Four different decagonal quasicrystalline phases are round in the Al_(65)Cu_(20)Co_(15) alloys. Their periodicities along the unique ten-fold axes are 0.4, 0.8, 1.2 and 1.6nm respectively. The founding of the periodicity of 0.8nm confirms the suggestion by X.Z. Li and K.H. Kuo that the decagonal phase with a periodicity of 0.4nm is the fundamental one. The decagonal phase with a periodicity of 0.8nm along the ten-fold axis is a perfect and stable quasicrystalline phase. The reciprocal space is more densely occupied by its diffraction spots than any other decagonal phases found before. After heating at 800 ℃ for 40hrs, part of the decagonal phase remains unchanged. A 1D quasicrystalline phase derived from the decagonal phase with a periodicity of 0.8nm is found after annealing the sample for 40hrs at 800 ℃. The 1D quasicrystal phase (with 2D translational symmetry) conjuncts the margin between the 2D decagonal phase (with 1D translational symmetry) and crystal structure (with 3D translational symmetry). The periodicity of the 1D quasicrystal phase along the original ten-fold axis of the matrix decagonal phase becomes to be 0.4nm. This furthermore confirms the suggestion by X.Z. Li et al. A series of vacancy ordered crystalline phases based on the CsCl-type structure are also found in this alloy system. These crystalline phases are derived from the 2D decagonal phase (with a periodicity of 0.8nm along the ten-fold axis) via the 1D quasicrystal. They are τ_2, τ_3, τ_5, τ_8, τ_(13) and τ_(21) phases. The subscripts are in a Fibonacci number sequence. Among them τ_(21) had not been observed before. The τ_(21) phase gives supports to K. Chattopadhyay's explanation of the vacancy ordered structure found in Al-Pd alloy system as τ_∞ if the subscript becomes infinitely large in a Fibonacci number sequence.
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