The average unit cell approach has been successfully used to construct the
probability distributions of atomic displacements from the reference lattic
e points and to calculate the diffraction patterns for two aperiodic struct
ures - the Thue-Morse sequence and decorated Fibonacci chains. For the sing
ular continuous diffraction pattern of the Thue-Morse sequence fractal expo
nents and multiplication factors have been found for scaling with the numbe
r of atoms. General method able to distinguish between various quasilattice
decorations has been elaborated and tested for decorated Fibonacci chains.
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