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H Sato - One of the best experts on this subject based on the ideXlab platform.
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the original concepts of the hume Rothery Rule extended to alloys and compounds whose bonding is metallic ionic or covalent or a changing mixture of these
Progress in Materials Science, 2021Co-Authors: U Mizutani, H Sato, T B MassalskiAbstract:Abstract In this review we discuss the recent work on the interference phenomena of valence electrons with lattice planes in the presence of sp/d and sp/sp orbital hybridization effects by utilizing the FLAPW-Fourier theory calculations. Binary cubic compounds with Pearson symbols cI32, cI52, cP12, cP52, cF8, cF12 and cF16 were employed. Five different electron concentration parameters (e/a)NFE, (e/a)local, (e/a)av, (e/a)itin and VEC were introduced. The plot of (e/a)NFE as a function of the ratio (e/a)itin/VEC can be shown to be a powerful indicator of the degree of competition between interference-induced and orbital hybridization-induced effects on the band gap formation, and to judge the range over the validity of the Hume-Rothery-type stabilization effects as they change with increasing covalency and ionicity at the expense of metallicity. As the ratio (e/a)itin/VEC is approached to unity, the interference effects dominate and the electronic structure becomes more NFE (Nearly Free Electron)-like. Conversely, the orbital hybridization effects become more important and the electronic structure becomes more TB (Tight-Binding)-like as the ratio is lowered towards zero. The introduction of the FLAPW-Fourier calculations thus deepens our understanding of the Hume-Rothery electron concentration Rule.
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interpretation of the hume Rothery Rule in quasicrystals and their approximants
Journal of Non-crystalline Solids, 2004Co-Authors: Uichiro Mizutani, Tsunehiro Takeuchi, H SatoAbstract:Abstract We have performed the LMTO-ASA band calculations for the γ-phase Cu5Zn8 compound, the Frank–Kasper type Al30Mg40Zn30 and Al52.5Li32.5Cu15 1/1–1/1–1/1 approximants. In γ-brass, where d-states exist in the middle of the valence band and the sp-d hybridization effect is significant near the Fermi level EF, we show that it is critically important that the {3 3 0} and {4 1 1} zones satisfy the Hume-Rothery matching Rule and that they are strongly coupled with the sp-d hybridization to produce a deep pseudogap across EF. In the nearly-free-electron-like Al–Mg–Zn approximant, it is shown that the {5 4 3}, {7 1 0} and {5 5 0} zone planes are essentially responsible for a pseudogap at EF. In the Al–Li–Cu approximant, the deep pseudogap at EF is proven to arise mainly from the Al-3p/Al-3p hybridization effect, but that the {6 3 1} zone effect is still significantly important.
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interpretation of the hume Rothery Rule in complex electron compounds γ phase cu5zn8 alloy fk type al30mg40zn30 and mi type al68cu7ru17si8 1 1 1 1 1 1 approximants
Progress in Materials Science, 2004Co-Authors: Uichiro Mizutani, Tsunehiro Takeuchi, H SatoAbstract:The Hume–Rothery matching Rule 2kF=Khkl has been theoretically investigated by performing the LMTO-ASA (Linear Muffin-Tin Orbital–Atomic Sphere Approximation) band calculations for the three electron compounds: the γ-phase Cu5Zn8 compound or γ-brass, the nearly-free-electron-like Frank–Kasper-type Al30Mg40Zn30 1/1–1/1–1/1 approximant and the Mackay–Icosahedral-type Al68Cu7Ru17Si8 1/1–1/1–1/1 approximant. The zone planes responsible for the formation of the pseudogap across the Fermi level are identified. In the free-electron-like Al–Mg–Zn approximant, the Fermi surface-Brillouin zone interaction participating in the Hume-Rothery matching Rule solely gives rise to a sizable pseudogap at the Fermi level. In the case of the γ-brass and the Al–Cu–Ru–Si approximant, where d-states are involved in the middle of the valence band, we could demonstrate that the particular Fermi surface-Brillouin zone interactions are strongly coupled with the sp-d hybridization to produce a deep pseudogap across the Fermi level.
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identification of the brillouin zone planes in the hume Rothery matching Rule and their role in the formation of pseudogap from ab initio band calculations for the al mg zn 1 1 1 1 1 1 approximant
Physical Review B, 2001Co-Authors: H Sato, Tsunehiro Takeuchi, Uichiro MizutaniAbstract:The Hume-Rothery matching Rule has been widely used for many years as a practically useful guide to search for new quasicrystals and their approximants. In this work, we have performed the linear muffin-tin orbital atomic-sphere approximation band calculations for the nearly-free-electron-like ${\mathrm{Al}}_{30}{\mathrm{Mg}}_{40}{\mathrm{Zn}}_{30}$ 1/1-1/1-1/1 approximant. It is shown that highly degenerate free-electron states in the vicinity of the center of (543), (710), and (550) planes, whose reciprocal lattice vectors well coincide with the Fermi diameter ${2k}_{\mathrm{F}}$ in the extended zone scheme, are all reduced to the regions centered at the point N corresponding to the center of the (110) zone planes in the reduced-zone scheme and that the lifting of these degenerate states leads to the sizable pseudogap at the Fermi level, thereby lowering the electronic energy in this system. This is, to our knowledge the first attempt to identify the Brillouin zone planes in the empirical Hume-Rothery Rule and to extract their role in the formation of the pseudogap from ab initio band calculations.
