Five-dimensional structure analysis of decagonal Al₆₅Cu₂₀Co₁₅

Abstract

A single-crystal X-ray structure analysis of decagonal Al65Cu20Co15 has been performed using the n-dimensional approach. Five-dimensional space group P10(5)/mmc, a(i)* = 0.2656 (2), a5* = 0.24107 (3)-angstrom-1, d(i) = 3.368 (1), d5 = 4.1481 (3)-angstrom, alpha-ij = 60, alpha-i5 = 90-degrees (i, j = 1,..,4), volume of the five-dimensional unit cell-OMEGA = 298.2-angstrom-5, M(r) = 39.08, F(00000) = 15.0, D(x) = 4.4 Mg m-3, mu = 12.0 mm-1, Mo K-alpha, lambda = 0.71069-angstrom, wR = 0.098 for 259 independent reflections with I > 2-sigma-(I) and 11 variables. The structure was solved by Patterson analysis and subsequent least-squares refinement, both in the five-dimensional description. There are three atoms in the asymmetric unit. Five-dimensional Fourier and difference Fourier syntheses show the pentagonal shape and chemical structure of the atoms parallel to the internal space. The three-dimensional decagonal structure is built up of periodically stacked sandwiches which consist of two planar quasiperiodic layers related by the tenfold screw axis. Characteristic large motifs of the crystalline Al13Fe4 structure type are found in a new arrangement in the quasiperiodic layers. The appearance of pentagonal channels which are partly empty or occupied statistically is noteworthy.