The crystal structure of YCd6

Atomic-Scale Tuning of Tsai-Type Clusters in RE-Au-Si Systems (RE = Gd, Tb, Ho)

Tsai-type quasicrystals and approximants are distinguished by a cluster unit made up of four concentric polyhedral shells that surround a tetrahedron at the center. Here we show that for Tsai-type 1/1 approximants in the RE–Au–Si systems (RE = Gd, Tb, Ho) the central tetrahedron of the Tsai clusters can be systematically replaced by a single RE atom. The modified cluster is herein termed a “pseudo-Tsai cluster” and represents, in contrast to the conventional Tsai cluster, a structural motif without internal symmetry breaking. For each system, single-phase samples of both pseudo-Tsai and Tsai-type 1/1 approximants were independently prepared as millimeter-sized, faceted, single crystals using the self-flux synthesis method. The full replacement of tetrahedral moieties by RE atoms in the pseudo-Tsai 1/1 approximants was ascertained by a combination of single-crystal and powder diffraction studies, as well as energy dispersive X-ray spectroscopy (EDX) analyses with a scanning electron microscope (SEM). Differential scanning calorimetry (DSC) studies revealed distinctly higher decomposition temperatures, by 5–35 K, for the pseudo-Tsai phases. Furthermore, the magnetic properties of pseudo-Tsai phases are profoundly and consistently different from the Tsai counterparts. The onset temperatures of magnetic ordering (T_mag) are lowered in the pseudo-Tsai phases by ∼30% from 24 to 17 K, 11.5 to 8 K, and 5 to 3.5 K in the Gd–Au–Si, Tb–Au–Si, and Ho–Au–Si systems, respectively. In addition, the Tb–Au–Si and Ho–Au–Si systems exhibit some qualitative changes in their magnetic ordering, indicating decisive changes in the magnetic state/structure by a moment-bearing atom at the cluster center.

Formation conditions of Tsai (IT) and pseudo-Tsai (CC) phases have been established, and their atomic structures and magnetic properties have been investigated for the RE−Au−Si systems (RE = Gd, Tb, Ho). Following a schematic pseudobinary (Au₇₉Si₂₁ versus RE) phase diagram, millimeter-sized single crystals were obtained for both structure types using the self-flux synthesis method. Variations in atomic structure, thermal behaviors, and magnetic properties were identified using SCXRD, DSC, and magnetic property measurements, respectively.

Synthesis and Atomic Structure of the Yb-Ga-Au 1/1 Quasicrystal Approximant

The Yb-Ga-Au 1/1 quasicrystal approximant (AP) composition ranges from Yb_14.0Ga_20.6Au_65.4 to Yb_14.8Ga_46.3Au_38.9, and single crystals of the 1/1 AP having the composition Yb_13.8Ga_26.1Au_60.1 were obtained by the self-flux technique. X-ray structural analysis demonstrated that the atomic structure [space group Im3; a = 14.6889(9) Å] can be described by the body-centered packing of Tsai-type rhombic triacontahedron (RTH) clusters. The positional disorder in these clusters, interpreted as the average of an orientationally disordered tetrahedron and triangle, results in positional disorder in the outer shells. The elemental distributions and positions of mixtures of Au and Ga atoms in the RTH clusters correspond to those in the isostructural Yb₁₅Al₃₆Au₄₉ 1/1 AP.

Complex cubic metallides AM ~6 (A=Ca, Sr; M=Zn, Cd, Hg). Synthesis, crystal chemistry and chemical bonding

In a systematic synthetic, crystallographic and bond theoretical study, the stability ranges as well as the distribution of the isoelectronic late d-block elements Zn, Cd and Hg (M) in the polyanions of the YCd6-type phases (Ca/Sr)Cd6 have been investigated. Starting from Ca(Cd/Hg)6, 12−30% of the M atoms can be substituted by Zn, which gradually occupies the center of the empty cubes. In all ternary compounds, smaller/less electronegative Zn/Cd atoms occupy the disordered tetrahedra explaining the lack of the YCd6-type for pure mercurides. Along the section SrCd6-SrHg6, the ordered Eu4Cd25-type is formed (Sr4Cd16.1Hg8.9: cF1392, Fd3̅, a=3191.93(5) pm, R1=0.0404). Besides, two new complex cubic Ca phases appear at increased Zn proportion: Ca2Zn5.1Cd5.8, which exhibits a nearly complete site preference of Zn and Cd, crystallizes in the rare cubic Mg2Zn11-type structure (cP39−δ, Pm3̅, a=918.1(1) pm, R1=0.0349). In the Ca–Hg system, an increased Zn proportion yielded the new compound CaZn1.31Hg3.69 (cF480, F4̅3m, a=2145.43(9) pm, R1=0.0572), with a complex cubic structure closely related to Ba20Hg103. All structures, which are commonly described using nested polyhedra around high-symmetric sites, are alternatively described in accordance with the calculated electron densities and charge distribution: building blocks are face-sharing [M 4] tetrahedra (star polyhedra such as TS, IS, OS), each with a cage-critical point in its center, and [M 8] cubes (deformed TS), which are either empty, distorted or filled. The M element distribution in the anion is determined by size criteria and the difference in electronegativity, which induces a preferred formation of heteroatomic polar bonds.

