Structure determinations for random-tiling quasicrystals

How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are avai lable to do it? One path is to solve the phase problem first, obtaining the density in a higher dimensional space which yields the averaged scattering density in 3-dimensional space by the usual construction of an incommensur ate cut. A novel direct method for this is summarized and applied to an i(A LPdMn) data set. This averaged density falls short of a hue structure deter mination (which would reveal the typical unaveraged atomic patterns.) We di scuss the problematic validity of inferring an ideal structure by simply fa ctoring out a "perp-space" Debye-Waller factor, and we test this using simu lations of rhombohedral tilings. A second, "unified" path is to relate the measured and modeled intensities directly, by adjusting parameters in a sim ulation to optimize the fit. This approach is well suited for unifying stru ctural information from diffraction and from minimizing total energies deri ved ultimately from ab-initio calculations. Finally, we discuss the special pitfalls of fitting random-tiling decagonal phases.