The atomic structure and chemical ordering of aluminum ruthenium copper quasicrystal

Understanding the atomic structure of quasicrystals has fundamental importance in studying the formation and properties of this class of materials. In this thesis, the atomic structure and chemical ordering of AlRuCu, one of the stable and phason defect free quasicrystal material, was studied extensively by X-ray diffraction techniques which include regular and anomalous X-ray diffraction measurements at the Ru and Cu K-edges. The diffraction data have been analyzed in both reciprocal and real spaces, yielding the total structure factor and partial structure factors of Ru and Cu in reciprocal space and the atomic pair distribution function (PDF) and the differential partial atomic pair distribution function (DDF) of Ru in real space. An atomic structural model, including chemical ordering, was obtained based on the information of local atomic correlations and short range chemical order provided by the PDF and DDF of Ru. The model of atomic structure can be described by a direct projection of a 6-dimensional hypercubic lattice with vertex decoration using a non-Penrose window. A direct comparison of the structural model with the diffraction pattern in reciprocal space shows that this model can also describe the long range order of the atomic structure. As a comparison, the atomic structures of AlLiCu and MnTiSi, which have moderate and very high concentration of phason defects, were studied based on the PDFs from both X-ray and neutron powder diffraction experiments. Fundamental differences were observed among these quasicrystals in the preferred local atomic environment and nature of the projection window in the perpendicular space. The difference between these three quasicrystals and possible physical meaning were carefully discussed. The conclusion is that the compatibility of the short range order with the long range order is the most plausible reason why the AlRuCu exhibits such a perfect quasicrystalline ordering. Because of the complex nature of the quasicrystal atomic structure, real space analysis of diffraction pattern has been the most important experimental method used in this work. To improve the technique and to study a local atomic structure which has an icosahedral symmetry, the local inter-molecular atomic correlations in C$\sb{60}$ solid at 10 K was studied by real space refinement of PDF. As an example of real space analysis of diffraction data, the result is also presented in this thesis. We found that the orientation of the C$\sb{60}$ molecules is often locally deviated from the long range average structure, and a significant number (30$\sim$40 %) of molecules have a six-fold face oriented toward adjacent molecules