Electron Theory of Complex Metallic Alloys

Mizutani, Uichiro; Inukai, Manabu; Sato, Hírokazu; Zijlstra, Eeuwe S.

doi:10.1016/b978-0-444-53770-6.00002-2

Cited by 22 publications

(80 citation statements)

References 78 publications

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“…The FLAPW-Fourier spectra and Hume-Rothery plot for the Al 6 Mn and Al 6 Re compounds were already reported elsewhere [11]. As listed in Table for a series of Al 6 TM compounds, the critical |G| 2 is distributed in the vicinity of 17.5 and the e/a = 2.74±0.05 rule holds well.…”

Section: Resultsmentioning

confidence: 64%

“…In the case of the isostructural Al 8 V 5 gamma-brass in the subgroup 2, however, we revealed that a critical |G| 2 is increased to 22, appearing next to |G| 2 = 18 at symmetry points N of the bcc Brillouin zone, and that e/a = 2.19 [11]. The pseudogap is masked by the V 3d states and is no longer found at E F in its total DOS.…”

Section: Resultsmentioning

confidence: 84%

“…The pseudogap is masked by the V 3d states and is no longer found at E F in its total DOS. Thus, the e/a = 1.60 ± 0.02 rule holds in the subgroup 1 but not in the subgroups 2 and 3 [1,11]. The data for the subgroup 1 gamma-brasses obeying the e/a = 1.60 rule are listed in Table. X 1 = Al, Ga, In, and Tl) and MX 2 (M = Li and X 2 = Zn and Cd) with F d3m and cF 32.…”

Section: Resultsmentioning

confidence: 98%

“…(1) noble metals and polyvalent elements, (2) TM elements and polyvalent elements, and (3) monovalent Ag and Li [1,11]. To begin with, we direct our attention to the Cu 5 Zn 8 and Al 4 Cu 9 gamma-brasses in the subgroup 1.…”

Section: Resultsmentioning

confidence: 99%

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Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys

et al. 2014

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An electron concentration parameter, expressed as the number of itinerant electrons per number of atoms N in a structural unit cell of an alloy, e/uc, is a useful parameter that can be used in interpreting the origin of a band structure pseudogap often evident at the Fermi level for structurally complex metallic alloy phases. It can be expressed in terms of the interference condition e/uc =3/2 , where |G| 2 c is the square of the critical reciprocal lattice vector associated with the specic set of lattice planes interfering with electrons at the Fermi level. This parameter is similar to the well-known Hume-Rothery electron concentration parameter e/a, which represents the number of electrons per atom and is linked with e/uc through the relation e/uc = N (e/a). We have demonstrated that certain complex metallic alloy structures appear to be stable at or near certain values of e/a. We show that the e/a = 1.60 rule holds for the sub-group of gamma-brasses with space group I43m and Pearson symbol cI52, the e/a = 4.34 rule for skutterudite compounds with Im3 and cI32, the e/a = 2.74 rule for Al6TM (TM = Mn, Tc, Re, Fe, and Ru) compounds with Cmcm and oC28, the e/a = 1.62 rule for the sub-group of the Heusler compounds with F m3m and cF 16, and the e/a = 2.09 rule for the sub-group of Zintl compounds MX1 (M = Li and Na, X1 = Al, Ga, In, and Tl) with F d3m and cF 32. The e/a rule holds in sub-groups of isostructural compounds, regardless of the degree of orbital hybridizations and the polarity involved.

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Section: Resultsmentioning

confidence: 64%

Section: Resultsmentioning

confidence: 84%

Section: Resultsmentioning

confidence: 98%

Section: Resultsmentioning

confidence: 99%

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Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys

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“…48, while in (b) it touches the bcc Figure 4. Formation of stationary electron waves as a result of interference with periodically arranged ionic potentials [11,14,19].…”

Section: Figurementioning

confidence: 99%

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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Heterophase Interface and Surface Functionalization of TiO_x/TiSi_x Metastable Nanofilms

Echeverrigaray

Figueroa

Zanatta

et al. 2022

Adv Materials Inter

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In this paper, topographically asymmetric TiOx/TiSix metastable ultrathin (nano)films on SiO2/Si(100) are produced by controlling interface reactions through ion beam synthesis. The film growth process involves a dual ion beam system, combining Ar+ sputtering a Ti target and in situ postirradiation (Ar+ + H2+ ion etching) at normal incidence to modify the surface morphology. The film's production and characterization are challenging due to the formation of a complex mixed interface+layers (heterophases) containing nanocrystalline and amorphous compounds of Ti and Si. The results for different ion etching times (0–600 s) are systematically presented and analyzed. With the experimental+theoretical information, it is possible to deduce that the heterophase interface is originated by oxide intermixing in combination with the formation of titanium silicides taking place at the early stages of growth. The reactivity of oxygen and hydrogen species is the dominating factor influencing the metastable film growth mediated by solid‐state phase reactions. Given its crucial role at the (Ti/Si):O interface, the chemical route and control of intrinsic defects (non‐stoichiometry) are defined by domain ordering mechanisms followed by surface restructuring. In view of their main characteristics, taken altogether, the current functional metastable films represent a promising alternative for high‐performance photonic and optoelectronic applications.

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Electron Theory of Complex Metallic Alloys

Cited by 22 publications

References 78 publications

Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys

Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys

The Physics of the Hume-Rothery Electron Concentration Rule

Heterophase Interface and Surface Functionalization of TiO_x/TiSi_x Metastable Nanofilms

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Electron Theory of Complex Metallic Alloys

Cited by 22 publications

References 78 publications

Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys

Theoretical Foundation for the Hume-Rothery Electron Concentration Rule for Structurally Complex Alloys

The Physics of the Hume-Rothery Electron Concentration Rule

Heterophase Interface and Surface Functionalization of TiOx/TiSix Metastable Nanofilms

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Heterophase Interface and Surface Functionalization of TiO_x/TiSi_x Metastable Nanofilms