Interpretation of the Hume-Rothery rule in quasicrystals and their approximants

We present single-crystal studies of Pd(0.213)Cd(0.787) and Pd(0.235)Cd(0.765), synchrotron powder studies of Pd(1-x)Cd(x), 0.755> or =x> or =0.800, and LDA-DFT and extended Hückel (eH) calculations on these or related phases. The two single-crystal structures have a, b, and c axis lengths of 9.9013(7), 14.0033(10), 37.063(24) and 9.9251(3), 14.0212(7), 60.181(3) A, respectively and they crystallize in the space groups Ccme and F2mm, respectively (solved as (3+1)-dimensional crystals their most convenient superspace group is Xmmm(00gamma)s00). The structures have two different structural components each with their own separate axis parameters. Powder data shows that the ratio of these separate axes (S/L) varies from 1.615 to 1.64, values near the golden mean (1.618). For Pd(0.213)Cd(0.787), different Pd and Cd site occupancies lead to variation in the R factor from 2.6-3.6 %. The site occupancy pattern with the lowest R factor (among the 26 820 variants studied) is the exact site occupancy pattern predicted by LDA-DFT parameterized eH Mulliken charge populations. The phases can be understood through a chemical twinning principle found in gamma-brass, the parent structure for the above phases (a relation with the MgCu(2) Laves phase is also noted). This twinning principle can be used to account for Cd and Pd site preferences. At the same time there is a clean separation among the Cd and Pd atoms for the two separate chain types at height b=0 and 1/2. These results indicate that Cd:Pd stoichiometry plays a role in phase stability.

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“…First we carried out LDA-DFT calculations on the parent structure of the family, g-brass. [37,41,42] We then found…”

Section: Methodsmentioning

confidence: 97%

Pd_0.213Cd_0.787 and Pd_0.235Cd_0.765 Structures: Their Long c Axis and Composite Crystals, Chemical Twinning, and Atomic Site Preferences

Schmidt

Fredrickson

Conrad

et al. 2007

Chemistry A European J

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“…Such a pseudogap has been found experimentally and from first-principles calculations in many sp quasicrystals and approximants [5,8,9]. It has also been found in many icosahedral approximants containing TM elements [5,10,11]; whereas there are contradictory results about decagonal phases (Ref. [12] and Refs.…”

Section: Introductionmentioning

confidence: 93%

“…The origin of the stabilization of quasicrystals is still unclear in spite of many experimental and theoretical studies. For Al-based quasicrystals, a Hume-Rothery mechanism [1,2] has been shown to play a significant role (see for instance [3][4][5] and Refs. therein).…”

Section: Introductionmentioning

confidence: 99%

Effective medium-range Mn–Mn pair interaction induces pseudogap in the density of states of Al(Si)–Mn approximants

Laissardière¹,

Nguyen-Manh²,

Mayou³

2004

Journal of Non-Crystalline Solids

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The effect on the electronic structure of an effective medium-range Mn-Mn interaction mediated by the valence states and the spd hybridization is presented. In Al(rich)-Mn phases related to quasicrystals (Al 12 Mn, o-Al 6 Mn, a-Al 9 Mn 2 Si), this effective interaction creates a Hume-Rothery pseudogap in the density of states together with a minimization of the band energy. It is shown that the Mn-Mn interaction up to the distance around 10-20A plays an essential role in stabilizing related quasicrystal structures. Ó 2004 Published by Elsevier B.V.

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“…Theoretically, it has been reported that the pseudogap opening of 1/1-Al 52.5 Li 32.5 Cu 15 approximant is not due to the sp-d hybridization, but the interatomic hybridization between Al 3p states. 15 Experimentally, it has been shown that the Fermi sphere in i-Al 6 Li 3 Cu just touches the q-BZs formed by dominant reflections. 16,25 Therefore, the existence of two components in i-Cd 84 Yb 16 suggests that a mechanism other than the Hume-Rothery scenario also works for the pseudogap formation.…”

Section: ͑1͒mentioning

confidence: 99%

Electron momentum distribution of icosahedralCd84Yb16studied by Compton scattering

et al. 2003

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The electron momentum distribution in icosahedral Cd 84 Yb 16 has been studied using the high-resolution Compton scattering technique with a momentum resolution of 0.16 a.u. The experimental valence-electron Compton profile is decomposed into two components: an inverted parabolalike one and a broad Gaussian-like one. We have found that the Fermi sphere, deduced from the number of electrons under the inverted parabolalike component, just coincides with the quasi-Brillouin zones constructed from the intense ͑211111͒ and ͑221001͒ reciprocal points. The Gaussian-like part is attributed to the electron occupation of the Yb 5d states. These facts are taken as signature that both the Hume-Rothery mechanism and the sp-d hybridization mechanism contribute to the formation of the pseudogap, stabilizing the icosahedral phase of Cd 84 Yb 16 .

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Interpretation of the Hume-Rothery rule in quasicrystals and their approximants

Cited by 21 publications

References 13 publications

Pd_0.213Cd_0.787 and Pd_0.235Cd_0.765 Structures: Their Long c Axis and Composite Crystals, Chemical Twinning, and Atomic Site Preferences

Pd_0.213Cd_0.787 and Pd_0.235Cd_0.765 Structures: Their Long c Axis and Composite Crystals, Chemical Twinning, and Atomic Site Preferences

Effective medium-range Mn–Mn pair interaction induces pseudogap in the density of states of Al(Si)–Mn approximants

Electron momentum distribution of icosahedralCd84Yb16studied by Compton scattering

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Interpretation of the Hume-Rothery rule in quasicrystals and their approximants

Cited by 21 publications

References 13 publications

Pd0.213Cd0.787 and Pd0.235Cd0.765 Structures: Their Long c Axis and Composite Crystals, Chemical Twinning, and Atomic Site Preferences

Pd0.213Cd0.787 and Pd0.235Cd0.765 Structures: Their Long c Axis and Composite Crystals, Chemical Twinning, and Atomic Site Preferences

Effective medium-range Mn–Mn pair interaction induces pseudogap in the density of states of Al(Si)–Mn approximants

Electron momentum distribution of icosahedralCd84Yb16studied by Compton scattering

Contact Info

Product

Resources

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Pd_0.213Cd_0.787 and Pd_0.235Cd_0.765 Structures: Their Long c Axis and Composite Crystals, Chemical Twinning, and Atomic Site Preferences

Pd_0.213Cd_0.787 and Pd_0.235Cd_0.765 Structures: Their Long c Axis and Composite Crystals, Chemical Twinning, and Atomic Site Preferences