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Browsing by Author "Sikora, Wanda"

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    Item type:Doctoral Dissertation, Access status: Open Access ,
    Analiza dyfrakcyjna dwuwymiarowych kwazikryształów
    (Data obrony: 2007-10-12) Kozakowski, Bartłomiej
    Wydział Fizyki i Informatyki Stosowanej
    Quasicrystals are built of aperiodic but organized sets of atoms. The last feature leads to the discrete, typical for crystals, diffraction patterns. A method which is commonly used in analysis of the structure of the quasicrystals is multidimensional structure modeling - "cut-and-project". This method assumes quasicrystals to be periodic in higher dimensions. Thesis concentrates on the method which is an alternative to the "cut-and-project" method, i.e. on the statistical method, which operates only in physical space and describes every structure by a distribution function of atoms positions written in relation to a periodic reference lattice. The first part of the thesis focuses on the simplest quasicrystal the Fibonacci chain. The goal of this part is to describe and present in figures the most important features of quasicrystals, i.e. atomic surface, projection strip, clusters, average unit cell, physical and perpendicular space, Patterson analysis and so on. Then, the statistical method is used for a detailed description of freely decorated rhombuses of the Penrose tiling and for the derivation of the structure factor for this tiling. The rhombuses model is also compared to the cluster model for which the structural analysis and derivation of the structure factor is performed as well. The accuracy of the obtained models is verified with the help of the self-written computer program which refines the parameters describing the atomic structure by minimizing the error of the fit between the experimental and calculated diffraction patterns. The last part of the thesis presents the current knowledge of the structure of $Al_{72}Ni_{20}Co_{8}$ alloy and the outcome for the refinement process for this alloy which was got with the help of the statistical model. The results are in a very good agreement with the experimental data.