Giant Al-<i>M</i>(<i>M</i>=transitional metal) crystals as Penrose-tiling approximants of the decagonal quasicrystal

Abstract

The two-dimensional decagonal quasicrystal has been found in many Al-M (M=transitional metal) alloys, very often coexisting with a large-unit-cell phase of similar composition and local structure. By introducing phasons in two orthogonal directions in the quasiperiodic plane perpendicular to the periodic tenfold axis, i.e., approximating the irrational golden mean \ensuremath{\tau} with rational ratios of two consecutive Fibonacci numbers ${\mathit{F}}_{\mathit{n}+1}$/${\mathit{F}}_{\mathit{n}}$, the Penrose pattern in this plane gradually becomes periodic with fairly large unit-cell parameters (1--3 nm). Some giant Al-M crystals with cubic, orthorhombic, and monoclinic symmetries have thus been derived as Penrose-tiling approximants of the decagonal quasicrystal, and their simulated electron diffraction patterns agreed fairly well with experiments.