The structure of an Al-Fe-Ni decagonal quasicrystal with two quasiperiodic planes along the periodic axis in an Al_{72}Ni_{24}Fe_4 alloy has been examined by spherical aberration (Cs)-corrected scanning transmission electron microscopy with high-angle annular dark-field and annular bright-field techniques. The transition-metal atoms and mixed sites (MSs) of Al and transition-metal atoms are represented as separated bright dots in the observed high-angle annular dark-field scanning transmission electron microscopy images, and consequently the arrangements of transition-metal atoms and mixed sites on the two quasiperiodic planes can be directly determined. The transition-metal atoms are arranged on a pentagonal tiling of an edge-length of 0.76 nm. The close examination of observed annular bright-field- and high-angle annular dark-field scanning transmission electron microscopy images indicates the existence of large decagonal columnar clusters with 3.2 nm diameter, and their arrangement on pentagonal, thin rhombic and squashed hexagonal tiles with an edge-length of 3.2 nm. The arrangements of transition-metal atoms in these three tiles are placed on an ideal pentagonal tiling with an edge-length of 3.2 nm, which is generated by the projection of a five-dimensional hyper-cubic lattice. The vertices are denoted by 5D hyper-cubic indices and then they are projected on the occupation domains in perpendicular space. The arrangement of Al atoms as well as transition-metal atoms and mixed sites in the large decagonal atom cluster with about 3.2 nm diameter is interpreted from the observed high-angle annular dark-field- and annular bright-field scanning transmission electron microscopy ABF-STEM images.
The structure of an F-AlCoPdGe alloy was determined by single-crystal X-ray diffraction analysis: space group Pa3̅ (No. 205), Pearson symbol cP1128-142.4, a = 24.4338(4) Å; R1 = 0.0526 for the observed 5106 reflections with F_0 > 4.0σ(F_0). The F-AlCoPdGe alloy exhibited three types of pseudo-Mackay clusters (pMCs). The first shell of the Co(13)-pMC at 24d indicated a coordination polyhedron typically found in Al-Co binary approximants; the second shell was a combination of an M icosahedron and an Al icosidodecahedron, where M is a mixed site of Pd and/or Co. The first shell of the Co(14)-pMC at 4b consisted of 20 partially occupied Al positions arranged in a dodecahedral fashion; its second shell was also composed of an M icosahedron and an Al icosidodecahedron. The first shell of the Al(18)-pMC at 4a consisted of a combination of an M cube and an Al octahedron, resulting in the rhombic dodecahedral arrangement; its outer shell structure was similar to those of the other pMCs. The structure of the F-AlCoPdGe phase comprised an arrangement of these three types of pMCs together with interstitially placed Al icosahedra around the Pd/Al(1) and Pd/Al(2) sites.
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