Abstract
The detailed atomic structure of the binary icosahedral (i) ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33 and i-YbCd5.7 was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33 chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constants K 2/K 1 = -0.53, i.e. close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye-Waller factor, which explains the vanishing of 'high-Q perp' reflections.
Highlights
Quasicrystals (QCs) exhibit a diffraction pattern with sharp Bragg reflections, as a signature of long-range order, yet with symmetries that are incompatible with three-dimensional translational symmetry (Shechtman et al, 1984; Levine & Steinhardt, 1984)
In the i-ScZn7.33 we find that the chemical disorder occurs for one of the two sites located along the longer body diagonal: whereas, one site is fully occupied by Sc, the other site (C) is occupied by Sc or Zn
The structure of the i-ScZn7.33 appears to be isostructural to the i-YbCd5.7 one and is described by a quasiperiodic packing of Tsai-type rhombic triacontahedron (RTH) clusters and double Friauf polyhedra (DFP), both resulting from the close-packing of a large (Sc) and a small (Zn) atom
Summary
Quasicrystals (QCs) exhibit a diffraction pattern with sharp Bragg reflections, as a signature of long-range order, yet with symmetries that are incompatible with three-dimensional translational symmetry (Shechtman et al, 1984; Levine & Steinhardt, 1984). It is related to the translational degree of freedom of clusters are located at so-called 12-fold vertices of a three- the free energy expressed in Eperp in the framework of dimensional Ammann–Kramer–Neri (AKN) tiling proposed hydrodynamic theory that leads to a long wavelength diffusive by Henley (1986) and connected along their twofold axis by like excitation called a phason (Kalugin et al, 1985; Bak, sharing a face (b-linkage) and along their threefold axis where 1985a,b; Lubensky et al, 1985) This fluctuation gives rise to they overlap and define an oblate rhombohedron (c-linkage; phason diffuse scattering (PDS), located in the close vicinity of see Figs.
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