Neutron-diffraction study of icosahedral Al-Cu-Fe single quasicrystals

Cornier-Quiquandon, M.; Quivy, A.; Lefébvre, S.; Elkaı̈m, Erik; Heger, G.; Katz, A. S.; Gratias, D.

doi:10.1103/physrevb.44.2071

Cited by 195 publications

(69 citation statements)

References 32 publications

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“…As in our previous studies 7,8,17,18 a model for the structure of the five-fold surface of i-Al-Pd-Mn is derived from periodic approximants to the Katz-Gratias-Boudard ͑KGB͒ model [26][27][28][29][30] of the icosahedral structure. A model for the surface was constructed by cutting a thick slab perpendicular to one of the five-fold axes from the bulk structure.…”

Section: Computational Detailsmentioning

confidence: 99%

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Nucleation of Pb starfish clusters on the five-fold Al-Pd-Mn quasicrystal surface

et al. 2009

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The nucleation of Pb clusters on the five-fold Al-Pd-Mn quasicrystal surface has been investigated using scanning tunneling microscopy (STM) and ab initio calculations based on density-functional theory (DFT). In the submonolayer regime, Pb atoms are highly mobile and adsorb preferentially within equatorially truncated pseudo-Mackay clusters present at the surface. The decoration of these unique adsorption sites leads to the formation of five-fold islands dubbed "starfish" and eventually to a quasiperiodic Pb monolayer. From a comparison of measured and calculated STM images it is concluded that most starfish clusters on all terraces are composed of ten Pb adatoms. A model of the structure of the starfish cluster has been proposed. Our total-energy calculations confirm its stability. The experimentally measured height profile of the starfish cluster is also reproduced by the DFT calculations. Disciplines Condensed Matter Physics | Metallurgy CommentsThis article is from Physical Review B 79 (2009) The nucleation of Pb clusters on the five-fold Al-Pd-Mn quasicrystal surface has been investigated using scanning tunneling microscopy ͑STM͒ and ab initio calculations based on density-functional theory ͑DFT͒. In the submonolayer regime, Pb atoms are highly mobile and adsorb preferentially within equatorially truncated pseudo-Mackay clusters present at the surface. The decoration of these unique adsorption sites leads to the formation of five-fold islands dubbed "starfish" and eventually to a quasiperiodic Pb monolayer. From a comparison of measured and calculated STM images it is concluded that most starfish clusters on all terraces are composed of ten Pb adatoms. A model of the structure of the starfish cluster has been proposed. Our total-energy calculations confirm its stability. The experimentally measured height profile of the starfish cluster is also reproduced by the DFT calculations.

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Section: Computational Detailsmentioning

confidence: 99%

“…As in our previous ab initio studies 7,13,[17][18][19] a model of the surface has been derived from the KGB model [26][27][28][29][30] cleaving at a plane perpendicular to one of the five-fold axes. The position of the cleavage plane was chosen such as to create a surface of high atomic density.…”

Section: A Clean Surface Modelmentioning

confidence: 99%

Nucleation of Pb starfish clusters on the five-fold Al-Pd-Mn quasicrystal surface

et al. 2009

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“…Actually, the very notion of "atomic surface" widely used in the structure analysis of quasicrystals [20] arises as an attempt to impose some sort of piecewise continuity of u in the direction transverse to that of E on T N . Although this approach gives satisfactory results in X-ray structure determination [21], it may only be an approximation. In fact, it is clear on physical grounds that the precise location of any atom depends on the location of its neighbours; as is well known, the atomic surface is dissected in the so called "existence domains" of local structures, each of which with its own position.…”

Section: Quasicrystals and Their Hullsmentioning

confidence: 99%

Electrons in deterministic quasicrystalline potentials and hidden conserved quantities

Kalugin¹,

Katz²

2014

J. Phys. A: Math. Theor.

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Abstract. We propose an ansatz for the wave function of a non-interacting quantum particle in a deterministic quasicrystalline potential. It is applicable to both continuous and discrete models and includes Sutherland's hierarchical wave function as a special case. The ansatz is parameterized by a first cohomology class of the hull of the structure. The structure of the ansatz and the values of its parameters are preserved by the time evolution. Numerical results suggest that the ground states of the standard vertex models on Ammann-Beenker and Penrose tilings belong to this class of functions. This property remains valid for the models perturbed within their MLD class, e.g. by adding links along diagonals of rhombi. The convergence of the numerical simulations in a finite patch of the tiling critically depends on the boundary conditions, and can be significantly improved when the choice of the latter respects the structure of the ansatz.

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“…36 With time, it was modified and became known as the Katz-Gratias ͑KG͒ model. 11,12 Second, using x-ray and neutron diffraction, Boudard et al 13 constructed a bulk structural model for i-AlPdMn, and this is commonly referred to as the Boudard model.…”

Section: Bulk Structure Modelsmentioning

confidence: 99%

Comparison between experimental surface data and bulk structure models for quasicrystalline AlPdMn: Average atomic densities and chemical compositions

2008

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We have examined bulk structure models for icosahedral AlPdMn in terms of the densities, compositions, and interplanar spacings for the fivefold planes that might represent physical surface terminations. We focus on four models that contain no partial or mixed occupancies, but some comparison is made to a fifth model containing such sites. Each of the four models contains paired planes (layers) that can be separated into two main families on the basis of three features: the relative densities of the two planes, the gap separating the layer from the nearest atomic plane, and the Pd content in the topmost plane. The experimental data and other arguments lead to the conclusion that the family with no Pd in the top plane is favored. Finally, all models show that correlations should be expected between the heights of steps that delineate terraces and average compositional and/or structural features of the terraces. We have examined bulk structure models for icosahedral AlPdMn in terms of the densities, compositions, and interplanar spacings for the fivefold planes that might represent physical surface terminations. We focus on four models that contain no partial or mixed occupancies, but some comparison is made to a fifth model containing such sites. Each of the four models contains paired planes ͑layers͒ that can be separated into two main families on the basis of three features: the relative densities of the two planes, the gap separating the layer from the nearest atomic plane, and the Pd content in the topmost plane. The experimental data and other arguments lead to the conclusion that the family with no Pd in the top plane is favored. Finally, all models show that correlations should be expected between the heights of steps that delineate terraces and average compositional and/or structural features of the terraces.

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Neutron-diffraction study of icosahedral Al-Cu-Fe single quasicrystals

Cited by 195 publications

References 32 publications

Nucleation of Pb starfish clusters on the five-fold Al-Pd-Mn quasicrystal surface

Nucleation of Pb starfish clusters on the five-fold Al-Pd-Mn quasicrystal surface

Electrons in deterministic quasicrystalline potentials and hidden conserved quantities

Comparison between experimental surface data and bulk structure models for quasicrystalline AlPdMn: Average atomic densities and chemical compositions

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