Advertisement

Quasicrystals pp 183-198 | Cite as

Quasicrystals as Hierarchical Packing of Overlapping Clusters

  • Christian Janot
  • Jean-Marie Dubois
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 55)

Summary

It is possible to describe quasiperiodic structures in terms of a skeleton of a hierarchical self-similar packing of overlapping atomic clusters. The related inflation rules constrain both composition and atomic valences to have strictly defined values. Stability of the skeleton requires that bonding electrons are recurrently localized at site-forming self-similar isomorphic subsets of the structure and are distributed into “magic cluster” states. Properties can be understood in the framework of such a cluster description of quasicrystals.

Keywords

Jellium Model Icosahedral Quasicrystal Penrose Tiling Magic Cluster Cluster Description 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Akiyama H., Honda Y., Hashimoto T., Edagawa K., and Takeuchi A. (1993): Jpn. J. Appl. Phys. B 7, L1003CrossRefGoogle Scholar
  2. 2.
    Audier M., Durand-Charre M., and de Boissieu M. (1993): Phil. Mag. B 68, 607CrossRefGoogle Scholar
  3. 3.
    Baake M. and Joseph D. (1990): Phys. Rev. B 42, 8091ADSCrossRefGoogle Scholar
  4. 4.
    Basov D.N., Timusk T., Barakat F., Greedan J., and Grushkjo B. (1994): Phys. Rev. Lett. 72, 1937ADSCrossRefGoogle Scholar
  5. 5.
    E. Belin, Z. Dankhazi, A. Sadoc, and J.M. Dubois (1994): J. Phys.: Condens. Matter 6, 8771;ADSCrossRefGoogle Scholar
  6. 5a.
    E. Belin, Z. Dankhazi, A. Sadoc, and J.M. Dubois (1994): Eur. Phys. Lett. 26, 677ADSCrossRefGoogle Scholar
  7. 6.
    Berger C., Grenet T., Lindqvist P., Lanco P., Grieco J.C., Fourcaudot G. and Cyrot-Lackmann F. (1993): Solid State Commun. 87, 977ADSCrossRefGoogle Scholar
  8. 7.
    de Boissieu M., Durand-Charre M., Bastie P., Carabelli A., Boudard M., Bessiere M., Lefebvre S., Janot C., and Audier M. (1992): Phil. Mag. Lett. 65, 147ADSCrossRefGoogle Scholar
  9. 8.
    de Boissieu M., Boudard M., Hennion B., Bellissent R., Kycia S., Goldman A.I., Janot C., and Audier M. (1995): Phys. Rev. Lett. 75, 89;ADSCrossRefGoogle Scholar
  10. 9.
    Boudard M., de Boissieu M., Janot C., Heger G., Beeli C., Nissen H.U., Vincent H., Ibberson R., Audier M., and Dubois J.M. (1992): J. Phys: Condens Matter 4, 10149ADSCrossRefGoogle Scholar
  11. 10.
    Boudard M., Bourgeat-Lami E., de Boissieu M., Janot C., Durand-Charre M., H. Klein, M. Audier, and B. Hennion (1995): Phil. Mag. Lett. 71(1) 11ADSCrossRefGoogle Scholar
  12. 11.
    Boudard M., de Boissieu M., Letoublon A., Hennion B., Bellissent R., and Janot C. (1996): Europhys. Lett. 33, 199ADSCrossRefGoogle Scholar
  13. 12.
    Chang S.L., Anderegg J.W., and Thiel P.A. (1996): J. Non-Cryst. Sol. 195, 95;ADSCrossRefGoogle Scholar
  14. 12a.
    Chang S.L., Chin W.B., Zhang C.M., Jenks C.J., and Thiel P.A. (1995): Surf. Science 337, 135ADSCrossRefGoogle Scholar
  15. 13.
    Chernikov M.A., Bianchi A., and Ott H.R. (1995): Phys. Rev. B 51, 153ADSCrossRefGoogle Scholar
  16. 14.
    Cornier-Quiquandon M., Quivy M., Lefebvre S., Elkaim E., Heger G., Katz A., and Gratias D. (1991): Phys. Rev. B 44, 2071Google Scholar
