Numerical Simulation of Defects in Quasicrystals

  • H.-R. Trebin
Part of the NATO Science Series book series (NAII, volume 43)

Abstract

Quasicrystals are novel types of ordered material structures with noncrystallographic symmetries and quasiperiodic mass density. In addition to the translational displacement degree of freedom (akin also to periodic crystals) they possess a phason degree of freedom which can change the local neighborhood of atoms. The characteristic defects of quasicrystals are dislocations. These, however, are accompanied by phasonic fields. The mechanical properties of quasicrystals, plasticity and fracture, are strongly influenced by this degree of freedom. The motion of dislocations and cracks is studied by molecular dynamics simulations of sheared and torn two- and three-dimensional model quasicrystals.

Keywords

Brittle Hexagonal Peri Prolate 

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References

  1. 1.
    Wright, D.C., Mermin, N.D. (1989) Rev. Mod. Phys., 61, 385–432.ADSCrossRefGoogle Scholar
  2. 2.
    Filev, V.M. (1986) JETP Lett., 43, 677–681.ADSGoogle Scholar
  3. 3.
    Hornreich, R.M., Shtrikman, S. (1986) Phys. Rev. Lett., 56, 1723–1726.ADSCrossRefGoogle Scholar
  4. 4.
    Rokshar, D.S., Sethna, J.P. (1986) Phys. Rev. Lett., 56, 1727–1730.ADSCrossRefGoogle Scholar
  5. 5.
    Longa, L., Fink, W., Trebin, H.-R. (1993) Phys. Rev. E, 48, 2296–2299.ADSCrossRefGoogle Scholar
  6. 6.
    Gummelt, P. (1996) Geometriae Dedicata, 62, 1–17.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Steinhardt, P.J., Jeong, H.C., Saitoh, K., Tanaka, M., Abe, E., Tsai, A.P. (1998) Nature, 396, 55–57.ADSCrossRefGoogle Scholar
  8. 8.
    Yan, Y., Pennycook, S. (2001) Phys. Rev. Lett., 86, 1542–1545.ADSCrossRefGoogle Scholar
  9. 9.
    Bohsung, J., Trebin, H.-R. (1989) In Introduction to the Mathematics of Quasicrystals, volume 2 of Aperiodicity and Order, pp. 183–221, Jaric MV, (ed.), Academic Press, Boston.Google Scholar
  10. 10.
    Hiraga, K., Hirabayashi, M. (1987) Jpn. J. Appl. Phys., 26, L155–L158.ADSCrossRefGoogle Scholar
  11. 11.
    Wollgarten, M., Beyss, M., Urban, K., Liebertz, H., Köster, U. (1993) Phys. Rev. Lett., 71, 549–552.ADSCrossRefGoogle Scholar
  12. 12.
    Wollgarten, M., Bartsch, M., Messerschmidt, U., Feuerbacher, M., Rosenfeld, R., Beyss, M., Urban, K. (1995) Philos. Mag. Lett., 71, 99–105.ADSCrossRefGoogle Scholar
  13. 13.
    Feuerbacher, M., Baufeld, B., Rosenfeld, R., Bartsch, M., Hanke, G., Beyss, M., Wollgarten, M., Messerschmidt, U., Urban, K. (1995) Philos. Mag. Lett., 71, 91–98.ADSCrossRefGoogle Scholar
  14. 14.
    Feuerbacher, M., Bartsch, M., Grushko, B., Messerschmidt, U., Urban, K. (1997) Philos. Mag. Lett., 76, 369–375.CrossRefGoogle Scholar
  15. 15.
    Ebert, Ph., Feuerbacher, M., Tamura, N., Wollgarten, M., Urban, K. (1996) Phys. Rev. Lett., 77, 3827–3830.ADSCrossRefGoogle Scholar
  16. 16.
    Stadler, J., Mikulla, R., Trebin, H.-R. (1997) Int. J. Mod. Phys. C, 8, 1131–1140.ADSCrossRefGoogle Scholar
  17. 17.
    Lees, A.W., Edwards, S.F. (1972) J. Phys. C, 5, 1921–1929.ADSCrossRefGoogle Scholar
  18. 18.
    Mikulla, R., Stadler, J., Krul, F., Trebin, H.-R., Gumbsch, P. (1998) Phys. Rev. Lett., 81, 3163–3166.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • H.-R. Trebin
    • 1
  1. 1.Institut für Theoretische und Angewandte PhysikUniversität StuttgartStuttgartGermany

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