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determination of spatially hybridized charge distribution and its effect on electron transport in the al cu ru si 1 1 approximant theoretical basis for the hume Rothery Rule
MRS Proceedings, 2000Co-Authors: Uichiro Mizutani, Tsunehiro Takeuchi, Eiichi Banno, V Fournee, Masaki Takata, H SatoAbstract:The origin of the pseudogap across the Fermi level was investigated by analyzing the electronic structure calculated in the framework of the LMTO-ASA method for the RT-type Al-Mg-Zn and MI-type Al-Cu-Ru-Si 1/1-approximants. The pseudogap in the former is proved to originate from the interaction of electronic states with the Brillouin zone planes associated with reciprocal lattice vectors matching with the Fermi sphere in the extended zone scheme. In the latter, the Fermi surface-Brillouin zone interaction coupled with the hybridization effect between the Al-3p and transition metal d-states produces a deep pseudogap at the Fermi level. The real-space charge distribution for electrons at the Fermi level is calculated for the Al-Cu-Ru-Si 1/1-approximant. The charge distribution thus obtained could explain not only the possession of a large resistivity of this approximant but also evidenced that the icosahedral clusters play a key role in reducing the electronic energy in favor of quasicrystalline and approximant phases.
Uichiro Mizutani - One of the best experts on this subject based on the ideXlab platform.
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interpretation of the hume Rothery Rule in quasicrystals and their approximants
Journal of Non-crystalline Solids, 2004Co-Authors: Uichiro Mizutani, Tsunehiro Takeuchi, H SatoAbstract:Abstract We have performed the LMTO-ASA band calculations for the γ-phase Cu5Zn8 compound, the Frank–Kasper type Al30Mg40Zn30 and Al52.5Li32.5Cu15 1/1–1/1–1/1 approximants. In γ-brass, where d-states exist in the middle of the valence band and the sp-d hybridization effect is significant near the Fermi level EF, we show that it is critically important that the {3 3 0} and {4 1 1} zones satisfy the Hume-Rothery matching Rule and that they are strongly coupled with the sp-d hybridization to produce a deep pseudogap across EF. In the nearly-free-electron-like Al–Mg–Zn approximant, it is shown that the {5 4 3}, {7 1 0} and {5 5 0} zone planes are essentially responsible for a pseudogap at EF. In the Al–Li–Cu approximant, the deep pseudogap at EF is proven to arise mainly from the Al-3p/Al-3p hybridization effect, but that the {6 3 1} zone effect is still significantly important.
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interpretation of the hume Rothery Rule in complex electron compounds γ phase cu5zn8 alloy fk type al30mg40zn30 and mi type al68cu7ru17si8 1 1 1 1 1 1 approximants
Progress in Materials Science, 2004Co-Authors: Uichiro Mizutani, Tsunehiro Takeuchi, H SatoAbstract:The Hume–Rothery matching Rule 2kF=Khkl has been theoretically investigated by performing the LMTO-ASA (Linear Muffin-Tin Orbital–Atomic Sphere Approximation) band calculations for the three electron compounds: the γ-phase Cu5Zn8 compound or γ-brass, the nearly-free-electron-like Frank–Kasper-type Al30Mg40Zn30 1/1–1/1–1/1 approximant and the Mackay–Icosahedral-type Al68Cu7Ru17Si8 1/1–1/1–1/1 approximant. The zone planes responsible for the formation of the pseudogap across the Fermi level are identified. In the free-electron-like Al–Mg–Zn approximant, the Fermi surface-Brillouin zone interaction participating in the Hume-Rothery matching Rule solely gives rise to a sizable pseudogap at the Fermi level. In the case of the γ-brass and the Al–Cu–Ru–Si approximant, where d-states are involved in the middle of the valence band, we could demonstrate that the particular Fermi surface-Brillouin zone interactions are strongly coupled with the sp-d hybridization to produce a deep pseudogap across the Fermi level.
