| Al80.6Cr10.7Fe8.7 or approximately Al4(Cr,Fe), Immm (No. 71), a = 1.2500(6) nm, b = 1.2617(2) nm, c = 3.0615(8) nm, V = 4.8284 (8) nm3. Pearson symbol oI366-59.56, Dx = 3.432g/cm3, R1=0.0674 for 3206 reflections with I>4σ(I), goodness of fit S=0.846. There are 39 (28Al+11Cr/Fe) independent atoms in a unit cell, of which 5 Al and 10 (Cr/Fe) atoms have icosahedral or pesudo-icosahedral coordination (the remaining Cr/Fe atom is located at the centre of a CN15 polyhedron). As in other Al-TM (transition metal) intermetallic phases, a number of Al sites in Al4(Cr,Fe) have a partial occupancy of 0.64-0.67 and a split occupancy of 0.50. Al4(Cr,Fe) coexists with the Al-Cr-Fe decagonal quasicrystal having a periodicity of 1.25 nm consisting of six atomic layers along its tenfold axis. In the orthorhombic Al4(Cr,Fe), there are also six layers, PFP'pfp', along the a axis. F and fare flat layers at x = 0 and 1/2, respectively, and they are related by a body centre translation. Both F and / layers are sandwiched between two puckered layers, P/P' and p/p', respectively, in mirror reflection positions. The interconnection of icosahedra in the PFP' layer block forms topologically large triangular and hexagonal structural motifs. Similar structural motifs also exist in the structure of the hexagonal μ-Al4Mn, κ-Al(Cr,Ni), λ-Al4Mn, and ν-Al12Cr2Fe phases as well as in the orthorhombic ε-Al4Cr phase, which is closely related to the hexagonal μ-Al4Mn. There are indications that the orthorhombic Al4(Cr,Fe) is related to the hexagonal κ-Al(Cr,Ni).Two new quasicrystal approximant were found in Zn-Mg-Y system. One is hexagonal with cell parameters: a=0.90822nm c=0.94155nm. We got the single crystal of this phase. The structure was determined by single crystal X-ray diffraction. The layer structure and the connections between the icosahedra in the structure were discussed in detail. The other new phase is a cubic phase with the cell parameters: a=1.276 nm. This number is 1/τ(τis the golden point, τ=1. 618) of the cubic phase W'-(MgZnY)(with cell parameter a=2.05 nm) or R-Mg-Zn-Er (with cell parameters a=2.02 nm). Because the it is quite difficult to get the single crystal of this phase, at last, the structure was determined successfully using the powder X-ray diffraction.Two new single crystals were found in Al-Cr system. One is monoclinic with cell parameters: a = 1.7713(4) nm,b = 3.0417(6) nm,c = 1.7707(4) nm, β= 91.04(3). According to the former report, it is quite difficult to study the structure because there are quite a lot of defects and complicated phase transformation in it. We determine the structure and analysis the crystallography relations with the other two phases in the Al-Cr system. The other single crystal is an orthorhombic phase with cell parameters: a = 2.48623(50) nm, b =2.52908(51) nm, c = 3.04527(61) nm. We study the structure with the single crystal X-ray diffractionmethod and present some assured result.The work in this thesis can be summarized as: Five structure of the quasicrystal approximant were studied. Two new methods were used in the research: one is the combination of electron microscopy and single crystal diffraction, the other is the using of the powder X-ray diffraction method. Two new view points were used when we analyse the structure of the quasicrystal approximant: the icosahedra atom cluster and the layer structure.
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