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Shiv Nadar University

Using multifractal analysis we study extended, self-similar and non-self-similar type of wave functions in the Fibonacci model. Extended states arising due to commutation of transfer matrices for certain blocks of atoms in quasiperiodic systems are shown to have the same signature as the Bloch states in terms of the singularity spectrum with f($\alpha$)=$\alpha$=1. Numerically, however, the extended states show a typical multifractal behaviour for finite chain lengths. Finite size scaling corrections yield results consistent with that obtained analytically. The self-similar states at the band edges show a multifractal behaviour and they are energy dependent in the case of blocks of atoms arranged in a Fibonacci sequence. For non-self-similar states we obtain a non-monotonic behaviour of f($\alpha$) as a function of the chain length. We also show that in cases where extended states exist, the cross-over from extended to non-self-similar states in gradual. {\textcopyright} 1991 the Indian Academy of Sciences.

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Center for Informatics

Pramana

A multifractal study of wave functions in 1-D quasicrystals

The electronic structure of two-component Penrose models of quasicrystals is studied by using a tight-binding model. The Penrose lattice is subdivided in non-equivalent sublattices and the local density of states are calculated at a site surrounded by clusters of distinct sizes. The strong dependence of the density of states on the cluster size and the local neighborhood is evidenced. In particular, the electronic structure of a decoration proposed to model the T-phase of AlFe, is calculated. An asymmetric density of states with no self-similar behaviour is obtained. {\textcopyright} 1990.

Solid State Communications

Local electronic density of states in two-component penrose lattices

Indira Gandhi Centre for Atomic Research

Materials Science Division progress report 1986-1988

A Comment on the Letter by V. Kumar and G. Ananthakrishna, Phys. Rev. Lett. 59, 1476 (1987). {\textcopyright} 1988 The American Physical Society.

Physical Review Letters

Extended electronic states in a Fibonacci superlattice

A brief review of various types of defects on surfaces and their role in surface reactions is presented. Particular emphasis is given on defects like steps/kinks and additives (promoters and poison). {\textcopyright} 1988 Indian Academy of Sciences.

Bulletin of Materials Science

Defects on surfaces

Ananthakrishna and Kumar reply

Current Trends in the Physics of Materials: Proceedings of the Symposium

ELECTRONIC STRUCTURE OF A TWO DIMENSIONAL PENROSE LATTICE

The electronic structure of the Penrose lattice is studied using a tight-binding model. The local densities of states are calculated for 15 vertices having distinct nearest neighbors and the averaging is done exactly. The density of states shows a strong dependence on the local environment of a vertex and consists of several peaks and gaps but shows no self-similarity behavior. In conformity with a recent study we also find a-function-like localized state lying in a gap at the center of the band. {\textcopyright} 1987 The American Physical Society.

Physical Review B

Local-environment dependence of the electronic structure of a Penrose lattice

The electronic structure of a quasiperiodic superlattice with slabs of A- and B-type layers is studied within a tight-binding model by use of the transfer matrix and a perturbative approach. It is found that the band gaps vary strongly within the two-dimensional Brillouin zone and, in the case of more than one layer in a slab, there are a few eigenvalues for each k? for which the eigenstates appear to be extended in the quasiperiodic direction. The latter is true even for the Fibonacci chain with more than one atom per cell. {\textcopyright} 1987 The American Physical Society.

Electronic structure of a quasiperiodic superlattice

Materials Science Forum

An Atomistic Model for the Decagonal Phase of Al-Fe Alloy

We present a tight-binding calculation of the electronic local density of states (LDOS) and binding energy for chemisorbed oxygen on a Ni(001) surface at various coverages. The electronic structure is determined by treating explicitly the 4s and 3d electrons and their hybridization for the substrate Ni atoms and the oxygen 2p electrons. The continued-fraction technique is used to determine the LDOS. The obtained LDOS for the p(2 × 2) and c(2 × 2) structures is in good agreement with photoemission measurements. Our calculation shows that with increasing oxygen coverage, the binding energy of oxygen decreases, whereas the charge transfer on oxygen increases. These results are discussed in connection with oxidation of the surface nickel occuring at high coverages. {\textcopyright} 1986.

