Dynamical Diffraction and X-Ray Standing Waves from Atomic Planes Normal to a Twofold Symmetry Axis of the Quasicrystal AlPdMn

We have observed dynamical diffraction in the $[[\left(0240\overline{2}4\right)$ and $[[\left(0460\overline{4}6\right)$ reflections of the icosahedral quasicrystal AlPdMn in the back-reflection geometry ( ${\ensuremath{\theta}}_{B}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}90\ifmmode^\circ\else\textdegree\fi{}$). The x-ray fluorescence from the Al and Pd atoms exhibits strong standing wave behavior, similar to that observed in crystalline materials. The data indicate a long-range order of each species of atoms, with the coherent positions attributable to distributions of the Al and Pd, which we compare to a centrosymmetric model. We observe deviations from the model which imply small departures from inversion symmetry along the twofold symmetry axis and from the expected coherent fractions for Al.