Average unit-cell approach to diffraction on Thue–Morse sequence and decorated quasicrystals

The average unit cell approach has been successfully used to construct the probability distributions of atomic displacements from the reference lattice points and to calculate the diffraction patterns for two aperiodic structures — the Thue–Morse sequence and decorated Fibonacci chains. For the singular continuous diffraction pattern of the Thue–Morse sequence fractal exponents and multiplication factors have been found for scaling with the number of atoms. General method able to distinguish between various quasilattice decorations has been elaborated and tested for decorated Fibonacci chains.