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Unconventional properties of dislocations in quasicrystals

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Abstract

Dislocations in quasicrystals are defined as the intersections of dislocations in a high dimensional lattice with an irrational cut which figures the physical space. This definition confers to them a number of unusual geometrical properties which can be studied either by suitable extensions of the Volterra process, or by topological approaches, which often offer complementary points of view and are presented in this paper. Amongst these unusual properties, the production of stacking faults under shear at low temperature, reshuffling processes on stacking faults, and properties of non-commutativity which could have some incidences on the interplay between dislocations in deformation processes are mentioned.

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References

  1. [1]

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

  2. [2]

    Kuo K.H.:in Quasicrystals, Proc. ICTP, Trieste 1989 (Eds. M.V. Jaric and S. Lundqvist), World Scientific, Singapore, 1990.

  3. [3]

    Senechal M.:in Aperiodicity and Order, Vol. 2, (Ed. M.V. Jaric), Academic Press, San Diego, 1989.

  4. [4]

    Duneau M. and Katz A.: Phys. Rev. Lett.54 (1985) 2688.

  5. [5]

    Penrose R.: Math. Intelligencer2 (1979) 32.

  6. [6]

    Socolar J.E.S.: Commun. Math. Phys.129 (1990) 599.

  7. [7a]

    The Physics of Quasicrystals (Eds. P.J. Steinhardt and S. Ostlund), World Scientific, Singapore, 1987.

  8. [7b]

    Quasicrystals. The State of the Art (Eds. D.P. DiVincenzo and P.J. Steinhardt), World Scientific, Singapore, 1991.

  9. [8a]

    Levine D., Lubensky T.C., Ostlund S., Ramaswamy S., Steinhardt P.J., and Toner J.: Phys. Rev. Lett.54 (1985) 1520.

  10. [8b]

    Kléman M., Gefen Y., and Pavlovitch A.: Europhys. Lett.1 (1986) 61.

  11. [9]

    Bohsung J. and Trebin H.-R.:in Aperiodicity and Order, Vol. 2 (Ed. M.V. Jaric), Academic Press, San Diego, 1989.

  12. [10a]

    Wougarten M., Gratias D., Zhang Z., and Urban K.: Philos. Mag. A64 (1991) 819.

  13. [10b]

    Wang R. and Dai M.X.: Phys. Rev. B47 (1993) 15326.

  14. [11a]

    Kléman M.: J. Physique (France)51 (1990) 2431.

  15. [11b]

    Kléman M.:in ‘Sir Charles Frank, OBE, FRS; an eightieth birthday tribute’ (Eds. R.G. Chambers et al.). Adam Hilger, Bristol, 1991, p. 232.

  16. [11c]

    Kléman M.: J. Phys. I (France)2 (1992) 69.

  17. [12a]

    Mermin N.: Rev. Mod. Phys.51 (1979) 591.

  18. [12b]

    Michel L.: Rev. Mod. Phys.52 (1980) 617.

  19. [13a]

    Kléman M.:in Proceed. I.L.L./Codest Workshop on quasi-crystalline materials, 1988 (Eds. Ch. Janot and J.M. Dubois), World Scientific, Singapore, 1988, p. 318.

  20. [13b]

    Kléman M. and Sommers C.: Acta Met. Mat.39 (1991) 287.

  21. [14]

    Amelinckx S.:in Dislocations in Solids (Ed. F.R.N. Nabarro) Vol. 2, North Holland, Amsterdam, 1979, p. 398.

  22. [15a]

    Yu D.P.: PhD thesis, October 1993, University Paris-XL

  23. [15b]

    Baluc N., Yu D.P., and Kléman M.: Philos. Mag. Lett. (1995), in print.

  24. [16]

    Friedel J.: The Physics of Quasicrystals (plenary lecture), 5th Int. Conf. on QC's, Avignon-France, May 1995.

  25. [17a]

    Penrose R.: Math. Intelligencer2 (1979) 32.

  26. [17b]

    de Bruijn N.G.: Kon. Nederl. Akad. Wetensch. Proceed. A84 (1981) 38, 53.

  27. [18]

    Frenkel D.M., Henley C.L., and Siggia E.D.: Phys. Rev. B34 (1986) 3689.

  28. [19]

    Coxeter H.S.M. and Moser W.O.: Generators and Relations for Discrete Groups, Springer, Berlin, 1972.

  29. [20a]

    Kléman M.: J. Phys. Lett. (Paris)38 (1977) L199.

  30. [20b]

    Trebin H.R.: Phys. Rev. B30 (1984) 4338.

  31. [21]

    Misirpashaev T.Sh.: J. Phys. I (France)5 (1995) 399.

  32. [22]

    Hilbert D. and Cohn-Vossen S.: Geometry and the Imagination, Chelsea Publ. Co., New-York, 1952.

  33. [23]

    Olami Z. and Alexandes S.: Phys. Rev. B39 (1989) 1478.

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Dedicated to Dr. František Kroupa in honour of his 70th birthday.

Unité de Recherche Associée 009 du CNRS, associée aux Universités de Paris VI at Paris VII

We are very grateful to Dr. Vladimir Dmitrienko for discussions and useful remarks.

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Kléman, M. Unconventional properties of dislocations in quasicrystals. Czech J Phys 45, 935–946 (1995). https://doi.org/10.1007/BF01692011

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Keywords

  • Geometrical Property
  • Physical Space
  • Deformation Process
  • Unusual Property
  • Dimensional Lattice