Skip to main content

The Symmetry Groups in Three-Dimensional Space

  • Chapter
  • First Online:
Theoretical Modeling of Inorganic Nanostructures

Part of the book series: NanoScience and Technology ((NANO))

  • 1435 Accesses

Abstract

The theoretical modeling of inorganic nanostructures described in this book is based on the consideration of 3D-2D-1D three-dimensional objects (three-periodic bulk crystals, diperiodic nanolayers, monoperiodic nanotubes and nanorods).

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

References

  1. 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 

  2. T. Hahn (ed.), International Tables for Crystallography. Space-group Symmetry, vol. A (Reidel, Dordrecht, 1983)

    Google Scholar 

  3. M. Damnjanović, I. Milosěvić, Line Groups in Physics. Lecture Notes in Physics, vol. 801 (Springer, Berlin, 2010)

    Google Scholar 

  4. M. Vujičić, I.B. Božović, F. Herbut, J. Phys. A: Math. Gen. 10, 1271 (1977)

    Article  ADS  MATH  Google Scholar 

  5. V. Kopsky, D.B. Litvin (eds.), International Tables for Crystallography. Subperiodic Groups, vol. E (Kluwer Academic Publishers, Dodrecht, 2002)

    Google Scholar 

  6. R.A. Evarestov, V.P. Smirnov, Site Symmetry in Crystals: Theory and Applications, 2nd edn. Springer Series in Solid State Sciences, vol. 108 (Springer, Berlin, 1997)

    Google Scholar 

  7. M.I. Petrashen, E.D. Trifonov, Applications of Group Theory in Quantum Mechanics (M.I.T. Press, Massachusetts, 1969)

    MATH  Google Scholar 

  8. Bilbao Crystallographic Server. The Crystallographic Site at the Condensed Matter (Physics Department of the University of the Basque Country), http://www.cryst.ehv.es/

  9. L.L. Boyle, Acta Cryst. A 29, 353 (1973)

    Article  Google Scholar 

  10. http://cst-www.nrl.navy.mil/lattice/

  11. http://cst-www.nrl.navy.mil/lattice/others.html

  12. H.A. Jahn, E. Teller, Proc. R. Soc. Lond. A 161, 220 (1937)

    Article  ADS  Google Scholar 

  13. Inorganic Crystal Structure Database (ICSD), http://www.fiz-informationsdienste.de/en/DB/icsd/

  14. 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 

  15. O.A. Graeve, Zirconia, in Ceramic and Glass Materials: Structure, Properties and Processing, ed. by J.F. Shackelford, R.H. Doremus (Springer Science, New York, 2008), p. 169

    Google Scholar 

  16. D. Vollath, F.D. Fischer, M. Hagelstein, D.V. Szabó, J. Nanopart. Res. 8, 1016 (2006)

    Google Scholar 

  17. C.M. Wang, S. Azad, S. Thevuthasan, V. Shutthanandan, D.E. McCready, C.H.F. Peden, J. Mater. Res. 19, 1315 (2004)

    Article  ADS  Google Scholar 

  18. A. Aarik, A. Aidla, H. Mundar, T. Uustrate, V. Sammelselg, Thin Solid Films 408, 97 (2002)

    Article  ADS  Google Scholar 

  19. P. Goudochnikov, A.J. Bell, J. Phys.: Condens. Matter 19, 176201 (2007)

    ADS  Google Scholar 

  20. V. Kopsky, Acta Cryst. A 45, 805, 816 (1989)

    Google Scholar 

  21. V. Kopsky, Acta Cryst. A 56, 370 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. E.A. Wood, 80 Diperiodic Groups in Three Dimensions, Bell System Monograph No 4680 (1964)

    Google Scholar 

  23. I. Milosević, B. Nikolić, M. Damnjanović, M. Krc̃mar, J. Phys. A: Math. Gen. 31, 3625 (1998)

    Google Scholar 

  24. P.W. Tasker, J. Phys. C: Solid State Phys. 12, 4977 (1979)

    Article  ADS  Google Scholar 

  25. F. Finocchi, F. Bottin, C. Noguera, in Computational Materials Science, ed. by C.R.A. Catlow, E.A. Kotomin (IOS Press, Amsterdam, 2003), p. 196

