244Search in Google Scholar
[22] F. Alvarez-Ramirez, Y. Ruiz-Morales, Chem. Mater. 19,2947 (2007) http://dx.doi.org/10.1021/cm062162l10.1021/cm062162lSearch in Google Scholar
[23] A. Vittadini, M. Casarin, Theor. Chem. Acc. 120, 551 (2008) http://dx.doi.org/10.1007/s00214-008-0425-810.1007/s00214-008-0425-8Search in Google Scholar
[24] D. Szieberth, A.M. Ferrari, Y. Noel, M. Ferrabone, Nanoscale 2, 81 (2010) http://dx.doi.org/10.1039/b9nr00214f10.1039/B9NR00214FSearch in Google Scholar
[25] M. Vujičić, J. Phys. A: Math. Gen. 10, 1271 (1977) http://dx.doi.org/10.1088/0305-4470/10/8/00510.1088/0305-4470/10/8/005Search in Google Scholar
[26] M. Damnjanović, I. Milošević, Line Groups in Physics: Theory and Applications to Nanotubes and Polymers, Lecture Notes in Physics, Vol. 801 (Springer Verlag, Berlin, Heidelberg, 2010) 10.1007/978-3-642-11172-3_9Search in Google Scholar
[27] M. Ernzerhof, G.E. Scuseria, J. Chem. Phys. 110, 5029 (1999) http://dx.doi.org/10.1063/1.47840110.1063/1.478401Search in Google Scholar
[28] C. Adamo, V. Barone, J. Chem. Phys. 110, 6158 (1999) http://dx.doi.org/10.1063/1.47852210.1063/1.478522Search in Google Scholar
[29] M.M. Hurley, L.F. Pacios, P.A. Christiansen, R.B. Ross, W.C. Ermler, J. Chem. Phys. 84, 6840 (1986) http://dx.doi.org/10.1063/1.45068910.1063/1.450689Search in Google Scholar
[30] A. Schäfer, C. Huber, R. Ahlrichs, J. Chem. Phys. 100, 5829 (1994) http://dx.doi.org/10.1063/1.46714610.1063/1.467146Search in Google Scholar
[31] R.A. Evarestov, Quantum Chemistry of Solids. The LCAO First Principles Treatment of Crystals, Springer Series in Solid State Sciences, Vol. 153 (Springer Verlag, Berlin, 2007) 10.1007/978-3-540-48748-7Search in Google Scholar
[32] B.D. Bunday, Basic Optimization Methods (Edward Arnold Ltd., London, 1984) Search in Google Scholar
[33] R.A. Evarestov, A.I. Panin, A.V. Bandura, M.V. Losev, J. Phys. Conf. Ser. 117, 012015 (2008) http://dx.doi.org/10.1088/1742-6596/117/1/01201510.1088/1742-6596/117/1/012015Search in Google Scholar
[34] W.H. Press, S.A. Teukolski, W.T. Vetterling, B.P. Flannery, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing, Vol. 1, 3rd Ed. (Cambridge University Press, New York, 2007) Search in Google Scholar
[35] F. Labat, P. Baranek, C. Domain, C. Minot, C. Adamo, J. Chem. Phys. 126, 154703 (2007) http://dx.doi.org/10.1063/1.271716810.1063/1.2717168Search in Google Scholar PubMed
© 2011 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