Reinvestigation of the Cd-Gd phase diagram

The complete Cd-Gd equilibrium phase diagram was investigated by a combination of powder-XRD, SEM and DTA. All previously reported phases, i.e., CdGd, Cd₂Gd, Cd₃Gd, Cd₄₅Gd₁₁, Cd₅₈Gd₁₃, and Cd₆Gd, could be confirmed. In addition, a new intermetallic compound with a stoichiometric composition corresponding to "Cd₈Gd" was found to exist. It was obtained that "Cd₈Gd" decomposes peritectically at 465 °C. Homogeneity ranges of all intermetallic compounds were determined at distinct temperatures. In addition, the maximum solubilities of Cd in the low- and high-temperature modifications of Gd were determined precisely as 4.6 and 22.6 at.%, respectively. All invariant reaction temperatures (with the exception of the formation of Cd₅₈Gd₁₃) as well as liquidus temperatures were determined, most probably, Cd₅₈Gd₁₃ is formed in a peritectoid reaction from Cd₄₅Gd₁₁ and Cd₆Gd at a temperature below 700 °C.

Phase equilibria in the neodymium-cadmium binary system

The equilibrium phase diagram of the neodymium-cadmium system has been established by thermal, metallographic and X-ray analysis based on a study of 70 alloys. The system contains three congruently melting intermetallic compounds, i.e. NdCd (1040 °C), NdCd₂ (995 °C), Nd₁₁Cd₄₅ (855 °C), and four incongruently melting compounds NdCd₃ (860 °C), Nd₁₃Cd₅₈ (740 °C), NdCd₆ (655 °C) and NdCd₁₁ (520 °C). Four eutectic reactions are found in this binary system, i.e. at ∼25 at.% Cd and 770 °C, at 58 at.% Cd and 955 °C, at 79 at.% Cd and 850 °C, and very close to pure Cd at 318 °C, as well as one eutectoid reaction at ∼15 at.% Cd and 500 °C. The solid solubility of Nd in Cd is negligible. Dilatometric curves were recorded for three Nd-Cd compositions up to 4 at.% Cd, to accurately determine phase transitions between the solid solutions of Cd in the low- and high-temperature modification of Nd.

Low-temperature superstructures of a series of Cd6M (M = Ca, Y, Sr, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu) crystalline approximants

The low-temperature (LT) superstructure and the phase transition temperature have been investigated for a series of Cd6M crystalline approximants by transmission electron microscopy as well as electrical resistivity measurements. Except for M = Lu, Cd6M is found to undergo a phase transition to a monoclinic phase at a low temperature and the transition temperature (Tc) scales well with the size of the M atom. For M = Ca, Y, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Tm the LT superstructure is explained by a √2a × a × √2a lattice with the space group C2/c, and for M = Sr and Yb a √2a × 2a × √2a monoclinic lattice with P2/m. On the other hand, no phase transition is observed for M = Lu, indicating that a Cd4 tetrahedron at the cluster center remains disordered down to the lowest temperature, i.e. 16 K. It is shown that the volume inside the Cd20 dodecahedron plays a crucial role in the occurrence of the phase transition, and long-term aging in particular promotes the phase transition for late rare-earth elements such as Ho, Er and Tm, suggesting that the transition is sensitive to and is even hindered by disorder such as atomic vacancies. The absence of the transition for M = Lu is attributed to the highest activation energy for the transition due to the smallest volume inside the Cd20 dodecahedron.

