X-RAY STANDING WAVES IN QUASICRYSTALS: ATOMIC POSITIONS IN AN APERIODIC LATTICE

The observation of the Borrmann effect in quasicrystals demonstrates the presence of dynamical diffraction and, by inference, the existence of X-ray standing waves. In this chapter, we investigate the nature of the atomic order in icosohedral quasicrystals and the manner in which dynamical diffraction comes about. While atoms in quasicrystals do not occupy periodic atomic planes, they occur in distributions that give rise to well-defined X-ray standing wave effects. It is possible to demonstrate that the coherent fraction and coherent position obtained from a specific X-ray reflection correspond to a correlation function and centroid of the atomic distribution relative to that “reciprocal quasi-lattice vector.” We show experimental X-ray standing wave effects in the quasicrystal Al-Pd-Mn and their relation to the symmetries of the different elemental distributions.