Development of an Icosahedral Quasicrystal and Two Approximants in the Ca−Au−Sn System: Syntheses and Structural Analyses

Abstract

The realm of Tsai-type (YCd 6 -type) quasicrystals (QCs) and their approximants (ACs) continues to expand to the east in the periodic table. The heavy tetrel Sn is now one of the major components in the new Ca 15.0(5) Au 60.0(4) Sn 25.0(2) (atom %) icosahedral QC and in the corresponding 1/1 and 2/1 ACs. (The 2/1 AC with Yb is also established.) Single-crystal X-ray diffraction on a 1/1 AC gives the refined formula of Ca 3 Au 14.36(3) Sn 4.38(5) in space group Im3, a = 15.131(1) Å , whereas a representative 2/1 AC gives Ca 13 Au 47.2(1) Sn 28.1(1) , Pa3 and a = 24.444(1) Å . Both ACs contain five-shell multiply endohedral triacontahedral clusters as the common building blocks, as in the parent structure of YCd 6 . The 2/1 AC also contains four Ca 2 -dimer-centered prolate rhombohedra (PRs) in the unit cell. The long-range order between triacontahedra and PRs in the 2/1 AC is the same as those in Bergman-type 2/1 ACs. A TB-LMTO-ASA calculation on an ideal 1/1 AC model reveals a shallow pseudogap in the total densities-of-states data around the Fermi energy, as expected. The depth of the pseudogap is considerably enhanced through interactions between the Ca 3d states and s and p states of Au and Sn.

Gold-Tin Ordering in SrAu2Sn2

“…So far only the stannides MgAuSn [3], CaAuSn [4], Ca 14 Au 46 Sn 5 [5], the icosahedral quasicrystal approximants Ca 3 Au 14.36 Sn 4.38 and Ca 13 Au 47.2 Sn 28.1 [6], SrAuSn [7], SrAuSn 2 [8], the solid solutions SrAu x Sn 4−x (1.3 ≤ x ≤ 2.2) [9], and BaAuSn [7] have been reported. Gold-tin ordering in such stannides is driven by the formation of strong covalent Au-Sn bonds with lengths close to the sum of the covalent radii for gold and tin of 274 pm [10].…”

Crystal chemistry and chemical order in ternary quasicrystals and approximants

“…A comparison between the binary i-Cd 84 Yb 16 and the ternary i-Mg 52 Cd 36 Yb 12 quasicrystals is seen in Figure 2. The figure shows two planes cutting through the 6-dimensional electron densities of the binary i-Cd 84 Yb 16 and the ternary i-Mg 52 Cd 36 Yb 12 QCs.…”

“…The figure shows two planes cutting through the 6-dimensional electron densities of the binary i-Cd 84 Yb 16 and the ternary i-Mg 52 Cd 36 Yb 12 QCs. We can clearly see three distinct occupation domains (ODs) in both quasicrystals located at the body-center (B), vertex (V) and edge-center (E) positions with the coordinates ½(111111), (000000) and ½(100000) respectively within the 6-dimensional unit cells.…”

“…Or so it was until the emergence of the binary icosahedral i-Cd 84 Yb 16 quasicrystal, [3] which due to its high quality, binary nature, complete chemical order and the existence of two different approximants resulted in the first complete structure solution of an icosahedral quasicrystal. [2] The impact of i-Cd 84 Yb 16 echoes far beyond the binary phase alone; it has greatly improved our understanding of icosahedral quasicrystals as a whole. First of all the binary i-Cd 84 Yb 16 quasicrystal and the two approximants Cd 6 Yb and Cd 76 Yb 13 are the parent structures for the now largest family of icosahedral quasicrystals and approximants.…”

“…[2] The impact of i-Cd 84 Yb 16 echoes far beyond the binary phase alone; it has greatly improved our understanding of icosahedral quasicrystals as a whole. First of all the binary i-Cd 84 Yb 16 quasicrystal and the two approximants Cd 6 Yb and Cd 76 Yb 13 are the parent structures for the now largest family of icosahedral quasicrystals and approximants. [4][5][6] Most members of this family are ternary and they form by substituting Cd by a pair of other elements; typically one late d-block and one p-block element or Mg.…”