X-ray Study of Phason Strains in an AlCuFeMn Decagonal Phase

Abstract

The peak profiles, shifts, and splittings of Bragg reflections, which are inherent in the phason strain of a quasicrystal, are carefully examined using a precise powder X-ray diffraction method for a wide range of different AlCuFeMn alloys and annealing temperatures. Based on the peak-shift dependences of the Bragg reflections on the phason momentum Q_⊥, two kinds of new approximant phases are identified. These phases have linear phason strains θ₁ = τ⁻⁶ and θ₂ = τ⁻⁵, and θ₁ = τ⁻¹⁰ and θ₂ = τ⁻⁵, corresponding to lattice spacings a = 3.814 nm and b = 2.005 nm, and a = 9.985 nm and b = 2.005 nm in the quasiperiodic plane of the orthorhombic system, respectively.