Skip to main content
Log in

Gorsky-Bragg-Williams theory of phase transitions in the approximants of icosahedral quasicrystals

  • Phase Transitions
  • Published:
Crystallography Reports Aims and scope Submit manuscript

Abstract

The Gorsky-Bragg-Williams (GBW) theory has been modified to describe phase transitions caused by the ordering of two kinds of atoms in the even and the odd sublattices of the structures of icosahedral quasicrystals with the dodecahedral local order (DLO) and their approximants. The modified method is exemplified by numerical calculations of such phase transitions in the structures of several simplest approximants.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D. Shechtman, I. Blech, D. Gratias, et al., Phys. Rev. Lett. 53, 1951 (1984).

    Article  ADS  Google Scholar 

  2. D. Levine and P. J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984).

    Article  ADS  Google Scholar 

  3. P. A. Kalugin, A. Yu. Kitaev, and L. S. Levitov, Pis’ma Zh. Éksp. Teor. Fiz. 41, 145 (1985).

    Google Scholar 

  4. M. Duneau and A. Katz, Phys. Rev. Lett. 54, 2688 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  5. V. Elser, Phys. Rev. Lett. 54, 1730 (1985).

    Article  ADS  Google Scholar 

  6. V. E. Dmitrienko, Acta Crystallogr., Sect. A: Found. Crystallogr. 50, 515 (1994).

    Article  Google Scholar 

  7. V. E. Dmitrienko, Mater. Sci. Forum 151, 199 (1994).

    Google Scholar 

  8. V. E. Dmitrienko and S. B. Astaf’ev, JETP Lett. 61, 331 (1995).

    ADS  Google Scholar 

  9. V. E. Dmitrienko and S. B. Astaf’ev, Phys. Rev. Lett. 75, 1538 (1995).

    Article  ADS  Google Scholar 

  10. T. Janssen, Acta Crystallogr., Sect. A: Found. Crystallogr. 42(2), 61 (1986).

    Google Scholar 

  11. D. S. Rokhsar, N. D. Mermin, and D. C. Wright, Phys. Rev. B: Condens. Matter. 35, 5487 (1987).

    ADS  MathSciNet  Google Scholar 

  12. L. S. Levitov and J. Rhyner, J. Phys. (Paris) 49, 1853 (1988).

    MathSciNet  Google Scholar 

  13. V. A. Chizhikov and V. E. Dmitrienko, in Proceedings of Int. Conf. on Aperiodic Crystals, Aperiodic’97 (1997), p. 581.

  14. V. A. Chizhikov, Kristallografiya 44(5), 814 (1999) [Crystallogr. Rep. 44, 755 (1999)].

    Google Scholar 

  15. L. D. Landau, Zh. Éksp. Teor. Fiz. 7, 19 (1937).

    Google Scholar 

  16. L. D. Landau and E. M. Lifshitz, Theoretical Physics. vol. 5. Statistical Physics [in Russian] (Nauka, Moscow, 1975; Pergamon, New York, 1980), Chap. 14.

    Google Scholar 

  17. W. Gorsky, Z. Phys. 50, 64 (1928).

    Google Scholar 

  18. W. L. Bragg and E. J. Williams, Proc. R. Soc. London A: 145, 699 (1934).

    ADS  Google Scholar 

  19. T. Muto and Y. Takagi, The Theory of Order-Disorder Transitions in Alloys (Academic, New York, 1955; IL, Moscow, 1959).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Kristallografiya, Vol. 45, No. 1, 2000, pp. 128–133.

Original Russian Text Copyright © 2000 by Chizhikov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chizhikov, V.A. Gorsky-Bragg-Williams theory of phase transitions in the approximants of icosahedral quasicrystals. Crystallogr. Rep. 45, 122–127 (2000). https://doi.org/10.1134/1.171147

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.171147

Keywords

Navigation