Nested polyhedra units: a geometrical concept for describing complicated cubic structures

Chabot, B.; Cenzual, K.; Parthé, E.

doi:10.1107/s0567739481000028

Cited by 50 publications

(74 citation statements)

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“…As seen from Figure 5a and b, m becomes 0 for d % 1 = 4 . Consequently, there is no suitable matrix adopting exclusively Zn 26 or Zn 29 clusters. In accordance with our findings, these two cluster types are only stable if they are chemically intergrown.…”

Section: Structure-composition Relationsmentioning

confidence: 98%

“…Nevertheless, the purely geometric description of the structure in terms of specific atomic aggregates receives its justification from the fact that it concisely visualizes constitutive structural features and uncovers distinctive structural properties in an easy recognizable way. [26] According to this concept each cluster is defined by a sequence of three or four symmetrically independent atomic sites arranged in polyhedral shells around an occupied or empty center of high symmetry. The shells are congruent to one of the Platonic or Archimedean solids.…”

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confidence: 99%

“…Such atomic sets have been termed clusters, [7] sets of nested polyhedra, [25] or nested polyhedra units. [26] We choose the second method for extracting structural characteristics of this new binary Znrich phase from the positional parameters determined by single crystal X-ray diffraction means for three distinctly composed crystals. Subsequently we shall use the term cluster well knowing that we do not address the question of chemical bonding in the selected atomic sets.…”

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confidence: 99%

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Structure–Composition Relations for the Partly Disordered Hume‐Rothery Phase Ir_7+7δZn_97−11δ (0.31≤δ≤0.58)

Hornfeck

Thimmaiah

Lee

et al. 2004

Chemistry A European J

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The crystal structure, its variation within the homogeneity range and some physical properties of the new zinc-rich, partly disordered phase Ir7+7deltaZn97-11delta (0.31< or =delta< or =0.58) are reported. The structures of three phases with distinct composition were determined by means of single crystal X-ray diffraction. Ir7+7deltaZn97-11delta exhibits a significant homogeneity range, adopts a complex gamma-brass related cubic structure (cF403-406), is stable up to 1201(2) K, and transforms sluggishly below 1048(4) K into a phase with 394 atoms in the monoclinic primitive unit cell. It is a diamagnetic, moderate metallic conductor. Six distinguishable clusters consisting of 22-29 atoms comprise the structure. The clusters are situated about the 16 high symmetry points of the cubic F lattice. The structure can be subdivided into two partial structures, one with constant composition IrZn5 and 192 atoms per unit cell and a second being significantly richer in zinc with variable composition and 211-214 atoms per unit cell. The meandering triply periodic minimal surface of two interpenetrating diamond-like nets separates the compositionally variable from its complementary invariant part. The phase width is coupled with substitutional and positional disorder. A comprehensive analysis of composition-dependent site occupancy factors reveals a linear correlation between the various types of disorder which can be conclusively interpreted in terms of an incoherent intergrowth of distinctive partial structures in variable proportions on a length scale comparable to the size of the approximately 2 nm large unit cell. On the basis of the structural findings we derive the structure chemically meaningful formula Ir7+7delta)Zn97-11delta which quantitatively accounts for the interrelation between substitutional and positional disorder and provides a measure for the homogeneity range in structural terms.

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Section: Structure-composition Relationsmentioning

confidence: 98%

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confidence: 99%

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confidence: 99%

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Structure–Composition Relations for the Partly Disordered Hume‐Rothery Phase Ir_7+7δZn_97−11δ (0.31≤δ≤0.58)

Hornfeck

Thimmaiah

Lee

et al. 2004

Chemistry A European J

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“…As described by the topological analysis of the Tb117Fe52Ge112 structure type in our previous paper [23], the crystal structure of R117Co52+δSn112+γ can be understood as an assembly of multi-shell polyhedra, following the early ideas of Jones [30] and Parthé [31]. Thus, the structure is built of three multi-shell, face-sharing truncated octahedra (TOH), labeled as A, B, and C in Figure 2.…”

Section: Crystal Structuresmentioning

confidence: 99%

Synthesis, Crystal Structure, and Magnetic Properties of Giant Unit Cell Intermetallics R117Co52+δSn112+γ (R = Y, La, Pr, Nd, Ho)

