Numéro
J. Phys. I France
Volume 4, Numéro 12, December 1994
Page(s) 1855 - 1866
DOI https://doi.org/10.1051/jp1:1994226
DOI: 10.1051/jp1:1994226
J. Phys. I France 4 (1994) 1855-1866

Topology of the phason degree of freedom, phason singularities, and diffusive motion in octagonal quasicrystals

Anke Trub and Hans-Rainer Trebin

Institut für Theoretische und Angewandte Physik der Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany


(Received 29 December 1993, revised 13 May 1994, accepted 25 August 1994)

Abstract
The phason degree of freedom in quasicrystals is studied in two respects: first it is pointed out, that the orthogonal space E1 is not connected and not simply connected and that therefore wall, line and point defects exist in the phason variable of quasicrystalline tilings. Second, both by global and local changes of the phason variable vertices can be transported either along loops or along paths extending to infinity. Thus we provide explicit examples for the recently proposed phason-mediated selfdiffusion.

Résumé
Nous étudions deux points particuliers du degré de liberté des phasons: premièrement, nous montrons que l'espace perpendiculaire n'est ni connecté ni simplement connecté et que les défauts ponctuels, linéaires ou plans peuvent donc exister dans les pavages quasicristallins. Deuxièmement, en changeant la variable de phason localement ou globalement, on peut déplacer les sommets le long d'une boucle ou bien le long des chemins étendus jusqu'à l'infini. Nous donnons des exemples explicites pour l'autodiffusion assistée par les phasons, qui a été proposée récemment.



© Les Editions de Physique 1994

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