Jump kinetics on the Fibonacci quasilattice. Exactly solvable model of the layer growth and dislocation kinetics in quasicrystals
PACS: 61.72.Hh, 68.35.M, 81.10.Aj
The jump kinetics on a quasiperiodic pinning potential is analyzed under small external force in a model of ID Fibonacci quasilattice. The model describes planar (layer) growth of stable quasicrystals from the melt and is also relevant to the movement of qua-sicrystal dislocations under small stress. Exact solution is found for the spectrum of jump length as function of the driving force. The solution describes the supercooling dependence of the nucleus heights spectrum on the growing surface of a quasicrystal. The spectrum appears to be universal and its shape has a periodical dependence on the logarithm of supercooling. Resulting quasicrystal growth kinetics agrees well with that found in the computer simulations and in the analysis of continuous thermodynamic models.