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identification of the brillouin zone planes in the hume Rothery matching Rule and their role in the formation of pseudogap from ab initio band calculations for the al mg zn 1 1 1 1 1 1 approximant
Physical Review B, 2001Co-Authors: H Sato, Tsunehiro Takeuchi, Uichiro MizutaniAbstract:The Hume-Rothery matching Rule has been widely used for many years as a practically useful guide to search for new quasicrystals and their approximants. In this work, we have performed the linear muffin-tin orbital atomic-sphere approximation band calculations for the nearly-free-electron-like ${\mathrm{Al}}_{30}{\mathrm{Mg}}_{40}{\mathrm{Zn}}_{30}$ 1/1-1/1-1/1 approximant. It is shown that highly degenerate free-electron states in the vicinity of the center of (543), (710), and (550) planes, whose reciprocal lattice vectors well coincide with the Fermi diameter ${2k}_{\mathrm{F}}$ in the extended zone scheme, are all reduced to the regions centered at the point N corresponding to the center of the (110) zone planes in the reduced-zone scheme and that the lifting of these degenerate states leads to the sizable pseudogap at the Fermi level, thereby lowering the electronic energy in this system. This is, to our knowledge the first attempt to identify the Brillouin zone planes in the empirical Hume-Rothery Rule and to extract their role in the formation of the pseudogap from ab initio band calculations.
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determination of spatially hybridized charge distribution and its effect on electron transport in the al cu ru si 1 1 approximant theoretical basis for the hume Rothery Rule
MRS Proceedings, 2000Co-Authors: Uichiro Mizutani, Tsunehiro Takeuchi, Eiichi Banno, V Fournee, Masaki Takata, H SatoAbstract:The origin of the pseudogap across the Fermi level was investigated by analyzing the electronic structure calculated in the framework of the LMTO-ASA method for the RT-type Al-Mg-Zn and MI-type Al-Cu-Ru-Si 1/1-approximants. The pseudogap in the former is proved to originate from the interaction of electronic states with the Brillouin zone planes associated with reciprocal lattice vectors matching with the Fermi sphere in the extended zone scheme. In the latter, the Fermi surface-Brillouin zone interaction coupled with the hybridization effect between the Al-3p and transition metal d-states produces a deep pseudogap at the Fermi level. The real-space charge distribution for electrons at the Fermi level is calculated for the Al-Cu-Ru-Si 1/1-approximant. The charge distribution thus obtained could explain not only the possession of a large resistivity of this approximant but also evidenced that the icosahedral clusters play a key role in reducing the electronic energy in favor of quasicrystalline and approximant phases.
Tsunehiro Takeuchi - One of the best experts on this subject based on the ideXlab platform.
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interpretation of the hume Rothery Rule in quasicrystals and their approximants
Journal of Non-crystalline Solids, 2004Co-Authors: Uichiro Mizutani, Tsunehiro Takeuchi, H SatoAbstract:Abstract We have performed the LMTO-ASA band calculations for the γ-phase Cu5Zn8 compound, the Frank–Kasper type Al30Mg40Zn30 and Al52.5Li32.5Cu15 1/1–1/1–1/1 approximants. In γ-brass, where d-states exist in the middle of the valence band and the sp-d hybridization effect is significant near the Fermi level EF, we show that it is critically important that the {3 3 0} and {4 1 1} zones satisfy the Hume-Rothery matching Rule and that they are strongly coupled with the sp-d hybridization to produce a deep pseudogap across EF. In the nearly-free-electron-like Al–Mg–Zn approximant, it is shown that the {5 4 3}, {7 1 0} and {5 5 0} zone planes are essentially responsible for a pseudogap at EF. In the Al–Li–Cu approximant, the deep pseudogap at EF is proven to arise mainly from the Al-3p/Al-3p hybridization effect, but that the {6 3 1} zone effect is still significantly important.
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interpretation of the hume Rothery Rule in complex electron compounds γ phase cu5zn8 alloy fk type al30mg40zn30 and mi type al68cu7ru17si8 1 1 1 1 1 1 approximants
Progress in Materials Science, 2004Co-Authors: Uichiro Mizutani, Tsunehiro Takeuchi, H SatoAbstract:The Hume–Rothery matching Rule 2kF=Khkl has been theoretically investigated by performing the LMTO-ASA (Linear Muffin-Tin Orbital–Atomic Sphere Approximation) band calculations for the three electron compounds: the γ-phase Cu5Zn8 compound or γ-brass, the nearly-free-electron-like Frank–Kasper-type Al30Mg40Zn30 1/1–1/1–1/1 approximant and the Mackay–Icosahedral-type Al68Cu7Ru17Si8 1/1–1/1–1/1 approximant. The zone planes responsible for the formation of the pseudogap across the Fermi level are identified. In the free-electron-like Al–Mg–Zn approximant, the Fermi surface-Brillouin zone interaction participating in the Hume-Rothery matching Rule solely gives rise to a sizable pseudogap at the Fermi level. In the case of the γ-brass and the Al–Cu–Ru–Si approximant, where d-states are involved in the middle of the valence band, we could demonstrate that the particular Fermi surface-Brillouin zone interactions are strongly coupled with the sp-d hybridization to produce a deep pseudogap across the Fermi level.
