Superstructure of EU4CD25: a quasicrystal approximant

Eu Doping in the GdCd7.88 Quasicrystal and Its Approximant Crystal GdCd6

The effect of Eu doping in the Tsai quasicrystal (QC) GdCd7.88 and its periodic 1/1 approximant crystal (AC) GdCd6 are investigated. This represents the first synthesis of Eu-containing stable QC samples, where three samples with the final composition Gd1-xEuxCd7.6±α at Eu doping concentrations x = 0.06, 0.13, and 0.19 are obtained (α ∼ 0.2). They are compared to two 1/1 ACs with compositions Gd1-xEuxCd6 (x = 0.12, 0.16). In addition, a new type of 1/1 AC, differing only by the inclusion of extra Cd sites unique to the Eu4Cd25 1/1 AC, has been discovered and synthesized for the concentrations Gd1-xEuxCd6+δ (x = 0.25, 0.33, 0.45, 0.69, 0.73, and 0 < δ ≤ 0.085). Due to the preferred cube morphology of its single grains, we refer to them as c-type 1/1 ACs and to the conventional standard ones as s-type. In both QCs and s-type ACs, the Eu content appears to saturate at a concentration of ∼20%. On the other hand, any Gd| Eu ratio is allowed in the c-type ACs, varying continuously between GdCd6 and Eu4Cd25. We describe and contrast the changes in composition, atomic structure, specific heat, and magnetic properties induced by Eu doping in the quasicrystalline phase and the s-type and c-type 1/1 ACs. By comparing our results to the literature data, we propose that the occupancy of the extra Cd sites can be used to predict the stability of Tsai-type quasicrystalline phases.

Chemically driven superstructural ordering leading to giant unit cells in unconventional clathrates Cs8Zn18Sb28 and Cs8Cd18Sb28

The unconventional clathrates, Cs₈Zn₁₈Sb₂₈ and Cs₈Cd₁₈Sb₂₈, were synthesized and reinvestigated. These clathrates exhibit unique and extensive superstructural ordering of the clathrate-I structure that was not initially reported. Cs₈Cd₁₈Sb₂₈ orders in the Ia3̄d space group (no. 230) with 8 times larger volume of the unit cell in which most framework atoms segregate into distinct Cd and Sb sites. The structure of Cs₈Zn₁₈Sb₂₈ is much more complicated, with an 18-fold increase of unit cell volume accompanied by significant reduction of symmetry down to P2 (no. 3) monoclinic space group. This structure was revealed by a combination of synchrotron X-ray diffraction and electron microscopy techniques. A full solid solution, Cs₈Zn_18−xCd_xSb₂₈, was also synthesized and characterized. These compounds follow Vegard's law in regard to their primitive unit cell sizes and melting points. Variable temperature in situ synchrotron powder X-ray diffraction was used to study the formation and melting of Cs₈Zn₁₈Sb₂₈. Due to the heavy elements comprising clathrate framework and the complex structural ordering, the synthesized clathrates exhibit ultralow thermal conductivities, all under 0.8 W m⁻¹ K⁻¹ at room temperature. Cs₈Zn₉Cd₉Sb₂₈ and Cs₈Zn_4.5Cd_13.5Sb₂₈ both have total thermal conductivities of 0.49 W m⁻¹ K⁻¹ at room temperature, among the lowest reported for any clathrate. Cs₈Zn₁₈Sb₂₈ has typical p-type semiconducting charge transport properties, while the remaining clathrates show unusual n–p transitions or sharp increases of thermopower at low temperatures. Estimations of the bandgaps as activation energy for resistivity dependences show an anomalous widening and then shrinking of the bandgap with increasing Cd-content.

Giant clathrate supercell driven by ordering of Zn/Sb bonding in the framework and Cs-guest vacancies is found in unconventional clathrate Cs₈Zn₁₈Sb₂₈.

Structural-transition-driven antiferromagnetic to spin-glass transition in Cd-Mg-Tb 1/1 approximants

The magnetic susceptibility of the 1/1 approximants to icosahedral quasicrystals in a series of Cd85-xMgxTb15(x= 5, 10, 15, 20) alloys was investigated in detail. The occurrence of antiferromagnetic (AFM) to spin-glass (SG)-like transition was noticed by increasing Mg. Transmission electron microscopy analysis evidenced a correlation between the magnetic transition and suppression of the monoclinic superlattice ordering with respect to the orientation of the Cd4tetrahedron atT> 100 K. The possible origins of this phenomenon were discussed in detail. The occurrence of the AFM to SG-like magnetic transition is associated with the combination of chemical disorder due to a randomized substitution of Cd with Mg and the orientational disorder of the Cd4tetrahedra.

Metallic alloys at the edge of complexity: structural aspects, chemical bonding and physical properties

Complex metallic alloys belong to the vast family of intermetallic compounds and are hallmarked by extremely large unit cells and, in many cases, extensive crystallographic disorder. Early studies of complex intermetallics were focusing on the elucidation of their crystal structures and classification of the underlying building principles. More recently, ab initio computational analysis and detailed examination of the physical properties have become feasible and opened new perspectives for these materials. The present review paper provides a summary of the literature data on the reported compositions with exceptional structural complexity and their properties, and highlights the factors leading to the emergence of their crystal structures and the methods of characterization and systematization of these compounds.

