Skip to main content
SpringerLink
Log in

Disorder Diffuse Scattering of Crystals and Quasicrystals

  • Chapter
  • First Online:
Particle Scattering, X-Ray Diffraction, and Microstructure of Solids and Liquids

Part of the book series: Lecture Notes in Physics ((LNP,volume 610))

  • 1000 Accesses

Abstract

Diffuse scattering is due to departures of any kind from a perfectly ordered periodic array of identical structural units in n-dimensional space. Crystals and quasicrystals refer to n = 3 and n > 3, respectively. Periodicity of aperiodically ordered quasicrystals is restored in higher dimensional (hyper-) space. The term “disorder” covers a wide range of structural fluctuations including displacive, chemical, or lattice (= domain) disorder. Phasonic type fluctuations in quasicrystals describe displacements of hyperatoms in the perpendicular subspace of the superspace. Bragg diffraction provides information about the space/time-average of a (quasi-) crystal, i.e. about properties of single atomic sites. Diffuse scattering contains information about how pairs of atoms or larger structural units behave. Examples of layer-disorder in crystals and disorder in decagonal quasicrystals are discussed in some detail.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. C. Marais, V. Heine, C. M. Nex, and E. K. H. Salje. Phys. Rev. Lett. 66, 2480 (1991).

    Article  ADS  Google Scholar 

  2. J. M. Cowley. Diffraction Physics, North-Holland, Amsterdam (1981).

    Google Scholar 

  3. H. Boysen. Phase Trans. 55, 1 (1995).

    Article  Google Scholar 

  4. H. Boysen, F. Frey, H. Schrader, G. Eckold. Phys. Chem. Minerals 17, 629 (1991).

    Article  ADS  Google Scholar 

  5. F. Frey. Z. Kristallogr. 212, 257 (1997).

    Article  Google Scholar 

  6. F. Frey. ‘Diffuse Scattering by Domain Structures’. In: Local Structure from Diffraction. ed. by S. J. L. Billinge, M. F. Thorpe (Plenum Press, New York 1998), pp. 295.

    Google Scholar 

  7. F. Frey, H. Boysen. Acta Crystallogr. A37, 819 (1981).

    ADS  Google Scholar 

  8. F. Frey. Mat. Sci. Eng. 294–296, 175 (2000).

    Google Scholar 

  9. F. Frey, E. Weidner, K. Hradil, M. de Boissieu, R. Currat, K. Shibata, A. P. Tsai, J. Sato. Phil. Mag. A 80, 2375 (2000).

    Article  ADS  Google Scholar 

  10. F. Frey, E. Weidner, K. Hradil, M. de Boissieu, R. Currat, K. Shibata, A.-P. Tsai. Conference Quasicrystals 2001 at Sendai, Japan sep. 24.–28. 2001, Contrib. 2I01.