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identification of the brillouin zone planes in the hume Rothery matching Rule and their role in the formation of pseudogap from ab initio band calculations for the al mg zn 1 1 1 1 1 1 approximant
Physical Review B, 2001Co-Authors: H Sato, Tsunehiro Takeuchi, Uichiro MizutaniAbstract:The Hume-Rothery matching Rule has been widely used for many years as a practically useful guide to search for new quasicrystals and their approximants. In this work, we have performed the linear muffin-tin orbital atomic-sphere approximation band calculations for the nearly-free-electron-like ${\mathrm{Al}}_{30}{\mathrm{Mg}}_{40}{\mathrm{Zn}}_{30}$ 1/1-1/1-1/1 approximant. It is shown that highly degenerate free-electron states in the vicinity of the center of (543), (710), and (550) planes, whose reciprocal lattice vectors well coincide with the Fermi diameter ${2k}_{\mathrm{F}}$ in the extended zone scheme, are all reduced to the regions centered at the point N corresponding to the center of the (110) zone planes in the reduced-zone scheme and that the lifting of these degenerate states leads to the sizable pseudogap at the Fermi level, thereby lowering the electronic energy in this system. This is, to our knowledge the first attempt to identify the Brillouin zone planes in the empirical Hume-Rothery Rule and to extract their role in the formation of the pseudogap from ab initio band calculations.
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determination of spatially hybridized charge distribution and its effect on electron transport in the al cu ru si 1 1 approximant theoretical basis for the hume Rothery Rule
MRS Proceedings, 2000Co-Authors: Uichiro Mizutani, Tsunehiro Takeuchi, Eiichi Banno, V Fournee, Masaki Takata, H SatoAbstract:The origin of the pseudogap across the Fermi level was investigated by analyzing the electronic structure calculated in the framework of the LMTO-ASA method for the RT-type Al-Mg-Zn and MI-type Al-Cu-Ru-Si 1/1-approximants. The pseudogap in the former is proved to originate from the interaction of electronic states with the Brillouin zone planes associated with reciprocal lattice vectors matching with the Fermi sphere in the extended zone scheme. In the latter, the Fermi surface-Brillouin zone interaction coupled with the hybridization effect between the Al-3p and transition metal d-states produces a deep pseudogap at the Fermi level. The real-space charge distribution for electrons at the Fermi level is calculated for the Al-Cu-Ru-Si 1/1-approximant. The charge distribution thus obtained could explain not only the possession of a large resistivity of this approximant but also evidenced that the icosahedral clusters play a key role in reducing the electronic energy in favor of quasicrystalline and approximant phases.
R Ceolin - One of the best experts on this subject based on the ideXlab platform.
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hume Rothery Rule in v vi compounds
Solid State Communications, 1992Co-Authors: J P Gaspard, R CeolinAbstract:Abstract The crystal structures of compounds of the right hand side of the Mendeleiev table can be easily understood in terms of their electronic structure. The bonding mechanism is of ppσ type and the expected simple cubic structure is subsequently deformed by a Peirls transition: some bonds are shortened and some others are elongated among the directions of the axes of the cube. The alternation of short and long bonds is driven by the electron/atom ratio. Using simple theoretical arguments, we show that the periodicity of deformation is simply related to the average number N p of p electrons. If the filling of the p band isN p 6=nmwhere n and m are prime numbers, the structure shows a m-fold periodicity. We show that, up to very large m values, this Rule is confirmed without any exception by an important series of compounds including As x Te 1-x , Sb x Te 1-x , Bi x Se 1-x , Bi x Te 1-x and As 2 Ge x Te 3+x .
J P Gaspard - One of the best experts on this subject based on the ideXlab platform.
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hume Rothery Rule in v vi compounds
Solid State Communications, 1992Co-Authors: J P Gaspard, R CeolinAbstract:Abstract The crystal structures of compounds of the right hand side of the Mendeleiev table can be easily understood in terms of their electronic structure. The bonding mechanism is of ppσ type and the expected simple cubic structure is subsequently deformed by a Peirls transition: some bonds are shortened and some others are elongated among the directions of the axes of the cube. The alternation of short and long bonds is driven by the electron/atom ratio. Using simple theoretical arguments, we show that the periodicity of deformation is simply related to the average number N p of p electrons. If the filling of the p band isN p 6=nmwhere n and m are prime numbers, the structure shows a m-fold periodicity. We show that, up to very large m values, this Rule is confirmed without any exception by an important series of compounds including As x Te 1-x , Sb x Te 1-x , Bi x Se 1-x , Bi x Te 1-x and As 2 Ge x Te 3+x .
