Skip to main content

Symmetry and Modeling of BN, TiO2, and SrTiO3 Nanotubes

  • Chapter
  • First Online:
  • 3133 Accesses

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 153))

Abstract

The commensurate line groups (also called monoperiodic groups) are symmetry groups of three-dimensional objects translationally periodic along a line-stereoregular polymers, nanotubes, and nanorods. The symmetry groups of nanoribbons and nanowires (75 rod groups) form a finite subset of an infinite number of line groups.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Bilbao Crystallographic Server. The crystallographic site at the Condensed Matter; Physics Dept. of the University of the Basque Country. http://www.cryst.ehu.es/

  2. J. Muscat, V. Swamy, N.M. Harrison, Phys. Rev. B 65, 224112 (2002)

    Article  ADS  Google Scholar 

  3. J. Padilla, D. Vanderbilt, Surf. Sci. 418, 64 (1998)

    Article  ADS  Google Scholar 

  4. E. Heifets, R.I. Eglitis, E.A. Kotomin, J. Maier, G. Borstel, Phys. Rev. B 64, 235417 (2001)

    Article  ADS  Google Scholar 

  5. M.M. Hurley, L.F. Pacios, P.A. Christiansen, R.B. Ross, W.C. Ermler, J. Chem. Phys. 84, 6840 (1986)

    Google Scholar 

  6. 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, P. D’Arco, M. Llunell, CRYSTAL09 User’s Manual (University of Torino, Torino, 2010)

    Google Scholar 

  7. V. Kopsky, D. Litvin, Subperiodic Groups, International Tables for Crystallography, vol. E (Kluwer, Dordrecht, 2002)

    Google Scholar 

  8. V.P. Smirnov, P. Tronc, Phys. Solid State 48, 1373 (2006)

    Article  ADS  Google Scholar 

  9. B.K. Vainstein, Modern Crystallography: Fundamentals of Crystals, Symmetry and Methods of Structural Crystallography, vol. 1 (Springer, Berlin, 1994) Kristallographia 4, 842 (1959)

    Google Scholar 

  10. M. Vujicic, I.B. Bozovic, F. Herbut, J. Phys. A Math. Gen. 10, 1271 (1977)

    Article  ADS  MATH  Google Scholar 

  11. M. Damnjanovic, I. Milosevic, Line groups in physics. Lect. Note Phys. 801, 1 (2010)

    Article  MathSciNet  Google Scholar 

  12. M. Damnjanovic, M. Vujicic, Phys. Rev. B 25, 6987 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  13. M. Damnjanovic, I. Milosevic, M. Vukovic, R. Sredanivic, Phys. Rev. B 60, 2728 (1999)

    Article  ADS  Google Scholar 

  14. M. Damnjanovic, B. Nikolic, I. Milosevic, Phys. Rev. B 75, 033403 (2007)

    Article  ADS  Google Scholar 

  15. I. Noel, P. D’Arco, R. Demichelis, C.M. Zicovich-Wilson, R. Dovesi, J. Comput. Chem. 32, 855 (2010)

    Google Scholar 

  16. P.N. D’yachkov, D.V. Makaev, Phys. Rev. B 76, 195411 (2007)

    Article  ADS  Google Scholar 

  17. S. Ijima, Nature 354, 56 (1991)

    Article  ADS  Google Scholar 

  18. E.B. Barros, A. Jorio, G.G. Samsonidze, R.B. Capaz, A.G.S. Filho, J.M. Filho, G. Dresselhaus, Phys. Rep. 431, 261 (2006)