Discerning Chemical Pressure amidst Weak Potentials: Vibrational Modes and Dumbbell/Atom Substitution in Intermetallic Aluminides

The space requirements of atoms are generally regarded as key constraints in the structures, reactivity, and physical properties of chemical systems. However, the empirical nature of such considerations renders the elucidation of these size effects with first-principles calculations challenging. DFT-chemical pressure (DFT-CP) analysis, in which the output of DFT calculations is used to construct maps of the local pressures acting between atoms due to lattice constraints, is one productive approach to extracting the role of atomic size in the crystal structures of materials. While in principle this method should be applicable to any system for which DFT is deemed an appropriate treatment, so far it has worked most successfully when semicore electrons are included in the valence set of each atom to supply an explicit repulsive response to compression. In this Article, we address this limiting factor, using as model systems intermetallics based on aluminum, a key component in many structurally interesting phases that is not amenable to modeling with a semicore pseudopotential. Beginning with the Laves phase CaAl₂, we illustrate the difficulties of creating a CP scheme that reflects the compound's phonon band structure with the original method due to minimal core responses on the Al atoms. These deficiencies are resolved through a spatial mapping of three energetic terms that were previously treated as homogeneous background effects: the Ewald, E_α, and nonlocal pseudopotential components. When charge transfer is factored into the integration scheme, CP schemes consistent with the phonon band structure are obtainable for CaAl₂, regardless of whether Ca is modeled with a semicore or valence-only pseudopotential. Finally, we demonstrate the utility of the revised method through its application to the La₃Al₁₁ structure, which is shown to soothe CPs that would be encountered in a hypothetical BaAl₄-type parent phase through the substitution of selected Al₂ pairs with single Al atoms. La₃Al₁₁ then emerges as an example of a more general phenomenon, CP-driven substitutions of simple motifs.

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.

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.

Short- and long-range ordering during the phase transition of the Zn6Sc 1/1 cubic approximant

Using in situ x-ray scattering and synchrotron radiation, we have experimentally elucidated the mechanism of the cubic to monoclinic phase transition in the Zn6Sc 1/1 approximant to an icosahedral quasicrystal. The high-temperature cubic phase is described as a bcc packing of a large Tsai-type icosahedral cluster whose center is occupied by an orientationally disordered Zn4 tetrahedron. A clear monoclinic distortion has been found to take place within 2 K around Tc = 157 K, in excellent agreement with the observed anomalies in the electrical resistivity and heat capacity. Also, a rapid variation of the super-structure reflection intensity is observed. The low-temperature monoclinic phase, as determined by single-crystal x-ray diffraction at 40 K, has been confirmed to consist of ordered Zn4 tetrahedra, oriented in an anti-parallel way along the [[Formula: see text]] direction. Above Tc, a diffuse scattering signal is observed at the position of the super-structure reflections, which evidences that a short-range ordering of the Zn4 tetrahedra takes place. In a way similar to a second-order phase transition, the correlation length describing this short-range ordering increases rapidly when the temperature diminishes and almost diverges when the temperature is close to Tc, going from 200 Å at 220 K to reach the very large value of 1200 Å at 161 K. Finally, using single-crystal x-ray diffraction, the atomic structure of the low-temperature monoclinic super-structure (space group C2/c) could be solved. The ordering of the Zn4 tetrahedra is accompanied by a strong distortion of the surrounding shells.

Structural building principles of complex face-centered cubic intermetallics

Fundamental structural building principles are discussed for all 56 known intermetallic phases with approximately 400 or more atoms per unit cell and space-group symmetry F\bar{4}3m, Fd\bar{3}m, Fd\bar{3}, Fm\bar{3}m or Fm\bar{3}c. Despite fundamental differences in chemical composition, bonding and electronic band structure, their complex crystal structures show striking similarities indicating common building principles. We demonstrate that the structure-determining elements are flat and puckered atomic {110} layers stacked with periodicities 2p. The atoms on this set of layers, which intersect each other, form pentagon face-sharing endohedral fullerene-like clusters arranged in a face-centered cubic packing (f.c.c.). Due to their topological layer structure, all these crystal structures can be described as (p × p × p) = p 3-fold superstructures of a common basic structure of the double-diamond type. The parameter p, with p = 3, 4, 7 or 11, is determined by the number of layers per repeat unit and the type of cluster packing, which in turn are controlled by chemical composition.

Binary intermetallic phases formed by Ca, Sr, Ba, Eu and Yb: similarities and differences

The binary intermetallic phases formed by Ca, Sr, Ba, Eu and Yb with Li, Be and group 7 to 15 elements are a family of nearly 570 members, distributed over 50 compositions and 140 structure types. A graphical overview of all phases is given, and they are examined regarding their crystal chemistry, atomic sizes and volume effects in alloying.

