HREM study and structural models of the (1/1,2/1) and (2/1,1/1) orthorhombic approximants in an Al₇₀Co₁₅Ni₁₀Tb₅ alloy

Abstract

The (010) layers of the (1/1,2/1) and (2/1,1/1) approximants (these rational ratios of two consecutive Fibonacci numbers were used to substitute for the irrational τ in two orthogonal quasiperiodic directions) of the Al₇₀Co₁₅Ni₁₀Tb₅ decagonal quasicrystal were found to consist of elongated hexagonal subunits with an edge length of 0.76 nm in different tessellations by means of high-resolution electron microscopy (HREM). This explains why these two approximants inter-grow easily with a fixed orientational relationship and domains occur abundantly in them. The primitive orthorhombic unit cell of the (1/1,2/1) approximant, a = 1.26, b = 1.60 and c = 2.30nm, consists of two differently oriented hexagons. Its structure is similar to that of Al₃Pd reported recently by Matsuo and Hiraga (1994). On the other hand, the base-centred orthorhombic unit cell of the related (2/1,1/1) approximant, a = 2.00, b = 1.60, c = 1.38 nm, consists of two hexagons of a single orientation. Its pentagonal and decagonal layer structure, derived from that of Al₃Pd or the (1/1,2/1) approximant, consists of subunits similar to those that exist in a decagonal quasicrystal. The simulated images based on these structures compared favourably with the observed [010] HREM images of these two approximants.