Fractal behaviour of diffraction pattern of Thue-Morse sequence

The Thue-Morse sequence is an example of an aperiodic structure with a sing ular continuous contribution to the diffraction pattern. Many satellites ob served near the main diffraction peaks have been indexed and their intensit ies have been numerically calculated. Details of such a calculation are pre sented for satellite peaks indexed by 1/3. An average-unit-cell approach wa s successfully used to describe probabilities of atomic displacements from the points of the reference lattice. For a certain parameterisation of such probabilities, the results of fairly simple integer calculations could be easily generalised, For some defined sets of points, the analytical express ions for diffraction intensities were found and tested numerically on a wid e range of scattering vectors and for up to 2(32) atoms. (C) 2000 Academic Press.