Atomic structure of the binary icosahedral Yb–Cd quasicrystal

Abstract

Icosahedral quasicrystals (i-QCs) are long-range ordered solids that show non-crystallographic symmetries such as five-fold rotations. Their detailed atomic structures are still far from completely understood, because most stable i-QCs form as ternary alloys suffering from chemical disorder. Here, we present the first detailed structure solution of i-YbCd 5.7 , one of the very few stable binary i-QCs, by means of X-ray structure determination. Three building units with unique atomic decorations arrange quasiperiodically and fill the space. These also serve as building units in the periodic approximant crystals. The structure is not only chemically feasible, but also provides a seamless structural understanding of the i-YbCd 5.7 phase and its series of related i-QCs and approximant crystals, revealing hierarchic features that are of considerable physical interest.Icosahedral quasicrystals (i-QCs) are the only class to show quasiperiodicity in three dimensions 1,2 . Obviously, structural knowledge is essential for understanding the physical properties, stability and tailoring applications of these exotic materials 3 . However, in contrast to other types of QCs that show periodic order in at least one direction, i-QCs cannot make effective use of two-dimensional (2D) imaging techniques such as high-resolution electron microscopy or high-angle annular dark-field scanning transmission electron microscopy for their structural characterization 4 . The i-QCs' structure determination is best achieved in the context of hyperspace crystallography 5,6 , where the structure can be described as a periodic crystal in higher dimensions. For i-QCs, the periodic space is 6D and decomposes into two orthogonal 3D subspaces: the parallel (physical) space and the perpendicular (complementary) space. The 6D unit cell is decorated by 3D objects known as 'occupation domains' (OD), the 3D QCs being obtained as a section of this decorated 6D lattice. This approach allows modelling and refinement of the structure against experimental diffraction data in a way similar to that achieved for 3D periodic crystals 6 . Although much progress has been achieved recently, for instance in the i-AlPdMn phase 7 , the models proposed so far are still being debated 8 . Indeed, the amount of observed diffraction data is in general rather limited, which precludes a detailed refinement of the chemical order in ternary QCs. Therefore, the atomic order in i-QCs remains a challenging and outstanding question. The recent discovery of the first stable binary icosahedral YbCd 5.7 QCs 9,10 has been a breakthrough and led to discoveries of a whole series of related ternary i-QCs 11 . This i-QC offers a unique opportunity for the structural analysis of i-QCs. Indeed, the i-YbCd 5.7 phase can be obtained as high-quality single grains. Furthermore, it is binary and exhibits very good X-ray contrast between Cd (Z = 48) and Yb (Z = 70) atoms.Finally, there is a series of periodic 'approximant crystals' (ACs) to the QC, having almost the same chemical composition and for...

Structure determination of quasicrystals

“…Altogether 251 parameters have been refined against the 5000 measured integrated intensities. The overall R-factor is equal to 9.5% which is a very good result taking into account the large number of used data [27]. The calculated density and composition is 8.88 g/cm3 and Yb 16.3 Cd 83.7 , which is in excellent agreement with the available experimental data.…”

“…Going further requires a detailed modelling which is achieved using the 3 building blocks found in the approximants [27]. The basic principle of the modelling is to find a quasiperiodic packing of the three building blocks, the main one being the TRH.…”

Crystal electric field excitations in the quasicrystal approximantTbCd6studied by inelastic neutron scattering

“…For i-RCd quasicrystals, however, ∼60 -70% of the R ions are associated with the R icosahedron within the Tsai-type cluster, and the balance are contained within the double Friauf polyhedron (DFP) that fill the gaps between the clusters. 19,20 Furthermore, a recent 6-D structural refinement of the i-R-Cd quasicrystals (R = Gd, Dy and Tm) noted a degree of chemical disorder on the nominally R icosahedron itself. 20 Nevertheless, a comprehensive understanding of the nature of magnetism in the RCd 6 approximants provides an important starting point for elucidating the magnetic interactions in the corresponding quasicrystals.…”

Atomic structure of the i-R-Cd quasicrystals and consequences for magnetism

“…[1][2][3][4] In particular, the discovery of a stable binary icosahedral (i) YbCd 5.7 quasicrystal 5 and the elucidation of the structure via 6-dimensional (6-D) structural refinement 6 have provided a detailed structural model of the icosahedral phase. In terms of the physical properties of quasicrystals and related compounds, recent studies have unveiled phenomena ranging from quantum critical behavior in the i-Yb 15 Au 54 Al 34 quasicrystal to bulk superconductivity in a closely related large unit cell periodic crystal (approximant), Yb 14 Au 64 Ge 22 .…”

“…In particular, for i-YbCd 5.7 , the same Tsai-type clusters have been shown to comprise the backbone of the structure of the icosahedral phase with the same types of linkages, and full occupancy of the R icosahedron by Yb 2+ . 6 The Yb ions are divalent and do not carry a magnetic moment at ambient pressure. 32 For the i-R-Cd quasicrystals it has not yet been established whether the intercluster linkages, or even the R icosahedra themselves, are preserved in the icosahedral quasicrystal phase.…”