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Structure determinations for random-tiling quasicrystals

C. L. Henley·V. Elser·M. Mihalkovic
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Abstract

How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available 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 incommensurate cut. A novel direct method for this is summarized and applied to an i(AlPdMn) data set. This averaged density falls short of a true structure determination (which would reveal the typical_unaveraged_ atomic patterns.) We discuss the problematic validity of inferring an ideal structure by simply factoring out a ``perp-space'' Debye-Waller factor, and we test this using simulations of rhombohedral tilings. A second, ``unified'' path is to relate the measured and modeled intensities directly, by adjusting parameters in a simulation to optimize the fit. This approach is well suited for unifying structural information from diffraction and from minimizing total energies derived ultimately from ab-initio calculations. Finally, we discuss the special pitfalls of fitting random-tiling decagonal phases.

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C. L. Henley, V. Elser, M. Mihalkovic. 2000-04-09. Structure determinations for random-tiling quasicrystals. https://arxiv.org/abs/cond-mat/0004126

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