Rw. Peng et al., CHARACTERIZATION OF THE DIFFRACTION SPECTRA OF ONE-DIMENSIONAL K-COMPONENT FIBONACCI STRUCTURES, Physical review. B, Condensed matter, 52(18), 1995, pp. 13310-13316
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).