Skip to main content

Structures by Projection

  • Chapter
Beyond the Crystalline State

Abstract

In Chap. 2 we have seen that many structural arrangements of atoms and molecules are possible, corresponding to the various phases of condensed matter. A common feature is that the average density is generally constant in each case: equilibrium thermodynamic phases are almost always spatially homogeneous. From a purely geometric point of view, therefore, different phases represent the outcomes of different space-filling exercises, the building blocks being atoms, molecules or even clusters of atoms and molecules.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. G. Toulouse: Commun. Phys. 2, 115 (1977)

    Google Scholar 

  2. Quoted by G. Toulouse: “The Frustration Model”, In Modern Trends in the Theory of Condensed Matter, ed. by A. Pekalski, J. Przystawa ( Springer, Berlin, Heidelberg 1980 ) p. 195

    Google Scholar 

  3. M. Kleman, J. F. Sadoc: J. Physique 40, L569 (1979)

    Article  Google Scholar 

  4. G. Venkataraman, D. Sahoo: Contemp. Phys. 26, 579 (1985); 27, 3 (1986)

    Google Scholar 

  5. A. Janner, T. Janssen: Phys. Rev. B 15, 643 (1977)

    Article  ADS  Google Scholar 

  6. P. M. de Wolff: Acta Crystallogr. A 30, 777 (1974)

    Article  ADS  Google Scholar 

  7. V. Elser: Phys. Rev. B 32, 4892 (1985)

    Google Scholar 

  8. M. Duneau, A. Katz: Phys. Rev. Lett. 54, 2688 (1985); A. Katz, M. Duneau: J. Physique 47, 181 (1986)

    Article  MathSciNet  Google Scholar 

  9. P. Kalugin, A. Yu Kitaev, L. S. Levitov: Pis’ma Zh. Eksp. Teor. Fiz. 41, 119 (1985) [English transi.: JETP Lett. 41, 145 (1985)]; J. Physique Lett. 46, L601 (1985)

    Article  Google Scholar 

  10. R. K. P. Zia, W. J. Dallas: J. Phys. A 18, L341 (1985)

    Article  ADS  Google Scholar 

  11. H. S. M. Coxeter, G. J. Whitrow: Proc. Roy. Soc. A 201, 417 (1950)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. H. S. M. Coxeter: Regular Polytopes (Dover, New York 1973)

    Google Scholar 

  13. F. C. Frank, J. S. Kasper: Acta Cryst. I1, 184 (1958); 12, 483 (1959)

    Article  Google Scholar 

  14. F. C. Frank: Proc. Roy. Soc. A 215, 43 (1952)

    Article  ADS  Google Scholar 

  15. J. F. Sadoc, R. Mosseri: Phil. Mag. 45, 467 (1982)

    Google Scholar 

  16. J. F. Sadoc: J. Non-Cryst. Solids 44, 1 (1981)

    Article  ADS  Google Scholar 

  17. R. Zallen: Physics of Amorphous Solids ( Wiley, New York 1983 )

    Book  Google Scholar 

  18. J. D. Bernal: Proc. R. Soc. A 280, 299 (1964)

    Article  ADS  Google Scholar 

  19. J. F. Sadoc: J. Physique 44, L707 (1983)

    Google Scholar 

  20. J. F. Sadoc, R. Mosseri: J. Physique 46, 1809 (1985)

    Article  Google Scholar 

  21. D. R. Nelson: Phys. Rev. B 28, 5515 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  22. D. Polk: J. Non-Cryst. Solids 5, 365 (1971)

    Article  ADS  Google Scholar 

  23. G. A. N. Connell, R. J. Temkin: Phys. Rev. B 9, 5323 (1974)

    Article  ADS  Google Scholar 

  24. J. F. Sadoc, R. Mosseri: J. Non-Cryst. Solids 61/62, 487 (1984)

    Google Scholar 

  25. J. Sadoc: J. Physique Colloque C 8, 326 (1980)

    Google Scholar 

  26. N. P. Warner: Proc. R. Soc. A 383, 359, 379 (1982)

    Article  MathSciNet  Google Scholar 

  27. D. Nelson, M. Widom: Nucl. Phys. B 240, 113 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  28. M. Kleman: J. Physique 43, 1389 (1982); 44, L295 (1983)

    Google Scholar 

  29. M. Kleman, P. Donnadieu: Philos. Mag. B 52, 121 (1985)

    Article  Google Scholar 

  30. M. Kleman: J. Physique 46, L723 (1985)

    Article  Google Scholar 

  31. S. Meiboom, J. P. Sethna, P. W. Anderson, W. F. Brinkman: Phys. Rev. Lett. 46, 1216 (1981); S. Meiboom, M. Sammon, W. F. Brinkman: Phys. Rev. A 27, 438 (1983)

    Article  Google Scholar 

  32. N. G. de Bruijn: Ned. Akad. Weten. Proc. Ser. A 43, 39, 59 (1981)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  34. D. Shechtman, I. Blech, D. Gratias, J. W. Cahn: Phys. Rev. Lett. 53, 1951 (1984)

    Article  ADS  Google Scholar 

  35. J. E. S. Socolar, P. J. Steinhardt: Phys. Rev. B 34, 617 (1986)

    Article  ADS  Google Scholar 

  36. J. E. S. Socolar, P. J. Steinhardt, D. Levine: Phys. Rev. B 32, 5547 (1985)

    Google Scholar 

  37. P. Bak: Phys. Rev. B 32, 5764 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  38. M. Kleman, Y. Gefen, A. Pavlovitch: Europhys. Lett. 1, 61 (1986)

    Article  ADS  Google Scholar 

  39. J. Bohsung, H. R. Trebin: Phys. Rev. Lett. 58, 1204 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  40. M. C. Valsakumar: Private communication

    Google Scholar 

  41. D. Ruelle: Physica 113A, 619 (1982)

    Article  MathSciNet  Google Scholar 

  42. D. Ruelle: Physica 7D, 40 (1983)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Venkataraman, G., Sahoo, D., Balakrishnan, V. (1989). Structures by Projection. In: Beyond the Crystalline State. Springer Series in Solid-State Sciences, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83434-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-83434-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83436-3

  • Online ISBN: 978-3-642-83434-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics