Lithiation-Induced Zinc Clustering of Zn₃, Zn₁₂, and Zn₁₈ Units in Zintl-Like Ca_∼30Li_3+<i>x</i>Zn_{60–<i>x</i>} (<i>x</i> = 0.44–1.38)

Zinc clusters are not common for binary intermetallics with relatively low zinc content, but this work shows that zinc clustering can be triggered by lithiation, as exemplified by Ca_∼30Li_3+<i>x</i>Zn_{60–<i>x</i>}, <i>P</i>6/<i>mmm</i>, <i>Z</i> = 1, which can be directly converted from CaZn₂. Two end members of the solid solution (<i>x</i> = 0.44 and 1.38) were established and structurally characterized by single-crystal X-ray diffraction analyses: Ca₃₀Li_3.44(6)Zn_59.56(6), <i>a</i> = 15.4651(9) Å, <i>c</i> = 9.3898(3) Å; Ca_30.45(2)Li_4.38(6)Zn_58.62(6), <i>a</i> = 15.524(3) Å, <i>c</i> = 9.413(2) Å. The structures of Ca_∼30Li_3+<i>x</i>Zn_{60–<i>x</i>} feature a condensed anionic network of Zn₃ triangles, lithium-centered Zn₁₂ icosahedra, and <i>arachno</i>-(Zn,Li)₁₈ tubular clusters that are surrounded respectively by Ca₁₄, Ca₂₀, and Ca₃₀ polyhedra. These polyhedra share faces and form a clathrate-like cationic framework. The specific occupation of lithium in the structure is consistent with theoretical “coloring” analyses. Analysis by the linear muffin-tin orbital (LMTO) method within the atomic sphere approximation reveals that Ca_∼30Li_3+<i>x</i>Zn_{60–<i>x</i>} is a metallic, Zintl-like phase with an open-shell electronic structure. The contribution of Ca–Zn polar covalent interactions is about 41%

Lithiation-Induced Zinc Clustering of Zn₃, Zn₁₂, and Zn₁₈ Units in Zintl-Like Ca_∼30Li_3+<i>x</i>Zn_{60–<i>x</i>} (<i>x</i> = 0.44–1.38)

Zinc clusters are not common for binary intermetallics with relatively low zinc content, but this work shows that zinc clustering can be triggered by lithiation, as exemplified by Ca_∼30Li_3+<i>x</i>Zn_{60–<i>x</i>}, <i>P</i>6/<i>mmm</i>, <i>Z</i> = 1, which can be directly converted from CaZn₂. Two end members of the solid solution (<i>x</i> = 0.44 and 1.38) were established and structurally characterized by single-crystal X-ray diffraction analyses: Ca₃₀Li_3.44(6)Zn_59.56(6), <i>a</i> = 15.4651(9) Å, <i>c</i> = 9.3898(3) Å; Ca_30.45(2)Li_4.38(6)Zn_58.62(6), <i>a</i> = 15.524(3) Å, <i>c</i> = 9.413(2) Å. The structures of Ca_∼30Li_3+<i>x</i>Zn_{60–<i>x</i>} feature a condensed anionic network of Zn₃ triangles, lithium-centered Zn₁₂ icosahedra, and <i>arachno</i>-(Zn,Li)₁₈ tubular clusters that are surrounded respectively by Ca₁₄, Ca₂₀, and Ca₃₀ polyhedra. These polyhedra share faces and form a clathrate-like cationic framework. The specific occupation of lithium in the structure is consistent with theoretical “coloring” analyses. Analysis by the linear muffin-tin orbital (LMTO) method within the atomic sphere approximation reveals that Ca_∼30Li_3+<i>x</i>Zn_{60–<i>x</i>} is a metallic, Zintl-like phase with an open-shell electronic structure. The contribution of Ca–Zn polar covalent interactions is about 41%

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

The realm of Tsai-type (YCd6-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 Ca15.0(5)Au60.0(4)Sn25.0(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 Ca3Au14.36(3)Sn4.38(5) in space group Im3̅, a = 15.131(1) Å, whereas a representative 2/1 AC gives Ca13Au47.2(1)Sn28.1(1), Pa3̅ 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 YCd6. The 2/1 AC also contains four Ca2-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

Approximant Phases and an Icosahedral Quasicrystal in the Ca−Au−Ga System: The Influence of Size of Gallium versus Indium

Two crystalline approximants (ACs) and their corresponding icosahedral quasicrystal (i-QC) are obtained in the Ca−Au−Ga system through conventional solid-state exploratory syntheses. Single crystal structural analyses reveal that the 1/1 AC, Ca3AuxGa19-x (x = ∼ 9.3−12.1) [Im3̅, a = 14.6941(6)−14.7594(6) Å], has the empty cubes in the prototypic YCd6 (= Y3Cd18) now fully occupied by Ga, resulting in a 3:19 stoichiometry. In parallel, the distorted cubes in the 2/1 AC, Ca13Au57.1Ga23.4 [Pa3̅, a = 23.9377(8) Å] are fully or fractionally occupied by Ga. The valence electron count per atom (e/a) for the 2/1 AC (1.64) is smaller than that over the 1/1 AC composition range (1.76−2.02), and the e/a of the Ca15.2Au50.3Ga34.5 i-QC, 1.84, is somewhat distant from typical values for Tsai-type i-QCs (∼ 2.0). Comparisons of the gallium results with the corresponding In phases suggest that the structural differences result mainly from size rather than electronic factors. The 1/1 and 2/1 appear to be thermodynamically stable on slow cooling, as usual, whereas the i-QC isolated by quenching decomposes on heating at ∼660 °C, mainly into 2/1 AC and Ca3(Au,Ga)11. Calculations of the electronic structure of 1/1 AC suggest that the Fermi sphere−Brillouin zone interactions remain important for the Ca−Au−Ga i-QC

