The Hume-Rothery electron concentration rules and second moment scaling

Hoistad, Laura M.; Lee, Stephen

doi:10.1021/ja00022a004

Cited by 51 publications

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“…6 . It represents a structurally distinctive member of a class of g-brass related intermetallic phases; the structures are composed of 396 to 448 atoms contained in a nearly 2 nm large cubic face-centered unit cell.…”

Section: Resultsmentioning

confidence: 99%

“…The sequence of the elemental structure types like face-centered cubic, body centered cubic and hexagonal close packed being frequently found in Hume-Rothery systems has been rationalized this way. [2,6] An often cited text book example reflecting the e/a-scaled stabilization is the series of b-brasstype structures CuZn, AlCu 3 , and Cu 5 Sn: All three phases Abstract: The crystal structure, its variation within the homogeneity range and some physical properties of the new zinc-rich, partly disordered phase Ir 7+7d Zn 97À11d (0.31 d 0.58) are reported. The structures of three phases with distinct composition were determined by means of single crystal X-ray diffraction.…”

Section: Introductionmentioning

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: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…For the elemental systems the atomic parameters are the same ones used effciently in previous work on transition metal alloys 27, 50. These are the parameters for Fe, H ii (4s)=−9.10 eV, H ii (4p)=−5.32 eV, H ii (3d)=−12.60 eV; ζ (4s)= ζ (4p)=1.9, ζ 1 (3d)=5.35 (0.5505), ζ 2 (3d)=2.00 (0.6260).…”

Section: Methodsmentioning

confidence: 99%

Curing behavior of anionic poly(urethane urea) dispersions crosslinked with partially methylated melamine formaldehyde

Chiu

Huang

Chiang

2007

J of Applied Polymer Sci

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A rigid-body pendulum rheometer was used to observe the isothermal cure behavior of an anionic poly(urethane urea) dispersion crosslinked with different amounts of partially methylated melamine formaldehyde (PMMF). In this experiment, the anionic poly(urethane urea) dispersion had a large number of >NÀ ÀH crosslinking or branching sites in urethane and urea groups per molecule, which allowed a large amount of PMMF to couple with the elastic polyurethane (PU) backbone. The test results showed that the cure response of the PU dispersion crosslinked with PMMF was a function of the concentration of PMMF and indicated that 30 phr PMMF could be the optimum amount of the crosslinking agent and that 1208C was the optimum temperature for the curing process. In addition, PMMF self-condensation could take place during the curing process. The self-condensation of PMMF also was monitored by a thermogravimetric method. Moreover, the dynamic mechanical properties of PMMF-crosslinked PU films were affected by the concentration of PMMF. From the curing behavior and dynamic mechanical analysis test results, it was reasonable to assume that highly PMMF branched PUs with partial crosslinking structures could be formed.

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“…Ein Ansatz, um intermetallische Phasen auf der Basis von Elektronenstrukturen zu beschreiben, greift auf die Hume-Rothery-Regeln zurück. [47][48][49][50] In einem anderen Ansatz wurden modifizierte Wade-MingosRegeln verwendet, um Elektronenzahlen in komplexen Polyederstrukturen zu erklären. [51] Beispiele dafür sind die eleganten Analysen des Na 35 Cd 24 Ga 56 -Strukturtyps durch Tillard-Charbonnel und Belin [40] und des K 17 In 41 -Typs durch Lin und Corbett.…”

Section: Einfache Zusammensetzungen Komplexe Strukturenunclassified

Sich durchdringende polare und unpolare Untergitter in intermetallischen Phasen: die Struktur von NaCd₂

2007

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In den 1960er Jahren bestimmte Samson die Strukturen einiger der komplexesten intermetallischen Phasen, darunter NaCd2, Mg2Al3 und Cu3Cd4, die jeweils über 1000 Atome pro Elementarzelle aufweisen. Basierend auf den bemerkenswerten Arbeiten von Samson und Andersson verwenden wir quantenmechanische Rechnungen zur Beschreibung dieser Strukturen. Der formale Aufbau der Struktur auf der Grundlage der elektronischen Verhältnisse beginnt mit der relativ einfachen Mg17Al12‐Struktur und setzt sich bis zu Samsons NaCd2‐Struktur fort, wobei die Aufteilung in elektronenreiche und elektronenarme Gitterplätze (bezüglich der durchschnittlichen Elektronenzahl) bei beiden Strukturen das Vorliegen von Fragmenten des MgCu2‐Typs aufdeckt. Die äußeren und inneren Bereiche eines solchen Fragments weisen unterschiedliche Bindungsverhältnisse auf: Der innere Bereich ist eher polar, während die Grenzflächen relativ unpolar sind. Dieser Sachverhalt kann mit der Geometrie der Grenzflächenplätze begründet werden, die zugleich an elektronenreichen wie auch elektronenarmen Gittern beteiligt sind. Die polaren und unpolaren Gitterplätze in NaCd2 sind durch eine Minimalfläche, die D‐Fläche, voneinander getrennt. Die Argumente, die für eine solche Struktur sprechen, beruhen auf elektronischen Überlegungen. Ein entscheidendes Merkmal besteht darin, dass sich polare und unpolare Bindungstypen gegenseitig durchdringen. Diese Methode lässt sich auch auf andere Strukturen anwenden.

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The Hume-Rothery electron concentration rules and second moment scaling

Cited by 51 publications

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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)

Curing behavior of anionic poly(urethane urea) dispersions crosslinked with partially methylated melamine formaldehyde

Sich durchdringende polare und unpolare Untergitter in intermetallischen Phasen: die Struktur von NaCd₂

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The Hume-Rothery electron concentration rules and second moment scaling

Cited by 51 publications

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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)

Curing behavior of anionic poly(urethane urea) dispersions crosslinked with partially methylated melamine formaldehyde

Sich durchdringende polare und unpolare Untergitter in intermetallischen Phasen: die Struktur von NaCd2

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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)

Sich durchdringende polare und unpolare Untergitter in intermetallischen Phasen: die Struktur von NaCd₂