Diffraction properties of one-dimensional finite size Fibonacci quasilattice

Abstract

The diffraction patterns from Fibonacci quasilattices have been calculated. Finite-size effects are evaluated for weak and strong peaks. For a smaller number of scatterers (<100) there are fluctuations in the intensities of weak and strong peaks. The fluctuations in weak peaks are greater than that in strong peaks. The fluctuations in intensities of weak and strong peaks near the origin are larger than in the corresponding cases of weak and strong peaks far away from the origin. Small shifts in peak-positions are unexpectedly found, the shifts being proportional to $N^{-3/2}$ for a large number of scatterers. The diffraction pattern of a qne-dimensional crystal and random structure is compared with that of the Fibonacci quasilattice. The strong peaks observed in the diffraction pattern of l-d crystal show negligible peak-shifts, they being comparable with computational errors even when the number of scatterers is as small as 5. The implications for analysing the experiments are briefly indicated