123 research outputs found
Continuum elastic sphere vibrations as a model for low-lying optical modes in icosahedral quasicrystals
The nearly dispersionless, so-called "optical" vibrational modes observed by
inelastic neutron scattering from icosahedral Al-Pd-Mn and Zn-Mg-Y
quasicrystals are found to correspond well to modes of a continuum elastic
sphere that has the same diameter as the corresponding icosahedral basic units
of the quasicrystal. When the sphere is considered as free, most of the
experimentally found modes can be accounted for, in both systems. Taking into
account the mechanical connection between the clusters and the remainder of the
quasicrystal allows a complete assignment of all optical modes in the case of
Al-Pd-Mn. This approach provides support to the relevance of clusters in the
vibrational properties of quasicrystals.Comment: 9 pages without figure
Icosahedral multi-component model sets
A quasiperiodic packing Q of interpenetrating copies of C, most of them only
partially occupied, can be defined in terms of the strip projection method for
any icosahedral cluster C. We show that in the case when the coordinates of the
vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the
superspace can be reduced, namely, Q can be re-defined as a multi-component
model set by using a 6-dimensional superspace.Comment: 7 pages, LaTeX2e in IOP styl
Sound modes broadening for Fibonacci one dimensional quasicrystals
We investigate vibrational excitation broadening in one dimensional Fibonacci
model of quasicrystals (QCs). The chain is constructed from particles with two
masses following the Fibonacci inflation rule. The eigenmode spectrum depends
crucially on the mass ratio. We calculate the eigenstates and eigenfunctions.
All calculations performed self-consistently within the regular expansion over
the three wave coupling constant. The approach can be extended to three
dimensional systems. We find that in the intermediate range of mode coupling
constants, three-wave broadening for the both types of systems (1D Fibonacci
and 3D QCs) depends universally on frequency. Our general qualitative
conclusion is that for a system with a non-simple elementary cell phonon
spectrum broadening is always larger than for a system with a primitive cell
(provided all other characteristics are the same).Comment: 2o pages, 15 figure
Surface structure of i-Al(68)Pd(23)Mn(9): An analysis based on the T*(2F) tiling decorated by Bergman polytopes
A Fibonacci-like terrace structure along a 5fold axis of i-Al(68)Pd(23)Mn(9)
monograins has been observed by T.M. Schaub et al. with scanning tunnelling
microscopy (STM). In the planes of the terraces they see patterns of dark
pentagonal holes. These holes are well oriented both within and among terraces.
In one of 11 planes Schaub et al. obtain the autocorrelation function of the
hole pattern. We interpret these experimental findings in terms of the
Katz-Gratias-de Boisseu-Elser model. Following the suggestion of Elser that the
Bergman clusters are the dominant motive of this model, we decorate the tiling
T*(2F) by the Bergman polytopes only. The tiling T*(2F) allows us to use the
powerful tools of the projection techniques. The Bergman polytopes can be
easily replaced by the Mackay polytopes as the decoration objects. We derive a
picture of ``geared'' layers of Bergman polytopes from the projection
techniques as well as from a huge patch. Under the assumption that no surface
reconstruction takes place, this picture explains the Fibonacci-sequence of the
step heights as well as the related structure in the terraces qualitatively and
to certain extent even quantitatively. Furthermore, this layer-picture requires
that the polytopes are cut in order to allow for the observed step heights. We
conclude that Bergman or Mackay clusters have to be considered as geometric
building blocks of the i-AlPdMn structure rather than as energetically stable
entities
Random Tilings: Concepts and Examples
We introduce a concept for random tilings which, comprising the conventional
one, is also applicable to tiling ensembles without height representation. In
particular, we focus on the random tiling entropy as a function of the tile
densities. In this context, and under rather mild assumptions, we prove a
generalization of the first random tiling hypothesis which connects the maximum
of the entropy with the symmetry of the ensemble. Explicit examples are
obtained through the re-interpretation of several exactly solvable models. This
also leads to a counterexample to the analogue of the second random tiling
hypothesis about the form of the entropy function near its maximum.Comment: 32 pages, 42 eps-figures, Latex2e updated version, minor grammatical
change
Structure of the icosahedral Ti-Zr-Ni quasicrystal
The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined
by invoking similarities to periodic crystalline phases, diffraction data and
the results from ab initio calculations. The structure is modeled by
decorations of the canonical cell tiling geometry. The initial decoration model
is based on the structure of the Frank-Kasper phase W-TiZrNi, the 1/1
approximant structure of the quasicrystal. The decoration model is optimized
using a new method of structural analysis combining a least-squares refinement
of diffraction data with results from ab initio calculations. The resulting
structural model of icosahedral Ti-Zr-Ni is interpreted as a simple decoration
rule and structural details are discussed.Comment: 12 pages, 8 figure
Surface structure of Al-Pd-Mn quasicrystals: Existence of supersaturated bulk vacancy concentrations
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