Synthesis and TEM study of Ag–In–(Eu, Ce) ternary approximants

Ternary Ag–In–(Eu, Ce) 1/1 approximants are synthesized and their structures are studied by transmission electron microscopy (TEM). For both the approximants, superlattice spots are clearly observed at room temperature, and the superstructures of the Ag–In–(Eu, Ce) approximants are found to be similar to those of Cd25Eu4 and Cd37Ce6, respectively. The Ag–In–Eu 1/1 approximant has a double unit cell with space group Fd-3 while the Ag–In–Ce 1/1 approximant has a normal unit cell with space group Pn-3, both at room temperature. The results suggest that the tetrahedron at the center of the icosahedral cluster is ordered in the Ag–In–(Eu, Ce) approximants in the same manner as the corresponding binary approximants Cd6(Eu, Ce). Furthermore, TEM observations at high temperatures reveal that the Ag–In–(Eu, Ce) approximants undergo a phase transition to a bcc lattice at an elevated temperature. The transitions are understood as a consequence of disordering of the tetrahedron located at the center of the icosahedral cluster.

Complexity of hexagonal approximants in the RE 13Zn~58 system (RE = Ce, Pr, Nd, Sm, Gd, Tb and Dy)

For the RE 13Zn58quasi crystal approximants (RE = Ce, Pr, Nd, Sm, Gd, Tb, Dy), single crystals were prepared from the elements and their structures were refined from single-crystal X-ray diffraction data. They are derived from the Gd13Cd58type structure and crystallize in the space group P63/mmc or its subgroups. The crystal structures of Ce and Pr compounds are identical to that of the archetype, in the Nd compound a pair exchange disorder changes the composition and for Sm a further, partially occupied interstitial position lowers the symmetry to P63 mc. For the compounds with Gd, Tb and Dy, the occupancy may order, lowering the symmetry further. For the case of Tb13Zn59 high quality single crystals allowed us to refine the fully ordered orthorhombic super structure.

Occupation Waves the Way You Have Never Seen Them: the Orthorhombic Quasicrystal Approximants RE13Zn58+δ (RE = Ho, Er, Tm, and Lu)

A series of binary quasicrystal approximants RE13Zn58+delta (RE = Ho, Er, Tm, and Lu) have been prepared, and structural studies were performed by means of single-crystal X-ray diffraction. All four compounds crystallize in the orthorhombic system, but while the Ho-containing compound crystallizes in space group Pcmn, the rest of the compounds crystallize in Pc21n. This work is a continuation of the structural studies on RE13Zn approximately 58 (RE = Ce, Pr, Nd, Sm, Gd, Tb, and Dy), which all belong to the hexagonal system. The sequence of RE13Zn58+delta compounds exhibits a large variability in local ordering and composition, and therefore the crystal structures are generally rather more complex than those previously reported and exhibit a number of different ordering modes. These four compounds are structurally closely related to each other.

Interpenetrating Polar and Nonpolar Sublattices in Intermetallics: The NaCd2 Structure

In the 1960s, Samson solved the structures of some of the most complicated intermetallic phases known, including those of NaCd(2), Mg(2)Al(3), and Cu(3)Cd(4) (each with over 1000 atoms per unit cell). Following remarkable earlier constructions by Samson and by Andersson, we use quantum-mechanical calculations as a guide to describing and understanding these structures. Our electronic Aufbau begins with the relatively simple Mg(17)Al(12) structure and works up to Samson's NaCd(2) structure. In both structures, a division of the sites into electron-rich and electron-poor (with respect to an average electron count) reveals MgCu(2)-type fragments. Between the interiors and exteriors of these fragments, a change in bonding character takes place-the interiors are more polar, the interfaces relatively nonpolar. This electronic situation is traced to the geometry of the interface sites; they lie simultaneously on electron-rich and electron-poor networks. The resulting polar and nonpolar sites in NaCd(2) are separated by a minimal surface, the D surface. The driving force for assuming this structure is electronic: NaCd(2) features an interpenetration of polar and nonpolar bonding regions. This sort of thinking can be applied to other structures.

Pressure-induced phase transitions in the Cd-Yb periodic approximant to a quasicrystal

The phase study of a Cd-Yb 1/1 approximant crystal over a wide pressure and temperature range is crucial for the comparison study between periodic and quasiperiodic crystals. The Cd(4) tetrahedra, the most inner part of the atomic clusters, exhibited various structural ordering in the orientation sensitive to pressure and temperature. Five ordered phases appeared in a P-T span up to 5.2 GPa and down to 10 K. The propagation direction of ordering alternated from [110] to <111> to at about 1.0 GPa and again to [110] at 3.5-4.3 GPa. The primarily ordered phases that appeared by cooling to 210-250 K between 1.0-5.2 GPa further transformed to finely ordered ones at 120-155 K. Besides the original short-range type interaction, a long-range type interaction was likely developed under pressure to lead to the primary ordering of Cd(4) tetrahedra. Coexistence of these interactions is responsible for the complicated phase behavior.