Decagonal quasicrystalline or microcrystalline structures: The specific case of Al-Cu-Co(-Si)

Abstract

An extensive structural analysis of a decagonal ${\mathrm{Al}}_{63}$${\mathrm{Cu}}_{17.5}$${\mathrm{Co}}_{17.5}$${\mathrm{Si}}_{2}$ alloy is reported. The structure is analyzed within the context of both microcrystalline and quasicrystalline models through the examination of single-crystal x-ray diffraction patterns. We conclude that our sample is in a microcrystalline state formed of coherent twins of an approximant state of the quasicrystal. We underline that diffraction patterns exhibiting sharp peaks and perfect tenfold symmetry do not necessarily correspond to long-range quasiperiodic order, which could have implications for the physical properties of quasicrystal-like alloys. The present work also gives us the opportunity to point out and discuss some general features: (i) the intensity cutoff problem for quasicrystal structure determinations, (ii) the consequence in structure determination if a sample supposed to be a quasicrystal is in fact a microcrystal, and (iii) the proper determination of basis vectors in decagonal quasicrystals.