2016

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Ternary intermetallics R 117 Co 52+δ Sn 112+γ (R = Y, La, Pr, Nd, and Ho) have been prepared by arc-melting followed by annealing at 800 • C. All the compounds belong to the Tb 117 Fe 52 Ge 112 structure type (space group Fm3m) characterized by a complex giant cubic unit cell with a~30 Å. The single-crystal structure determination of Y-and La-containing compounds reveals a significant structural disorder. A comparison of these and earlier reported crystal structures of R 117 Co 52+δ Sn 112+γ suggests that more extensive disorder occurs for structures that contain larger lanthanide atoms. This observation can be explained by the need to maintain optimal bonding interactions as the size of the unit cell increases. Y 117 Co 56 Sn 115 exhibits weak paramagnetism due to the Co sublattice and does not show magnetic ordering in the 1.8-300 K range. Ho 117 Co 55 Sn 108 shows ferromagnetic ordering at 10.6 K. Both Pr 117 Co 54 Sn 112 and Nd 117 Co 54 Sn 111 exhibit antiferromagnetic ordering at 17 K and 24.7 K, respectively, followed by a spin reorientation transition at lower temperature.

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“…In Mg 44 Ir 7 , clusters are derived from Ti 2 Ni, g-brass, and a-Mn. [55] We first turn to the new cluster types found in this pair of structures.…”

Section: Resultsmentioning

confidence: 98%

Laves Phases, γ‐Brass, and 2×2×2 Superstructures: A New Class of Quasicrystal Approximants and the Suggestion of a New Quasicrystal

Berger

Johnson

Nebgen

et al. 2008

Chemistry A European J

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Of the most common cubic intermetallic structure types, several (MgCu(2), Cu(5)Zn(8), Ti(2)Ni, and alpha-Mn) have superstructures with unusual symmetry properties. These superstructures (Be(5)Au, Li(21)Si(5), Sm(11)Cd(45), and Mg(44)Ir(7)) have the unusual property of pairs of perpendicular pseudo fivefold axes, most apparent in their X-ray diffraction patterns. The current work shows that an 8D to 3D projection method cleanly describes most (and in one case, all) of the atomic positions in the four superstructures mentioned above. This type of projection, which maps the E(8) lattice (a mathematically simple 8D crystal) into 3D space, combines the desired higher dimensional point group's perpendicular fivefold rotations with 3D translational symmetry-exactly what we see in the experimental crystal structures. The projection method successfully accounts for all heavy atom positions in the four superstructures, and at least 60-70 % of the light atom positions. The results suggest that all of these structures, previously known to be connected only by qualitative similarities in their atomic "clusters", are approximants of a single, as-yet unknown, class of quasicrystal.

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Nested polyhedra units: a geometrical concept for describing complicated cubic structures

Cited by 50 publications

References 3 publications

Structure–Composition Relations for the Partly Disordered Hume‐Rothery Phase Ir_7+7δZn_97−11δ (0.31≤δ≤0.58)

Structure–Composition Relations for the Partly Disordered Hume‐Rothery Phase Ir_7+7δZn_97−11δ (0.31≤δ≤0.58)

Synthesis, Crystal Structure, and Magnetic Properties of Giant Unit Cell Intermetallics R117Co52+δSn112+γ (R = Y, La, Pr, Nd, Ho)

Laves Phases, γ‐Brass, and 2×2×2 Superstructures: A New Class of Quasicrystal Approximants and the Suggestion of a New Quasicrystal

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Nested polyhedra units: a geometrical concept for describing complicated cubic structures

Cited by 50 publications

References 3 publications

Structure–Composition Relations for the Partly Disordered Hume‐Rothery Phase Ir7+7δZn97−11δ (0.31≤δ≤0.58)

Structure–Composition Relations for the Partly Disordered Hume‐Rothery Phase Ir7+7δZn97−11δ (0.31≤δ≤0.58)

Synthesis, Crystal Structure, and Magnetic Properties of Giant Unit Cell Intermetallics R117Co52+δSn112+γ (R = Y, La, Pr, Nd, Ho)

Laves Phases, γ‐Brass, and 2×2×2 Superstructures: A New Class of Quasicrystal Approximants and the Suggestion of a New Quasicrystal

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Structure–Composition Relations for the Partly Disordered Hume‐Rothery Phase Ir_7+7δZn_97−11δ (0.31≤δ≤0.58)

Structure–Composition Relations for the Partly Disordered Hume‐Rothery Phase Ir_7+7δZn_97−11δ (0.31≤δ≤0.58)