    Google Scholar 

  26. R.A. Evarestov, Quantum Chemistry of Solids. LCAO Treatment of Crystals and Nanostructures, 2nd edn. Springer Series in Solid State Sciences, vol. 153 (Springer, Berlin, 2012)

    Google Scholar 

  27. M. Damnjanović, M. Vujicić, Phys. Rev. B 25, 6987 (1982)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. R.A. Evarestov, A.I. Panin, Acta Cryst. A 68, 582 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  30. M. Damnjanović, I. Milosević, M. Vuković, R. Sredanivić, Phys. Rev. B 60, 2728 (1999)

    Article  ADS  Google Scholar 

  31. M. Damnjanović, B. Nikolić, M. Milosěvić, Phys. Rev. B 75, 033403 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. 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 

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

    Article  Google Scholar 

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

    Google Scholar 

  36. A.V. Bandura, R.A. Evarestov, Surf. Sci. 603, L117 (2009)

    Article  ADS  Google Scholar 

  37. R.A. Evarestov, A.V. Bandura, M.V. Losev, Russ. J. Gen. Chem. 80, 1152 (2010)

    Article  Google Scholar 

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

    Google Scholar 

  39. 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, M. Causa, Y. Noel, CRYSTAL14 User’s Manual (University of Torino, Torino, 2014)

    Google Scholar 

  40. R. Dovesi, R. Orlando, A. Erba, C.M. Zicovich-Wilson, B. Civalleri, S. Casassa, L. Maschio, M. Ferrabone, M. Pierre, P. D’Arco, Y. Noel, M. Causa, M. Rerat, B. Kirtman, Int. J. Quant. Chem. 114, 1287 (2014)

    Google Scholar 

  41. M. Damnjanović, I. Milosěvić, T.V.E. Dobradzić, B. Nikolić, J. Phys. A 36, 10349 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  42. M. Damnjanović, T. Vuković, I. Milosěvić, Acta Phys. Pol. A 120, 224 (2011)

    Google Scholar 

  43. P.B. Allen, Nanoletters 7, 6, 11, 1220 (2007)

    Google Scholar 

  44. C. Herring, Phys. Rev. 82, 87 (1951)

    Article  ADS  MATH  Google Scholar 

  45. D.B. Migas, V.L. Shaposhnikov, V.E. Borisenko, F.A. D’Avitaya, J. Phys. Chem. C 114, 21013 (2010)

    Article  Google Scholar 

  46. C.A. Chen, Y.M. Chen, A. Korotcov, Y.S. Huang, D.S. Tsai, K.K. Tiong, Nanotechnology 19, 075611 (2007)

    Article  ADS  Google Scholar 

  47. B. Aradi, P. Deak, H.A. Huy, A. Rosenauer, T. Frauenheim, J. Phys. Chem. C 115, 18494 (2011)

    Article  Google Scholar 

  48. A.P. Cracknell, B.L. Davies, S.C. Miller, W.F. Love, Kronecker Product Tables, 1 General Introduction and Tables of Irreducible Representations of Space Groups (IFI/Plenum, New York, 1979)

    Google Scholar 

  49. C.J. Bradley, A.P. Cracknell, The Mathematical Theory of Symmetry in Solids (Clarendon, Oxford, 1972)

    MATH  Google Scholar 

  50. http://gernot-katzers-spice-pages.com/character_tables/index.html

  51. I.B. Božović, M. Vujičić, F. Herbut, J. Phys. A: Math. Gen. 11, 2133 (1978)

    Article  ADS  MATH  Google Scholar 

  52. I.B. Božović, M. Vujičić, J. Phys. A: Math. Gen. 14, 777 (1981)

    Article  ADS  MATH  Google Scholar 

  53. I. Božović, N. Božović, J. Phys. A: Math. Gen. 14, 1825 (1981)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. A. Evarestov .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Evarestov, R.A. (2015). The Symmetry Groups in Three-Dimensional Space. In: Theoretical Modeling of Inorganic Nanostructures. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44581-5_2

Download citation

Publish with us

Policies and ethics