A non-Fibonacci type of orthorhombic decagonal approximant

Abstract

An orthorhombic phase with a = 1.23 nm, b = 1.24 nm and c = 3.07nm has been found in the Al₁₂Fe₂Cr alloy. The distribution of strong diffraction spots in the [010], [100] and [001] electron diffraction patterns (EDPs) corresponds to the tenfold, the 2D twofold, and the 2P twofold EDPs respectively of a decagonal quasicrystal. Therefore this orthorhombic phase is called a decagonal approximant. However, unlike other orthorhombic approximants, its parameter c = 3.07 nm does not agree with any of the values obtained by substituting a rational ratio of two consecutive Fibonacci numbers, such as 1/1, 2/1, 3/2, 5/3, etc., for the irrational τ in one of the quasiperiodic directions in a decagonal quasicrystal. Its [010] high-resolution electron microscopy image consists of a network of 72° and 36° rhombi whose vertices are surrounded by a decagon of image points. The ratio of the thick to thin rhombi is 4 to 1 rather than a Fibonacci ratio. This is a new type of decagonal approximant. On ordering, a C-centred monoclinic superlattice with a _M = c/sin β = 3.31 nm, b _M = a = 1.23nm, c _M = 2b = 2.48 nm and β = 112° results.