The 1/1 and 2/1 Approximants in the Sc−Mg−Zn Quasicrystal System: Triacontahedral Clusters as Fundamental Building Blocks

Single-crystal structures are reported for Sc3Mg0.18(1)Zn17.73(3), the 1/1 approximant crystal (AC), and Sc11.18(9)Mg2.5(1)Zn73.6(2), the 2/1 AC, in the corresponding icosahedral quasicrystal (i-QC) system. The 1/1 AC crystallizes in space group Im3̄, a = 13.863(2) Å, Z = 8, and the 2/1 AC, in Pa3̄, a = 22.412 (2) Å, Z = 8. The latter, which is valuable in pointing the way to the QC structure, is the best ordered and refined 2/1 example to date. The fundamental building blocks in both ACs are triacontahedral clusters centered by smaller multiply endohedral Tsai-type arrays; the former are condensed through body-centered-cubic packing in the 1/1 and primitive cubic packing in the 2/1 AC. Novel prolate rhombohedra centered by Sc−Sc dimers are also generated between triacontahedra in the 2/1 AC

Interpenetrating Networks of Three-Dimensional Penrose Tiles in CaAu₃Ga, the Structurally Simplest Cubic Approximant of an Icosahedral Quasicrystal

Double-Friauf polyhedra (DFPs) which play important roles in quasicrystal (QC) models are the unique building blocks in the novel 1/0 AC, CaAu3+ΔGa1−Δ (Δ ≈ 0–0.13) [Pa3̅; a = 9.0875(3)–9.1107(5) Å]. The packing of DFPs generates interpenetrating networks of condensed three-dimensional Penrose tiles, the geometry of which is close to that assumed for QCs

Synthesis and Structure of Five Sc₃Cu<i>_y</i>Zn₁₈_-<i>_y</i>-Type Compositions (0 ≤ <i>y</i> ≤ ∼2.2), 1/1 Crystalline Approximants of a New Icosahedral Quasicrystal. Direct Example of Tuning on the Basis of Size Effects and Hume−Rothery Concepts

The newly reported icosahedral quasicrystalline phase ∼Sc3Cu2.1Zn12.9 was approached through four synthetic, structural, and EDX analyses of the range of approximants formed by systematic substitutions of 0−4 Zn by Cu in the reported Sc3Zn17 as well as for the corrected Sc3Zn18 (ScZn6) composition. Structures of high yield products of the 0, 1, 2, 3 Cu atom steps all refined as isotypic Sc3CuyZn18-y phases (Im3̄, Z = 8, a = 13.8311(5) to 13.7528(5) Å for 0 ≤ y ≤2.2), basically isostructural with RCd6 phases known for many rare-earth elements. The present phases all exhibit the novel feature of disordered zinc tetrahedra in the center of four concentric polyhedral clusters:  pentagonal dodecahedron (Zn/Cu), icosahedron (Sc), icosidodecahedron (Zn), and triacontahedron (Zn). The Cu tuning process reduces both the average electron count per atom (e/a) to 2.04 and the average atom size until major amounts of the zinc-poorer quasicrystal separate along with the present normal crystalline phase near four added Cu. The Cu is an important neighbor to the disordered Zn atoms. The approximant structure repeatedly exhibits components with pseudo-icosahedral symmetry

Electronic Tuning of Mg₂Cu₆Ga₅. A Route to Crystalline Approximant and Quasicrystalline Phases

Studies of Mg2Cu6Ga5 reveal that this compound contains incomplete Bergman clusters in its structure and shows a pseudogap and empty bonding states just above the Fermi energy according to band calculations. Under a rigid band assumption, such a compound may be tuned to approximant and quasicrystal phases in which the required number of electrons are attained. Here, we replace part of Mg in the isotypic Mg2Cu6Ga5 with Sc, and both 1/1 approximant and icosahedral quasicrystal phases are obtained after some fine-tuning. This method closely correlates the pseudogap and bonding with Hume−Rothery concepts, thus giving useful directions for future quasicrystal searches, especially when approximants are not known

Interpenetrating Networks of Three-Dimensional Penrose Tiles in CaAu₃Ga, the Structurally Simplest Cubic Approximant of an Icosahedral Quasicrystal

Double-Friauf polyhedra (DFPs) which play important roles in quasicrystal (QC) models are the unique building blocks in the novel 1/0 AC, CaAu3+ΔGa1−Δ (Δ ≈ 0–0.13) [Pa3̅; a = 9.0875(3)–9.1107(5) Å]. The packing of DFPs generates interpenetrating networks of condensed three-dimensional Penrose tiles, the geometry of which is close to that assumed for QCs

Li_14.7Mg_36.8Cu_21.5Ga₆₆: An Intermetallic Representative of a Type IV Clathrate

Synthetic explorations in the quaternary Li−Mg−Cu−Ga system yield the novel intermetallic Li14.7(8)Mg36.8(13)Cu21.5(5)Ga66 [P6̅m2, Z = 1, a = 14.0803(4) Å, c = 13.6252 (8) Å] from within a limited composition range. This contains a unique three-dimensional anionic framework consisting of distinct interbonded Ga12 icosahedra, dimerized Li@(Cu,Mg)10Ga6 icosioctahedra, and 15-vertex Li@(Cu,Mg)9Ga6 and Li@Cu3Ga12 polyhedra. These polyhedral clusters are hosted by M20 (512), M24 (51262), and M26 (51263) (M = Li/Mg) cages, respectively. The geometries and arrangements of these cages follow those in known type IV clathrate hydrates