Zum Aufbau der Legierungen

Westgren, Arne; Phragmén, Gösta

doi:10.1007/bf01451945

Cited by 8 publications

(17 citation statements)

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“…A distance from the origin Γ to centers of 36 zone planes in (b) is equal because of the condition G 2 = 18. Thus, the free electron Fermi sphere touches all 36-face zone planes simultaneously, leading to the satisfaction of the interference condition 2k F ( ) 2 = G 2 within the free electron model.…”

Section: Figurementioning

confidence: 93%

“…Here, Cu, Zn, Al and Sn were referred to as mono-, di-, tri-and tetra-valent metals, which are meant as being capable of donating one, two, three and four outermost electrons in its free atom to form the respective compounds. In 1928, Westgren and Phragmén [2] revealed that, through extensive powdered X-ray diffraction studies, Cu 5 Zn 8 and Al 4 Cu 9 compounds, both having been called the gamma-brass since that time, commonly contain 52 atoms per cubic unit cell and stabilize at an average valence electron concentration per atom equal to 21/13, in spite of different stoichiometric ratios involved in them. Since then, the stabilization of isostructural alloys and compounds at a specific composition-averaged valence has been referred to as the Hume-Rothery electron concentration rule.…”

Section: E/a Versus Valence In the Hume-rothery Electron Concentratiomentioning

confidence: 99%

“…in the reciprocal space, where 2k F ( ) 2 is the square of the Fermi diameter and G 2 is the square of the reciprocal lattice vector corresponding to the set of lattice planes involved in the interference condition. Obviously, the electron wave vector and the reciprocal lattice vector are rigorously parallel to each other for the interference phenomenon to occur.…”

Section: E/a-dependent Hume-rothery-type Stabilization Mechanismmentioning

confidence: 99%

“…This refers to the electronic states at the Fermi level and, at the same time, represents the reciprocal lattice vector or the set of lattice planes or Brillouin zone planes interacting with electrons at the Fermi level. This means that we can simultaneously extract both quantities (2k F ) 2 and |G| 2 appearing in Equation (1) from the FLAPW-Fourier spectra.…”

Section: Figurementioning

confidence: 99%

“…Second, we construct the dispersion relation E = f (k i + G) for electrons, from which the square of the Fermi diameter and e/a can be deduced from Equation (2). The dispersion relation thus constructed is called the Hume-Rothery plot, since it allows us to determine e/a appearing in the Hume-Rothery electron concentration rule.…”

Section: Figurementioning

confidence: 99%

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The Physics of the Hume-Rothery Electron Concentration Rule

Mizutani

Sato

2017

Crystals

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For a long time we have shared the belief that the physics of the Hume-Rothery electron concentration rule can be deepened only through thorough investigation of the interference phenomenon of itinerant electrons with a particular set of lattice planes, regardless of whether d-states are involved near the Fermi level or not. For this purpose, we have developed the FLAPW-Fourier theory (Full potential Linearized Augmented Plane Wave), which is capable of determining the square of the Fermi diameter, (2k F ) 2 , and the number of itinerant electrons per atom, e/a, as well as the set of lattice planes participating in the interference phenomenon. By determining these key parameters, we could test the interference condition and clarify how it contributes to the formation of a pseudogap at the Fermi level. Further significant progress has been made to allow us to equally handle transition metal (TM) elements and their compounds. A method of taking the center of gravity energy for energy distribution of electrons with a given electronic state has enabled us to eliminate the d-band anomaly and to determine effective (2k F ) 2 , and e/a, even for systems involving the d-band or an energy gap across the Fermi level. The e/a values for 54 elements covering from Group 1 up to Group 16 in the Periodic Table, including 3d-, 4d-and 5d-elements, were determined in a self-consistent manner. The FLAPW-Fourier theory faces its limit only for elements in Group 17 like insulating solids Cl and their compounds, although the value of e/a can be determined without difficulty when Br becomes metallic under high pressures. The origin of a pseudogap at the Fermi level for a large number of compounds has been successfully interpreted in terms of the interference condition, regardless of the bond-types involved in the van Arkel-Ketelaar triangle map.

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Section: Figurementioning

confidence: 93%

Section: E/a Versus Valence In the Hume-rothery Electron Concentratiomentioning

confidence: 99%

Section: E/a-dependent Hume-rothery-type Stabilization Mechanismmentioning

confidence: 99%

Section: Figurementioning

confidence: 99%

Section: Figurementioning

confidence: 99%

See 3 more Smart Citations

The Physics of the Hume-Rothery Electron Concentration Rule

Mizutani

Sato

2017

Crystals

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Krystallbau und chemische Zusammensetzung

Goldschmidt¹

1927

Ber. dtsch. Chem. Ges. A/B

411

175

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Pseudo‐Fivefold Diffraction Symmetries in Tetrahedral Packing

Henderson¹,

Kaminsky²,

Nelson³

et al. 2013

Chemistry A European J

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We review the way in which atomic tetrahedra composed of metallic elements pack naturally into fused icosahedra. Orthorhombic, hexagonal, and cubic intermetallic crystals based on this packing are all shown to be united in having pseudo-fivefold rotational diffraction symmetry. A unified geometric model involving the 600-cell is presented: the model accounts for the observed pseudo-fivefold symmetries among the different Bravais lattice types. The model accounts for vertex-, edge-, polygon-, and cell-centered fused-icosahedral clusters. Vertex-centered and edge-centered types correspond to the well-known pseudo-fivefold symmetries in Ih and D5h quasicrystalline approximants. The concept of a tetrahedrally-packed reciprocal space cluster is introduced, the vectors between sites in this cluster corresponding to the principal diffraction peaks of fused-icosahedrally-packed crystals. This reciprocal-space cluster is a direct result of the pseudosymmetry and, just as the real-space clusters, can be rationalized by the 600-cell. The reciprocal space cluster provides insights for the Jones model of metal stability. For tetrahedrally-packed crystals, Jones zone faces prove to be pseudosymmetric with one another. Lower and upper electron per atom bounds calculated for this pseudosymmetry-based Jones model are shown to accord with the observed electron counts for a variety of Group 10-12 tetrahedrally-packed structures, among which are the four known Cu/Cd intermetallic compounds: CdCu2, Cd3Cu4, Cu5Cd8, and Cu3Cd10. The rationale behind the Jones lower and upper bounds is reviewed. The crystal structure of Zn11Au15Cd23, an example of a 1:1 MacKay cubic quasicrystalline approximant based solely on Groups 10-12 elements is presented. This compound crystallizes in Im3 (space group no. 204) with a = 13.842(2) Å. The structure was solved with R1 = 3.53 %, I > 2σ; = 5.33 %, all data with 1282/0/38 data/restraints/parameters.

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Zum Aufbau der Legierungen

Cited by 8 publications

References 0 publications

The Physics of the Hume-Rothery Electron Concentration Rule

The Physics of the Hume-Rothery Electron Concentration Rule

Krystallbau und chemische Zusammensetzung

Pseudo‐Fivefold Diffraction Symmetries in Tetrahedral Packing

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