    Article  ADS  Google Scholar 

  19. Y. Mao, S. Banerjee, S.S. Wong, Chem. Commun. 3, 408 (2003)

    Article  Google Scholar 

  20. A.V. Bandura, R.A. Evarestov, Surf. Sci. 603, L117 (2011)

    Article  Google Scholar 

  21. R.A. Evarestov, Yu.F. Zhukovskii, A.V. Bandura, S. Piskunov, Centr. Eur. J. Phys. 9, 492 (2011)

    Article  ADS  Google Scholar 

  22. R. Evarestov, IOP Conf. Ser. Mater. Sci. Eng. 23, 012012 (2011)

    Article  Google Scholar 

  23. M. Damnjanovic, I. Milosevic, T.V.E. Dobradzic, B. Nikolic, J. Phys. A 36, 10349 (2003)

    MATH  Google Scholar 

  24. M. Damnjanovic, T.V.E. Dobradzic, I. Milosevic, T. Vukovic, B. Nikolic, New J. Phys. 5 148, (2003)

    Article  ADS  Google Scholar 

  25. R.A. Evarestov, A.V. Bandura, M.V. Losev, S. Piskunov, Yu.F. Zhukovskii, Phys. E 43, 266 (2010)

    Article  Google Scholar 

  26. R.A. Evarestov, Yu.F. Zhukovskii, A.V. Bandura, S. Piskunov, J. Phys. Chem. C 114, 21061 (2010)

    Google Scholar 

  27. R.A. Evarestov, Yu.F. Zhukovskii, A.V. Bandura, S. Piskunov, M.V. Losev, J. Phys. Chem. C 115, 14067 (2011)

    Google Scholar 

  28. R. Evarestov, A. Bandura, IOP Conf. Ser. Mater. Sci. Eng. 23, 012013 (2011)

    Article  Google Scholar 

  29. D.A.H. Hanaor, C.C. Sorrell, J. Mater. Sci. 46, 855 (2011)

    Google Scholar 

  30. E. Bengu, L.D. Marks, Phys. Rev. Lett. 86, 2385 (2001)

    Article  ADS  Google Scholar 

  31. R. Czerw, S. Webster, D.L. Carroll, S.M.C. Vieira, P.R. Birkett, C.A. Rego, S. Roth, Appl. Phys. Lett. 83, 1617 (2003)

    Article  ADS  Google Scholar 

  32. W. Wang, O.K. Varghese, M. Paulose, C.A. Grimes, J. Mater. Res. 19, 417 (2004)

    Google Scholar 

  33. R. Tenne, G. Seifert, Ann. Rev. Mater. Res. 39, 387 (2009)

    Article  ADS  Google Scholar 

  34. D.J. Mowbray, J.I. Martinez, J.M. Garcia-Lastra, K.S. Thygesen, K.W. Jacobsen, J. Phys. Chem. C 113, 12301 (2009)

    Google Scholar 

  35. Y. Miyamoto, A. Rubio, S. Berber, M. Yoon, D. Tomnek, Phys. Rev. B 69, 121413 (2004)

    Article  ADS  Google Scholar 

  36. A. Zobelli, C.P. Ewels, A. Gloter, G. Seifert, O. Stephan, S. Csillag, C. Colliex, Nano Lett. 6, 1955 (2006)

    Article  ADS  Google Scholar 

  37. Yu.F. Zhukovskii, S. Piskunov, N. Pugno, B. Berzina, L. Trinkler, S. Bellucci, J. Phys. Chem. Solids 70, 796 (2009)

    Article  ADS  Google Scholar 

  38. Y.Q. Wang, C.G. Hu, X.F. Duan, H.L. Sun, Q.K. Hue, Chem. Phys. Lett. 365, 427 (2002)

    Article  ADS  Google Scholar 

  39. A.N. Enyashin, G. Seifert, Phys. Stat. Sol. (b) 242, 1361 (2005)

    Article  ADS  Google Scholar 

  40. A.N. Enyashin, A.L. Ivanovskii, J. Mol. Struct. THEOCHEM 766, 15 (2006)

    Article  Google Scholar 

  41. D. Szieberth, A.M. Ferrari, Y. Noel, M. Ferrabone, Nanoscale 2, 81 (2010)

    Article  ADS  Google Scholar 

  42. Z. Liu, Q. Zhang, Lu-Ch Qin, Solid. State Commun. 141, 168 (2007)

    Article  ADS  Google Scholar 

  43. J. Wang, L. Wang, L. Ma, J. Zhao, B. Wang, G. Wang, Phys. E 41, 838 (2009)

    Article  Google Scholar 

  44. T. He, M. Zhao, X. Zhang, H. Zhang, Z. Wang, Z. Xi, X. Liu, S. Yan, Y. Xia, L. Mei, J. Phys. Chem. C 113, 13610 (2009)

