X-RAY-DIFFRACTION ON FIBONACCI SUPERLATTICES

The exact diffraction curve of the Fibonacci superlattice is calculate d using the semi-kinematical approximation of dynamical X-ray diffract ion. The properties of the discrete Fourier transform of quasiperiodic ally arranged layers are employed to derive explicit approximate formu lae for the diffracted intensity and the angular positions of peaks. T he exact and approximate curves are compared by a numerical simulation and a good agreement is found. The measurement of the diffraction cur ve was performed on the generalized Fibonacci superlattice built by st acked Fibonacci generations. This superlattice belongs to the same cla ss of local isomorphism as the Fibonacci superlattice if both are infi nitely thick. The explicit approximate formulae enabled the fitting of the structural parameters of the superlattice even in the low-resolut ion experimental set-up when the fitting of the whole measured diffrac tion curve was not possible.