Advertisement

Average Unit Cell in Fourier Space and Its Application to Decagonal Quasicrystals

  • B. KozakowskiEmail author
  • J. Wolny
Conference paper

Abstract

This paper describes a new technique for solving the structure of quasicrystals. The technique is based on transformations between an average unit cell (AUC) and an envelope of diffraction peaks. For centrosymmetric structures like the Penrose tiling, the envelope makes it possible to determine the sign of the phase straight from the diffraction pattern. A Fourier transform of an envelope leads to a distribution of atomic positions within an AUC. Apart from theoretical and modeling aspects of the technique, the paper also presents the results of applying it to the well-known decagonal quasicrystal Al–Ni–Co.

Notes

Acknowledgements

The authors thank H. Takakura for providing us with experimental data. This work is supported by the Polish Ministry of Science and Higher Education and its grant for Scientific Research (N N202 326440).

References

  1. 1.
    Baake M, Schlottmann M, Jarvis PD (1991) J Phys A 24:4637 Google Scholar
  2. 2.
    de Bruijn NG (1981) Proc K Akad Wet, Ser A, Indag Math 43:38–66 Google Scholar
  3. 3.
    Buczek P, Sadun L, Wolny J (2005) Acta Phys Pol A 36:919 Google Scholar
  4. 4.
    Fleischer F, Weber T, Steurer W (2010) J Phys Conf Ser 226:012002 CrossRefGoogle Scholar
  5. 5.
    Fleischer F Weber T et al. (2010) J Appl Crystallogr 43:89–100 CrossRefGoogle Scholar
  6. 6.
    Kozakowski B, Wolny J (2006) Philos Mag 86:549–555 CrossRefGoogle Scholar
  7. 7.
    Kramer P, Neri R (1984) Acta Crystallogr, Ser A 40:580 Google 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.
    Oszlanyi G, Suto A (2004) Acta Crystallogr, Ser A 60:134–141 CrossRefGoogle Scholar
  11. 11.
    Senechal M (1995) Quasicrystals and geometry. Cambridge University Press, Cambridge Google Scholar
  12. 12.
    Shiono M, Woolfson MM (1992) Acta Crystallogr, Ser A 48:451–456 CrossRefGoogle Scholar
  13. 13.
    Steurer W, Haibach T (1999) Acta Crystallogr, Ser A 55:48 Google Scholar
  14. 14.
    Steurer W, Cervellino A (2001) Acta Crystallogr, Ser A 57:333 Google Scholar
  15. 15.
    Takakura H, Yamamoto A, Tsai AP (2001) Acta Crystallogr, Ser A 57:576–585 CrossRefGoogle Scholar
  16. 16.
    Tsai AP, Inoue A, Matsumoto T (1989) Mater Trans, JIM 30:463–473 Google Scholar
  17. 17.
    Wolny J, Kozakowski B (2003) Acta Crystallogr, Ser A 59:54 CrossRefGoogle Scholar
  18. 18.
    Wolny J (1998) Philos Mag A 77:395–412 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Faculty of Physics and Applied Computer ScienceAGH University of Science and TechnologyKrakowPoland

Personalised recommendations