Abstract
The jump kinetics on a quasiperiodic pinning potential is analyzed under small external force in a 1D Fibonacci quasilattice model. The model describes planar (layer) growth of stable quasicrystals from the melt and is also relevant to the movement of quasicrystal dislocations under small stress. An exact solution is found for the spectrum of jump length as function of the driving force. The solution describes the supercooling dependence of the spectrum of nucleus heights on the growing surface of a quasicrystal. The spectrum appears to be universal and its shape has a periodic dependence on the logarithm of the supercooling. The resulting quasicrystal growth kinetics agrees well with that found in computer simulations and in the analysis of continuous thermodynamic models.
Similar content being viewed by others
References
S. T. Chu and J. D. Weeks, Phys. Rev. Lett. 40, 733 (1978).
P. Nosieres and F. Gallet, J. Phys. (France) 48, 353 (1987).
A. A. Chernov, Modern Crystallography, Vol. 3, Springer-Verlag, Berlin, 1981.
A. Garg and D. Levine, Phys. Rev. Lett. 59, 1683 (1987).
R. Lipowsky and C. L. Henley, Phys. Rev. Lett. 60, 2394 (1988).
L. V. Mikheev, Phys. Lett. 132, 137 (1988).
M. A. Fradkin and A. A. Chernov, JETP Lett. 55, 162 (1992).
J. Toner, Phys. Rev. B 43, 915 (1991).
P. A. Kalugin, A. Yu. Kitaev, and L. S. Levitov, JETP Lett. 41, 145 (1985).
M. Kléman, in Quasicrystalline Materials, edited by Ch. Janot and J. M. Dubois, World Scientific, Singapore, 1988.
L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd edition, Oxford, Pergamon, 1981.
A. V. Artemyev and M. A. Fradkin, JETP Lett. 55, 343 (1992).
M. A. Fradkin, in Proceedings of the International Conference on Aperiodic Crystals, edited by G. Chapuis, World Scientific, Singapore, 1994.
Author information
Authors and Affiliations
Additional information
Pis’ma Zh. Éksp. Teor. Fiz. 69, No. 8, 531–536 (25 April 1999)
Published in English in the original Russian journal. Edited by Steve Torstveit.
Institute of Crystallography, Russian Academy of Sciences, 117333, Moscow, Russia
Rights and permissions
About this article
Cite this article
Fradkin, M.A. Jump kinetics on the Fibonacci quasilattice. Exactly solvable model of the layer growth and dislocation kinetics in quasicrystals. Jetp Lett. 69, 570–576 (1999). https://doi.org/10.1134/1.567962
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1134/1.567962