  17. 15.
    Degiorgi L., Chernikov M.A., Beeli C., and Ott H.R. (1993): Solid State Comm. 87, 721ADSCrossRefGoogle Scholar
  18. 16.
    Dubois J.M., Kang S.S., and Perrot A. (1994): Mater. Sc. Eng. A179-A180, 122Google Scholar
  19. 17.
    Dubois J.M. (2002): See Chapter 26 of this book; Dubois J.M. (1997) in: New Horizons in Quasicrystals, Goldman A.I., Sordelet D.J., Thiel P.A., and Dubois J.M. (Eds). World Scientific, SingaporeGoogle Scholar
  20. 18.
    Duneau M. (1995) in: Quasicrystals, 5th International Conference on Quasicrystals, Janot C. and Mosseri R. (Eds.). World Scientific, Singapore, 116Google Scholar
  21. 19.
    Dzugutov M. (1992): Phys. Rev. A 46, R2984;ADSCrossRefGoogle Scholar
  22. 19.
    Dzugutov M. (1993): Phys. Rev. Lett. 70, 2924ADSCrossRefGoogle Scholar
  23. 20.
    Ebert P., Feuerbacher M., Tamura N., Wollgarten M., and Urban K. (1996): Phys. Rev. Lett. 77, 3827ADSCrossRefGoogle Scholar
  24. 21.
    Elser V. (1996): Phil Mag. B 73, 641CrossRefGoogle Scholar
  25. 22.
    Feuerbacher M., Baufeld B., Rosenfeld R., Bartsch M., Hanke G., Beyss M., Wollgarten M., Messerschmitt U., and Urban K. (1995): Phil. Mag. Lett. 71, 91ADSCrossRefGoogle Scholar
  26. 23.
    Fujivara T. and Ogawa T. (Eds.) (1990): Quasicrystals, Springer-Verlag BerlinGoogle Scholar
  27. 24.
    Gähler F. and Jeong H.C. (1995): J. Phys. A 28, 1807MathSciNetADSCrossRefGoogle Scholar
  28. 25.
    Gödecke and Lück R. (1995): Z. Metallkd. 86, 2Google Scholar
  29. 26.
    Goldman A.I., Sordelet D.J., Thiel P.A., and Dubois J.M. (Eds.) (1997): New Horizons in Quasicrystals, World Scientific, SingaporeGoogle Scholar
  30. 27.
    Gummelt P. (1996): Geometriae Dedicata 62, 1MathSciNetMATHCrossRefGoogle Scholar
  31. 28.
    Guo B.C., Kerns K.P., and Castleman Jr. A.W. (1992): Science 255, 1411ADSCrossRefGoogle Scholar
  32. 29.
    Henley C.L. (1991) in: Quasicrystals: The State of the Art, DiVincenzo D.P. and Steindhardt P.J. (Eds.). World Scientific, Singapore, 111Google Scholar
  33. 30.
    Honda Y., Edagawa K., Yoshika A., Hashimoto T., and Takeuchi S. (1994): Jpn. J. Appl. Phys. A 9, 4929ADSCrossRefGoogle Scholar
  34. 31.
    Janot, C. (1994): Quasicrystals: A primer, 2nd edition, Oxford University Press, CambridgeMATHGoogle Scholar
  35. 32.
    Janot C. and de Boissieu M. (1994): Phys. Rev. Lett. 72, 1674.ADSCrossRefGoogle Scholar
  36. 33.
    Janot C. and Mosseri R. (Eds.) (1995): Quasicrystals, 5th International Conference on Quasicrystals, World Scientific, SingaporeGoogle Scholar
  37. 34.
    Janot C. (1996): Europhysics News 27, 60;Google Scholar
  38. 35.
    Janot C. (1996): Phys. Rev. B 53, 181ADSCrossRefGoogle Scholar
  39. 36.
    Janot C. (1997): J. Phys.: Condens. Matter 9, 1493ADSCrossRefGoogle Scholar
  40. 37.
    Jeong H.C. and Steinhardt P.J. (1997): Phys. Rev. B 553, 520Google Scholar
  41. 38.
    Joseph D. and Elser V. (1997): Phys. Rev. Lett. 79, 1066ADSCrossRefGoogle Scholar
  42. 39.
    Khanna S.N. and Jena P. (1992): Phys. Rev. Lett. 69, 1664;ADSCrossRefGoogle Scholar
  43. 39a.
    Khanna S.N. and Jena P. (1993): Phys. Rev. Lett. 71, 208ADSCrossRefGoogle Scholar
