Electronic confinement by clusters in quasicrystals and approximants (original) (raw)
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Coordination and cluster packing in quasicrystals
Philosophical Magazine, 2008
We discuss some local and global characteristics of quasicrystalline structures. Firstly, we present an analysis of the coordination numbers in the Cd 5.7 Yb binary quasicrystal. A majority of the Cd and Yb atoms occupy 12-and 16-fold coordinated sites, respectively. It is argued that the coordination properties are closely related to the local stability of the quasicrystals. Secondly, a simple inflation algorithm is presented for generating an icosahedral quasilattice which has a dense packing of a given structural motif or cluster. The atomic surface of a P-type icosahedral quasilattice generated in this way has a fractal boundary.
Journal of Non-Crystalline Solids, 1990
The electronic wave functions of an icosahedral quasicrystal are investigated with the numerical method based on the tight-binding model. It is found that the spectral density of states exhibits a dispersion-relation-like pattern. The critical points (stationary points) of the 'dispersionrelation' appear at the special points which correspond to high-symmetry points in the Brillouin zone of a periodic lattice. On the other hand, the Fourier-intensity vs. energy profile of the wave functions exhibits a size dependence obeying a power law with a fractal exponent. This shows that the wave functions are critical with respect to localization. Moreover, the wave functions obey weakly the 'generalized Bloch's theorem'
Bulk Electronic Structure of Quasicrystals
Physical Review Letters, 2012
We use hard x-ray photoemission to resolve a controversial issue regarding the mechanism for the formation of quasicrystalline solids, i.e., the existence of a pseudogap at the Fermi level. Our data from icosahedral fivefold Al-Pd-Mn and Al-Cu-Fe quasicrystals demonstrate the presence of a pseudogap, which is not observed in surface sensitive low energy photoemission because the spectrum is affected by a metallic phase near the surface. In contrast to Al-Pd-Mn, we find that in Al-Cu-Fe the pseudogap is fully formed; i.e., the density of states reaches zero at E F indicating that it is close to the metal-insulator phase boundary.
Covering Clusters in Icosahedral Quasicrystals
Springer Tracts in Modern Physics
The structural analysis of various approximant phases of icosahedral quasicrystals shows local environments with icosahedral symmetry: icosahedra, Mackay clusters (M) and Bergman clusters (B). For the icosahedral phases i-AlCuFe and i-AlPdMn, these clusters have been proposed as complementary building blocks centered on particular nodes. However, computations showed that these genuine 2-shells or 3-shells clusters don't cover all atomic positions given by 6D models. One the other hand, the recent concept of a unique covering cluster was shown to apply to 2D Penrose tilings and Amman-Beenker tilings. In this paper we examine the local environments in i-AlCuFe and i-AlPdMn models about Wyckoff positions of the 6D lattice. We consider extended Bergman clusters of 6 shells that appear naturally in the Katz-Gratias model. We discuss the cell decomposition of the atomic surfaces and the variable occupation number of some of the shells. We show that a fixed extended Bergman cluster of 6 shells and 106 atoms covers about 98% of atomic positions. We also prove that a variable extended Bergman cluster of 6 shells, which contains the previous fixed cluster, covers all atomic positions of the theoretical model.
Discussion of electronic properties of quasicrystals
Philosophical Magazine, 2008
This article gives a short review of some important achievements in the field of electronic properties of quasicrystals. It focuses essentially on : the nature of quasicrystals as Hume-Rothery alloys, the energetics of quasicrystals and related phases, the magnetic properties, the localization of electronic states, the transport properties. For each part one emphasizes some promising directions of research. We end by listing some problems that are related to that of electrons in a quasiperiodic potential.
A group-theoretic approach of quasicrystals
Ferroelectrics, 2001
A quasicrystal can be regarded as a packing of G-invariant atomic clusters, where the finite group G is the symmetry group of its diffraction pattern. We prove that a large variety of packings of G-invariant clusters can be obtained in an elegant way for any finite group G by using the strip projection method and some results from group theory.
Some new structural and electronic characteristics of quasicrystals
Bulletin of Materials Science, 1999
The quasicrystals being based on quasiperiodic order other than crystal like periodic translational order and embodying self similarity, present unique condensed matter phases. In addition to their curious structural characteristics the paucity of translational periodicity leads to drastic deviations in their electronic behaviour as compared to crystalline counterparts. This paper describes and discusses some new developments in regard to structural and electronic aspects of quasicrystalline materials. In regard to the structural aspects, two comparatively newer features will be described. One of them relates to the observation of variable strain approximants (VSA) first found in Ti68Fe26NiSi5, qc alloys; the other relates to the structure of decagonal phases. The variable strain approximants correspond to qc phases exhibiting variable strain for the different diffraction spots for the same reciprocal lattice row (possessing linear shifts). The VSA is thought to result from variable...
Spectral Properties of Quasicrystals via Analysis , Dynamics , and Geometric Measure Theory
2015
The 2011 Nobel Prize in Chemistry was awarded to Dan Shechtman for ”the discovery of quasicrystals” — materials with unusual structure, interesting from the point of view of chemistry, physics, and mathematics. In order to study electronic properties of quasicrystals, one considers Hamiltonians where the aperiodic order features are reflected either through the configuration of position space or the arrangement of the potential values. The spectral and quantum dynamical analysis of these Hamiltonians is mathematically very challenging. On the other hand, investigations of this nature are fascinating as one is invariably led to employ methods from a wide variety of mathematical subdisciplines. At present one understands very well the key quasicrystal models in one space dimension and the community is finally on the verge of making serious progress in the much more challenging higher-dimensional case by drawing on a new connection to yet another mathematical subdiscipline. At this mee...