Jump kinetics on the Fibonacci quasilattice. Exactly solvable model of the layer growth and dislocation kinetics in quasicrystals

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. 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