Surface Science

Calculation of coverage dependence of electronic density of states and binding energy for chemisorbed oxygen on Ni(001)

We study the electronic structure of a (001) face centered cubic quasi-periodic superlattice within a tight binding model using the transfer matrix method and a pertubative approach. The band gaps are found to vary strongly within the two dimensional Brillouin zone and there are a few eigenvalues for each k//1//1 for which the eigenstates appear to be extended in the quasi-periodic direction also.

Key Eng Mater

Electronic Structure of (001) Face Centered Cubic Quasi-Periodic Superlattice.

The self-similarity property of the two-dimensional Penrose lattice is utilized to characterize it in terms of the distribution of different kinds of vertices, the Voronoi cells and their nearest neighborhoods. Striking similarities are observed between the layer structures of the crystalline $\delta$-Al11Mn4, Al6Mn, Al13Fe4, Pt5P2 and Ni3Si2 with a sublattice of the Penrose lattice. The latter can be described in terms of cells which need not have fivefold rotational symmetry. Following the atomic distributions in the crystalline Al6Mn and Al13Fe4, decorations of such lattices are suggested to model the T phase of Al-Mn and other related quasicrystals. We find two types of layers with fivefold rotational symmetry in the T phase. This is in agreement with the electron diffraction from such quasicrystals. {\textcopyright} 1986 The American Physical Society.

Characterization and decoration of the two-dimensional Penrose lattice

Diffraction from a quasi-crystalline chain

The authors investigate the common qualitative idea that a solid is particularly stable if the electron states are filled up to some energy band gap. Such ideas have previously been advanced to explain the occurrence of a certain family of M5X4 compounds (M=transition metal, X=chalcogen) only for particular ranges of valence electron concentration (VEC). In these materials octahedral metal clusters condense to form infinite chains. The authors study the stability of such chains against break-up on two models, (i) a regular octahedral chain and (ii) the chain of the compound Nb 5Te4 and discuss the question of why only the compounds with 2.4<or=VEC<or=3.6 exist.

Journal of Physics F: Metal Physics

The fusion of metal clusters in M5X4 compounds

Inorganic Chemistry

Relation between the Electronic Structure and the Condensation of Metal Clusters in M5X4 Compounds

Using the cluster-variation method in the tetrahedron approximation, we study order-disorder transitions at the (100) surface of Cu-Au alloys. Depending on surface segregation, the order-disorder transition may be first or second order. Disordering of the surface may occur at temperatures above or below the bulk transition temperature. The recent low-energy ion-scattering data on Cu3Au is interpreted as evidence for stronger long-range order at the surface than in the bulk. {\textcopyright} 1984 The American Physical Society.

Order-disorder transitions and segregation at the (100) surface of Cu-Au alloys

With the use of a self-consistent tight-binding scheme, local electronic densities of states (LDOS) are calculated for commensurate (C) Pd* (110) and incommensurate (IC) Pd(111) layers on Nb(110). At low coverages (<1) Pd induces a Pd-Nb resonance near the bottom of the Nb d band. In agreement with the experimental results this resonance shifts to lower binding energy as the coverage is increased. Comparing detailed features of the LDOS with the photoemission data we predict a C-IC structural transformation for approximately one monolayer of Pd. This we also conclude from a simple interface energy calculation. The d-electron charge transfer across the interface and the LDOS of Pd at the Fermi energy (EF) are small. The latter, however, increases with the Pd coverage. The LDOS of the top Pd layer is nearly the same for Pd(111) on Pd* (110)-Nb(110) or Pd(111)-Nb(110) interfaces and in all cases there is a significant decrease of Nb d states near the EF. This shows that the LDOS is mainly perturbed at the interface. Implications of these results for hydrogen uptake and work-function changes are discussed. {\textcopyright} 1983 The American Physical Society.

Electronic structure of transition-metal-transition-metal interfaces: Pd on Nb(110)

The authors have developed a self-consistent coherent potential approximation generalised to take the effect of clusters into account. Off-diagonal disorder and short-range order are taken into account. A graphical method married to the recursion technique enables them to work on realistic three-dimensional lattices. Calculations are shown for a binary alloy on a diamond lattice.

Journal of Physics C: Solid State Physics

Electronic structure of disordered alloys I. Self-consistent cluster CPA incorporating off-diagonal disorder and short-range order

Numerical results are given for the surface core-level shifts at clean single crystal surfaces, stepped and reconstructed surfaces and surfaces with chemisorbed atoms. These results demonstrate that surface core-level shifts can be used as a diagnostic tool to study various surface effects. {\textcopyright} 1982.