  44. 40.
    Khanna S.N. and Jena P. (1994): Chem. Phys. Lett. 218, 383;ADSCrossRefGoogle Scholar
  45. 40a.
    Khanna S.N. and Jena P. (1994): Chem. Phys. Lett. 219, 479ADSCrossRefGoogle Scholar
  46. 41.
    Khanna S.N. and Jena P. (1995): Phys. Rev. B 51, 13705ADSCrossRefGoogle Scholar
  47. 42.
    Knight W.D., Clemenger K., de Heer W.A., Saunders W.A., Chou M.Y., and Cohen M.L. (1984): Phys. Rev. Lett. 52, 2141ADSCrossRefGoogle Scholar
  48. 43.
    Kycia S.W., Goldman A.I., Lograsso T.A., Delancy D.W., Sutton M., Dufresne E., Brüning R., and Rodricks B. (1993): Phys. Rev. B 48, 3544ADSCrossRefGoogle Scholar
  49. 44.
    Leuchtner R.E., Harms A.C., and Castleman Jr. A.W. (1989): J. Chem. Phys. 91, 2753ADSCrossRefGoogle Scholar
  50. 45.
    Mikulla R., Krul F., Gumbsch P., and Trebin H.R. (1997) in: New Horizons in Quasicrystals, Goldman A.I., Sordelet D.J., Thiel P.A., and Dubois J.M. (Eds.). World Scientific, Singapore, 200Google Scholar
  51. 46.
    Naumovic D., Aebi P., Schlapbach L., and Beeli C. (1997) in: New Horizons in Quasicrystals, Goldman A.I., Sordelet D.J., Thiel P.A. and Dubois J.M. (Eds.). World Scientific, Singapore, 86Google Scholar
  52. 47.
    Parker L.J., Atou T., and Badding J. (1996): Science 273, 95ADSCrossRefGoogle Scholar
  53. 48.
    Penrose R. (1974): Bull. Inst. Math. Appl. 10, 266Google Scholar
  54. 49.
    Perrot A. and Dubois J.M. (1995) in: Janot C. and Mosseri R. (Eds.) Quasicrystals, 5th International Conference on Quasicrystals. World Scientific, Singapore, 586Google Scholar
  55. 50.
    Pierce F.S., Poon S.J., and Guo Q. (1993): Science 261, 737ADSCrossRefGoogle Scholar
  56. 51.
    Pierce F.S., Guo Q., and Poon S.J. (1994): Phys. Rev. Lett. 73, 2220ADSCrossRefGoogle Scholar
  57. 52.
    Poon S. J. (1992): Adv. Phys. 41, 303ADSCrossRefGoogle Scholar
  58. 53.
    Quemerais P. (1994): J. Phys. (Paris) 4, 1669Google Scholar
  59. 54.
    Roche S., Trambly de Laissardire G., and Mayou D. (1997): J. Math. Phys. 38, 4CrossRefGoogle Scholar
  60. 55.
    Schaub T.M., Bürgler D.E., Güntherodt H.J., Suck J.B. and Audier M. (1995): Appl. Phys. A 61, 491ADSCrossRefGoogle Scholar
  61. 56.
    Steurer W., Haibach T., and Zhang B. (1993): Acta Cryst. B 49, 661.CrossRefGoogle Scholar
  62. 57.
    Trambly de Laissardiere G. and Mayou D. (1997): Phys. Rev. B 55, 2890Google Scholar
  63. 58.
    Tsai A.P., Inoue A., and Masumoto T. (1990): Phil. Mag. Lett. 62 (2), 95ADSCrossRefGoogle Scholar
  64. 59.
    Urban K., Wollgarten M., and Wittmann R. (1993): Physica Scripta T 49, 360ADSCrossRefGoogle Scholar
  65. 60.
    Di Vincenzo D.P. and Steinhardt P.J. (Eds.)(1991): Quasicrystals: The State of the Art, World Scientific, Singapore 61.Google Scholar
  66. 60a.
    Wu X., Kycia S.W., Olson C.G., Benning P.J., Goldman A.I., and Lynch D.W. (1995): Phys. Rev. Lett. 75, 4540Google Scholar
  67. 62.
    Zurkirsh M., Atrei A., Erbudak M., and Hochtstrasser M. (1996): Phil. Mag. Lett. 73, 107ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Christian Janot
    • 1
  • Jean-Marie Dubois
  1. 1.Dipartimento di Scienze della TerraUniversitá di Roma “La Sapienza”RomaItaly

Personalised recommendations