    Google Scholar 

  11. A. J. C. Wilson. X-Ray Optics. (Methuen, London 1962).

    Google Scholar 

  12. H. Jagodzinski, F. Frey. In: Int. Tables Vol.B, ed. U. Shmueli (Kluwer, Dordrecht 1993), Ch. 4. 2.

    Google Scholar 

  13. H. Jagodzinski. Progr. Crystal Growth and Charact. 114, 47 (1987).

    Article  Google Scholar 

  14. H. Jagodzinski. Acta Crystallogr. 2,201,208,298 (1949).

    Article  Google Scholar 

  15. H. Jagodzinski. Acta Crystallogr. 7, 17 (1954).

    Article  Google Scholar 

  16. H. Jagodzinski, M. Korekawa. Suppl. 3, Geochimica et Cosmochimica Acta 1, 555 (1972).

    Google Scholar 

  17. J. Kakinoki, Y. Komura. J. Phys. Soc. Japan 7, 30 (1952), 9 169, 177 (1954).

    Article  ADS  Google Scholar 

  18. J. Cowley. Acta Crystallogr. A32, 83 (1976).

    ADS  Google Scholar 

  19. K.-H. Jost. Röntgenbeugung an Kristallen. (Heyden, Rheine 1975).

    Google Scholar 

  20. B. E. Warren. X-Ray Diffraction. (Addison-Wesley, Reading 1969).

    Google Scholar 

  21. W. Adlhart. Acta Crystallogr. A37, 794 (1981).

    ADS  Google Scholar 

  22. T. R. Welberry, B. D. Butler. Chem. Rev. 95, 2369 (1995).

    Article  Google Scholar 

  23. T. R. Welberry. Rep. Progr. Phys. 48, 1543 (1985).

    Article  ADS  Google Scholar 

  24. A. Guinier. X-ray diffraction in crystals, imperfect solids and amorphous bodies. (Freeman, San Francisco 1963).

    Google Scholar 

  25. P. Launois, R. Moret. J. Phys. IV France 10, Pr 3–193 (2000).

    Google Scholar 

  26. L. H. Schwartz, J. B. Cohen. Diffraction from materials. (Acad. Press, New York 1977), ch. 7.

    Google Scholar 

  27. W. Steurer, F. Frey. Phase Transitions. 67, 319 (1998).

    Article  Google Scholar 

  28. R. Hosemann, S. N. Bagchi. Direct analysis of diffraction by matter. (North-Holland, Amsterdam 1962).

    MATH  Google Scholar 

  29. S. B. Hendricks, E. Teller. J. Chem. Phys. 10, 147 (1942).

    Article  ADS  Google Scholar 

  30. C. Thompson, M. E. Misenteiner, S. C. Moss. Acta Crystallogr. 44, 6 (1988).

    Article  Google Scholar 

  31. E. Blanc, H. B. Buergi, R. Restori, D. Schwarzenbach, Ph. Ochsenbein. Europhys. Lett. 33, 205 (1996).

    Article  ADS  Google Scholar 

  32. A. Babkevich, F. Frey, R. Neder, B. I. Nikolin. Phys. stat. sol. (a) 155, 3 (1996).

    Article  ADS  Google Scholar 

  33. R. Lifshitz. Conference Quasicrystals 2001 at Sendai, Japan sep. 24.–28. 2001, Contrib. 3IO2.

    Google Scholar 

  34. L.-H. Tang. Phys. Rev. Lett. 64, 2390 (1990).

    Article  ADS  Google Scholar 

  35. M. V. Jaric. Mat. Sci. Forum 22–24, 345 (1987).

    Article  Google Scholar 

  36. M. V. Jaric, D. R. Nelson. Phys. Rev B 37, 4458 (1988).

    Article  ADS  Google Scholar 

  37. M. Widom. Phil Mag. Lett. 64, 297 (1991).

    Article  ADS  Google Scholar 

  38. Y. Ishii. Phys. Rev. B 45, 5228 (1992).

    Article  ADS  Google Scholar 

  39. Y. Ishii. Mat. Sci. Eng. 294–296, 377 (2000).

    Google Scholar 

  40. M. de Boissieu, M. Boudard, B. Hennion, R. Bellissent, S. Kycia, A. Goldman, C. Janot, M. Audier. Phys. Rev. Lett. 75, 89 (1995).

    Article  ADS  Google Scholar 

  41. P. C. Gibbons, K. F. Kelton. Phil. Mag. B59, 593 (1993)

    Google Scholar 

  42. J. L. Robertson, S. C. Moss. J. of non-cryst. solids 153/154, 77 (1993).

    Article  Google Scholar 

  43. A. I. Goldman, C. A. Guryan, P. W. Stephens, J. M. Parsey, G. Aeppli, H. S. Chen, F. W. Gayle. Phys. Rev. Lett. 61, 1962 (1988).

    Article  ADS  Google Scholar 

  44. A. Proult, P. Donnadieu, K. Wang, P. Garoche. J. Phys. I France 5, 1615 (1995).

    Article  Google Scholar 

  45. J.-L. Lei, R. Wang, C. Hu, and D.-H. Ding. Phys. Rev. B 59, 822 (1999).

    Article  ADS  Google Scholar 

  46. E. Weidner, J.-L. Lei, F. Frey, R. Wang. To be published.

    Google Scholar 

  47. E. Weidner, F. Frey, K. Hradil. Phil. Mag. A 81, 2375 (2001).

    Article  ADS  Google Scholar 

  48. E. Weidner, F. Frey, K. Hradil, M. de Boissieu, G. McIntyre, A. P. Tsai. Conference Quasicrystals 2001 at Sendai, Japan sep. 24.–28. 2001, Contrib. 2012.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Kristallographie und Angewandte Mineralogie, Ludwig-Maximilians-Universität, Theresienstr. 41, 80333, München

    Friedrich Frey

Authors
  1. Friedrich Frey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937, Köln, Germany

    Manfred L. Ristig

  2. Department of Physics, UMIST, P. O. Box 88, Manchester, M60 1QD, UK

    Klaus A. Gernoth

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Frey, F. (2003). Disorder Diffuse Scattering of Crystals and Quasicrystals. In: Ristig, M.L., Gernoth, K.A. (eds) Particle Scattering, X-Ray Diffraction, and Microstructure of Solids and Liquids. Lecture Notes in Physics, vol 610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45881-6_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-45881-6_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44386-5

  • Online ISBN: 978-3-540-45881-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation