Analysis of X-Ray Diffraction Pattern in Quasi-Periodic Lattice

Theoretical analysis of X-ray diffraction patterns is sudied to make clear essential properties of three types of quasi-periodic (Fibonacci, Thue-Morse and Dragon sequences) superlattices. The calculated X-ray diffraction patterns are compared with the experimental data for complicated structures achieved by means of molecular beam epitaxy (MBE) techniques in good agreement, and are interpreted by identifying with the quasi-periodic order of Zinc-Blende structures. The origin of characteristic properties to quasi-periodic structures such as the self-similarity feature, and the differences among Fibonacci, Thue-Morse and Dragon lattices are analyzed in terms of the correlation functions for their sequences and of Raman spectra. Furthermore, by exploring the continued fraction expansion, the effects of quasi-periodic sequence on phonon properties are discussed in relation to the fractional quantum Hall effect and the devil's staircase.