Cubic structure types of rare-earth intermetallics and related compounds

Cubic structure types of rare-earth intermetallic and related compounds are reviewed and their structural similarities are discussed. The description of the structural relations is based on the ordered substitution or inclusion of atoms or atomic groups starting from the structures of four “aristotypes”: diamond, Cu, CsCl and W. Structural similarities between some types are illustrated by family trees of crystallographic group-subgroup relations.

Development of the Ca−Au−In Icosahedral Quasicrystal and Two Crystalline Approximants: Practice via Pseudogap Electronic Tuning

Electronic tuning and syntheses to gain the icosahedral quasicrystal (i-QC) (Ca14.1(2)Au44.2(8)In41.7(7), e/a = 1.98) and two approximant crystals (ACs) are reported. The tuning was derived from Na2Au6In5, another cubic Mg2Zn11-type structure, for which the Fermi level (e/a = 1.77) should tune to a calculated pseudogap (e/a = 2.02) under a rigid band assumption. The 1/1 AC, Ca3Au12.2(1)In6.3(2) (e/a = 1.73), crystallizes in space group Im, with a = 15.152(2) A, Z = 8, and the 2/1 AC, Ca12.6(1)Au37.0(2)In39.6(6) (e/a = 2.01), in Pa, with a = 24.632(3) A , Z = 8. Both have substantially fixed compositions according to lattice dimensions. Structure analyses reveal that both ACs contain triacontahedral clusters as the basic building blocks at the body-centered and primitive cubic unit cell levels, respectively. Densities-of-states (DOS) analyses for the 1/1 AC structure reveal a pseudogap at e/a = 2.00, close to the point at which the i-QC was predicted and experimentally tuned. Phase relationships of the ACs and the i-QC are reported according to DTA, XRD, and temperature-dependent XRD measurements. The QC is thermodynamically metastable below approximately 500 degrees C.

New building blocks in the 2/1 crystalline approximant of a Bergman-type icosahedral quasicrystal

The refined x-ray crystal structure of the phase Mg(27)Al(10.7(2))Zn(47.3(2)) (Pa3) establishes it as the new 2/1 Bergman-type approximant of the icosahedral quasicrystal. The primitive cubic lattice consists of condensed triacontahedral and novel prolate rhombohedral (PR) clusters. Each triacontahedron encapsulates the traditional, multiply endohedral Bergman-type clusters, and each PR encapsulates an Al(2) dimer. This phase exhibits the same long-range order as recently established for the Tsai-type Sc-Mg-Zn 2/1 approximant crystal, with substantial geometric and atomic distribution differences between the two only in the short range orders. This common feature suggests that Bergman- and Tsai-type quasicrystals may be more similar than earlier conceived. Factors germane to the formation of, and the differences between, Bergman- vs. Tsai-type 1/1 and 2/1 approximate structures are considered, including notably different distributions of the more electropositive elements.

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 Sc(3)Mg(0.18(1))Zn(17.73(3)), the 1/1 approximant crystal (AC), and Sc(11.18(9))Mg(2.5(1))Zn(73.6(2)), the 2/1 AC, in the corresponding icosahedral quasicrystal (i-QC) system. The 1/1 AC crystallizes in space group Im, a = 13.863(2) A, Z = 8, and the 2/1 AC, in Pa, a = 22.412 (2) A, 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.

Synthesis and Structure of Five Sc3CuyZn18-y-Type Compositions (0 ≤ y ≤ ∼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 approximately Sc(3)Cu(2.1)Zn(12.9) 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 Sc(3)Zn(17) as well as for the corrected Sc(3)Zn(18) (ScZn(6)) composition. Structures of high yield products of the 0, 1, 2, 3 Cu atom steps all refined as isotypic Sc(3)Cu(y)Zn(18-y) phases (Im(-)3, Z = 8, a = 13.8311(5) to 13.7528(5) A for 0 < or = y < or =2.2), basically isostructural with RCd(6) 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.

Hybridization mechanism for cohesion of Cd-based quasicrystals

The cohesion mechanism of cubic approximant crystals in newly discovered binary quasicrystals, Cd(6)M ( M = Yb or Ca), is studied theoretically. It is found that stabilization due to alloying is obtained if M is an element with low-lying unoccupied d states. This leads to the conclusion that the cohesion of Cd-based compounds is due to hybridization of the d states of Yb and Ca with a wide sp band. The Hume-Rothery mechanism does not play a principal role in the stability because neither a distinct pseudogap nor stabilization due to alloying is obtained for isostructural Cd-Mg. In addition to the electronic origin, matching of the atomic size is very crucial for quasicrystal formation in Cd-based compounds.