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Periodic X-ray standing waves in quasiperiodic systems

Abstract X-ray Standing Waves (XSW) in Bragg position are the direct space modulation of the electromagnetic (e.m.) field in a diffracting sample. Specifically in the two beam approximation, a modulation of the e.m. field intensity with a periodicity of 2π/Q// has to be considered in a quasiperiodic structure. As it is fully described within the Dynamical Theory of X-ray Diffraction (DTXD), the XSW can be smoothly displaced with respect to atomic positions in a perfect crystal. This results in a strong modulation of the absorption processes as the crystal position crosses the Bragg condition. In the special case of quasicrystals (QC) the application of this technique, probing the long range order, opens several basic questions. Using a Fibonacci sequence of diffracting planes, we show that the XSW signal highly depends on the qperp component of the Bragg peak. Within this model, we then test the XSW response as phason defects are introduced in the structure. A rapid decrease of the XSW signature is observed when high qperp peaks are considered.