Phase determination by multiple Bragg scattering of x-rays in an icosahedral quasicrystal

When a crystal set for diffraction from the (hkl) planes is rotated around the reflection (HKL) may be simultaneously excited for a particular value $\psi$ of the azimuthal angle. A plot of the (hkl) intensity vs. $\psi$ is called a Renninger plot. A peak in such a usually exhibits an asymmetric shape, as a result of interference between different reflections excited simultaneously, and phases of structure factors can be obtained from the asymmetric patterns. Renninger peaks by means of multi-beam diffractional experiment have been observed on icosahedral quasicrystals, Al$\sb{6.37}$Cu$\sb{2.36}$Fe$\sb{1.27}$, Al$\sb{6.87}$Pd$\sb{2.17}$Mn$\sb{0.96}$ and a microcrystal (a twinned rhombohedral crystal with overall icosahedral symmetry). The asymmetric features of these Renninger plots have generally been fitted with phases consistent with noncentrosymmetric structures. Since the problem of locating atomic sites and of calculating structure factors is still open in quasicrystals, a technique to measure the structure factors of weak Bragg reflections on an absolute basis has been presented. Also, measured integrated intensities on a relative basis and structure factors have been compared with different models