CHARACTERIZATION OF THE DIFFRACTION SPECTRA OF ONE-DIMENSIONAL K-COMPONENT FIBONACCI STRUCTURES

We study in this paper the diffraction spectrum (Fourier transform) of a one-dimensional k-component Fibonacci structure (KCFS), which conta ins k different intervals and can be generated by a substitution rule. Theoretical and numerical calculations based on the geometrical model s for atomic KCFS have been made. The structures with 1 < k less than or equal to 5 are quasiperiodic, and their Fourier transforms are the sum of weighted delta functions. These diffraction peaks can be indexe d by a finite set of base vectors. The structures with k > 5, however, do not possess the Pisot property, and the diffraction spectra consis t of neither Bragg peaks, nor diffuse scattering. They are singularly continuous instead, Multifractal analysis is employed to characterize the diffraction spectra in the case of k > 5. It is shown that the dif fraction spectra present scaling properties around the values of wave vector. Moreover, a dimensional spectrum of singularities associated w ith the diffraction spectrum, f(alpha), demonstrates a genuine multifr actality. We conclude that the one-dimensional k-component Fibonacci s tructures provide a generic structural model covering periodicity (k = 1), quasiperiodicity (1 < k less than or equal to 5), and multifracta lity between quasiperiodicity and disorder (k > 5).