Skip to main content
SpringerLink
Log in

Real Space Structure Factor and Scaling for Quasicrystals

  • Conference paper
Aperiodic Crystals

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.

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

References

  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. de Bruijn NG (1981) Proc K Ned Akad Wet, Ser A, Indag Math 43:38–66

    Google Scholar 

  3. Buczek P, Sadun L, Wolny J (2005) Acta Phys Pol B 36:919

    CAS  Google Scholar 

  4. Dabrowska A, Kozakowski B, Wolny J (2005) Acta Crystallogr, Sect A 61:350–357

    Article  Google Scholar 

  5. Kozakowski B, Wolny J (2010) Acta Crystallogr, Sect A 66:489–498

    Article  CAS  Google Scholar 

  6. Kramer P, Neri R (1984) Acta Crystallogr, Sect A 40:580

    Article  Google Scholar 

  7. Kuczera P, Kozakowski B, Wolny J, Steurer W (2010) J Phys Conf Ser 226:012001

    Article  Google Scholar 

  8. Kuczera P, Wolny J, Fleischer F, Steurer W (2011) Philos Mag 91:2500–2509

    Article  CAS  Google Scholar 

  9. Levine D, Steinhardt PJ (1984) Phys Rev Lett 53:2477

    Article  CAS  Google Scholar 

  10. Senechal M (1995) Quasicrystals and geometry. Cambridge University Press, Cambridge

    Google Scholar 

  11. Steurer W, Cervellino A (2001) Acta Crystallogr, Sect A 57:333

    Article  CAS  Google Scholar 

  12. Wolny J (1998) Philos Mag A 77:395–412

    Article  CAS  Google Scholar 

  13. Wolny J, Kozakowski B (2003) Acta Crystallogr, Sect A 59:54

    Article  Google Scholar 

  14. Wolny J et al. (2011) Isr J Chem 51:1275–1291

    Article  CAS  Google Scholar 

  15. Wolny J, Kozakowski B, Kuczera P, Takakura H (2008) Z Kristallogr 223:847–850

    Article  CAS  Google Scholar 

  16. Wolny J, Pytlik L, Lebech B (1990) J Phys Condens Matter 2:785–795

    Article  Google Scholar 

  17. Wolny J, Wnek A, Verger-Gaugry JL (2000) J Comput Phys 163:313–327

    Article  CAS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland

    J. Wolny, B. Kozakowski, P. Kuczera, L. Pytlik & R. Strzalka

Authors
  1. J. Wolny
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Kozakowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Kuczera
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. Pytlik
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. Strzalka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Wolny .

Editor information

Editors and Affiliations

  1. School of Chemistry, The University of Sydney, Sydney, 2006, New South Wales, Australia

    Siegbert Schmid

  2. Research School of Chemistry, The Australian National University, Building 35, Canberra, 0200, Australia

    Ray L. Withers

  3. School of Physics & Astronomy, Tel Aviv University, Tel Aviv, 69978, Israel

    Ron Lifshitz

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Wolny, J., Kozakowski, B., Kuczera, P., Pytlik, L., Strzalka, R. (2013). Real Space Structure Factor and Scaling for Quasicrystals. In: Schmid, S., Withers, R., Lifshitz, R. (eds) Aperiodic Crystals. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6431-6_28

Download citation

Publish with us

Policies and ethics

Search

Navigation