    Google Scholar 

  45. D.A. Evans, A.G. McGlynn, B.M. Towlson, M. Gunn, D. Jones, T.E. Jenkins, R. Winter, N.R.J. Poolton, J. Phys. Cond. Matt. 20, 075233 (2008)

    Article  ADS  Google Scholar 

  46. A. Schaefer, C. Huber, R.J. Ahlrichs, Chem. Phys. 100, 5829 (1994)

    ADS  Google Scholar 

  47. R.A. Evarestov, Quantum Chemistry of Solids. The LCAO First Principles Treatment of Crystals, vol. 153, Springer Series in Solid State Sciences (Springer, Berlin, 2007)

    Google Scholar 

  48. W.H. Press, S.A. Teukolski, V.T. Vetterling, B.P. Flannery, Numerical Recipes in FORTRAN 77: The Art of Scientific Computing (3d edn.), vol. 1 (Cambridge University Press, Cambridge, 2007)

    Google Scholar 

  49. F. Labat, P. Baranek, C. Domain, C. Minot, C. Adamo, J. Chem. Phys. 126, 154703 (2007)

    Google Scholar 

  50. A. Vittadini, M. Casarin, Theor. Chem. Accounts 120, 551 (2008)

    Article  Google Scholar 

  51. S. Okada, S. Saito, A. Oshiyama, Phys. Rev. 65, 165410 (2002)

    Google Scholar 

  52. H. Liu, G. Zhou, Q. Yan, J. Wu, B.-L. Gu, W. Duan, Phys. Rev. B 75, 125410 (2007)

    Article  ADS  Google Scholar 

  53. S.-H. Jhi, D.J. Roundy, S.J. Louie, M.L. Cohen, Solid State Commun. 134, 397 (2005)

    Article  ADS  Google Scholar 

  54. G.Y. Guo, J.C. Lin, Phys. Rev. B 72, 075416 (2005)

    Article  ADS  Google Scholar 

  55. D. Golberg, Y. Bando, L. Burgeois, K. Kurashima, T. Sato, Appl. Phys. Lett. 77, 1979 (2000)

    Article  ADS  Google Scholar 

  56. S. Sanvito, Y.-K. Kwon, D. Tomanek, C.J. Lambert, Phys. Rev. Lett. 84, 1974 (2000)

    Article  ADS  Google Scholar 

  57. S.S. Nonnemann, E.M. Galio, J.E. Spanier, Appl. Phys. Lett. 97, 102904 (2010)

    Article  ADS  Google Scholar 

  58. B. Hernandez, K.S. Chang, E.R. Fisher, P.K. Dorhout, Chem. Mater. 14, 480 (2002)

    Article  Google Scholar 

  59. R.A. Evarestov, Phys. Rev. B 83, 014105 (2011)

    Article  ADS  Google Scholar 

  60. G. Pilania, S.P. Alpay, R. Ramprasad, Phys. Rev. B 80, 014113 (2009)

    Article  ADS  Google Scholar 

  61. T. Shimada, S. Tomoda, T. Kitamura, Phys. Rev. B 79, 024102 (2009)

    Article  ADS  Google Scholar 

  62. L.A. LaJohn, P.A. Christiansen, R.B Ross, T. Atashroo, W.C. Ermler, J. Chem. Phys. 87, 2812 (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Evarestov, R.A. (2012). Symmetry and Modeling of BN, TiO2, and SrTiO3 Nanotubes. In: Quantum Chemistry of Solids. Springer Series in Solid-State Sciences, vol 153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30356-2_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30356-2_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30355-5

  • Online ISBN: 978-3-642-30356-2

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics