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Real Space Structure Factor and Scaling for Quasicrystals

  • J. WolnyEmail author
  • B. Kozakowski
  • P. Kuczera
  • L. Pytlik
  • R. Strzalka

Abstract

This paper describes the average unit cell (AUC) approach and its application to a derivation of the structure factor for quasicrystals. Scaling plays a special role in this approach. The TAU2-scaling in AUC simplifies the formulae for the structure factor. The TAU-scaling of peak positions distinguishes quasicrystals from twins, indicating a phase transition at some critical concentration of atoms.

Notes

Acknowledgements

Partially supported by the Polish Ministry of Science and Higher Education and its grants for Scientific Research: 3264/B/H03/2011/40 and DEC-2011/01/N/ST3/02250.

References

  1. 1.
    Baake M, Moody RV, Richard C, Sing B (2003) In: Trebin H-R (ed) Quasicrystals: structure and physical properties. Wiley-VCH, Berlin, pp 188–207 Google Scholar
  2. 2.
    de Bruijn NG (1981) Proc K Ned Akad Wet, Ser A, Indag Math 43:38–66 Google Scholar
  3. 3.
    Buczek P, Sadun L, Wolny J (2005) Acta Phys Pol B 36:919 Google Scholar
  4. 4.
    Dabrowska A, Kozakowski B, Wolny J (2005) Acta Crystallogr, Sect A 61:350–357 CrossRefGoogle Scholar
  5. 5.
    Kozakowski B, Wolny J (2010) Acta Crystallogr, Sect A 66:489–498 CrossRefGoogle Scholar
  6. 6.
    Kramer P, Neri R (1984) Acta Crystallogr, Sect A 40:580 CrossRefGoogle Scholar
  7. 7.
    Kuczera P, Kozakowski B, Wolny J, Steurer W (2010) J Phys Conf Ser 226:012001 CrossRefGoogle Scholar
  8. 8.
    Kuczera P, Wolny J, Fleischer F, Steurer W (2011) Philos Mag 91:2500–2509 CrossRefGoogle Scholar
  9. 9.
    Levine D, Steinhardt PJ (1984) Phys Rev Lett 53:2477 CrossRefGoogle Scholar
  10. 10.
    Senechal M (1995) Quasicrystals and geometry. Cambridge University Press, Cambridge Google Scholar
  11. 11.
    Steurer W, Cervellino A (2001) Acta Crystallogr, Sect A 57:333 CrossRefGoogle Scholar
  12. 12.
    Wolny J (1998) Philos Mag A 77:395–412 CrossRefGoogle Scholar
  13. 13.
    Wolny J, Kozakowski B (2003) Acta Crystallogr, Sect A 59:54 CrossRefGoogle Scholar
  14. 14.
    Wolny J et al. (2011) Isr J Chem 51:1275–1291 CrossRefGoogle Scholar
  15. 15.
    Wolny J, Kozakowski B, Kuczera P, Takakura H (2008) Z Kristallogr 223:847–850 CrossRefGoogle Scholar
  16. 16.
    Wolny J, Pytlik L, Lebech B (1990) J Phys Condens Matter 2:785–795 CrossRefGoogle Scholar
  17. 17.
    Wolny J, Wnek A, Verger-Gaugry JL (2000) J Comput Phys 163:313–327 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • J. Wolny
    • 1
    Email author
  • B. Kozakowski
    • 1
  • P. Kuczera
    • 1
  • L. Pytlik
    • 1
  • R. Strzalka
    • 1
  1. 1.Faculty of Physics and Applied Computer ScienceAGH University of Science and TechnologyKrakowPoland

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