6,937 research outputs found
Symmetry properties of Penrose type tilings
The Penrose tiling is directly related to the atomic structure of certain
decagonal quasicrystals and, despite its aperiodicity, is highly symmetric. It
is known that the numbers 1, , , , ..., where
, are scaling factors of the Penrose tiling. We show that
the set of scaling factors is much larger, and for most of them the number of
the corresponding inflation centers is infinite.Comment: Paper submitted to Phil. Mag. (for Proceedings of Quasicrystals: The
Silver Jubilee, Tel Aviv, 14-19 October, 2007
Hierarchical freezing in a lattice model
A certain two-dimensional lattice model with nearest and next-nearest
neighbor interactions is known to have a limit-periodic ground state. We show
that during a slow quench from the high temperature, disordered phase, the
ground state emerges through an infinite sequence of phase transitions. We
define appropriate order parameters and show that the transitions are related
by renormalizations of the temperature scale. As the temperature is decreased,
sublattices with increasingly large lattice constants become ordered. A rapid
quench results in glass-like state due to kinetic barriers created by
simultaneous freezing on sublattices with different lattice constants.Comment: 6 pages; 5 figures (minor changes, reformatted
A finite-temperature liquid-quasicrystal transition in a lattice model
We consider a tiling model of the two-dimensional square-lattice, where each
site is tiled with one of the sixteen Wang tiles. The ground states of this
model are all quasi-periodic. The systems undergoes a disorder to
quasi-periodicity phase transition at finite temperature. Introducing a proper
order-parameter, we study the system at criticality, and extract the critical
exponents characterizing the transition. The exponents obtained are consistent
with hyper-scaling
Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential
For the study of crystal formation and dynamics we introduce a simple
two-dimensional monatomic model system with a parametrized interaction
potential. We find in molecular dynamics simulations that a surprising variety
of crystals, a decagonal and a dodecagonal quasicrystal are self-assembled. In
the case of the quasicrystals the particles reorder by phason flips at elevated
temperatures. During annealing the entropically stabilized decagonal
quasicrystal undergoes a reversible phase transition at 65% of the melting
temperature into an approximant, which is monitored by the rotation of the de
Bruijn surface in hyperspace.Comment: 4 pages, 6 figures. Physical Review Letters, in Press (April 2007
Thermodynamically Stable One-Component Metallic Quasicrystals
Classical density-functional theory is employed to study finite-temperature
trends in the relative stabilities of one-component quasicrystals interacting
via effective metallic pair potentials derived from pseudopotential theory.
Comparing the free energies of several periodic crystals and rational
approximant models of quasicrystals over a range of pseudopotential parameters,
thermodynamically stable quasicrystals are predicted for parameters approaching
the limits of mechanical stability of the crystalline structures. The results
support and significantly extend conclusions of previous ground-state
lattice-sum studies.Comment: REVTeX, 13 pages + 2 figures, to appear, Europhys. Let
Energy levels and their correlations in quasicrystals
Quasicrystals can be considered, from the point of view of their electronic
properties, as being intermediate between metals and insulators. For example,
experiments show that quasicrystalline alloys such as AlCuFe or AlPdMn have
conductivities far smaller than those of the metals that these alloys are
composed from. Wave functions in a quasicrystal are typically intermediate in
character between the extended states of a crystal and the exponentially
localized states in the insulating phase, and this is also reflected in the
energy spectrum and the density of states. In the theoretical studies we
consider in this review, the quasicrystals are described by a pure hopping
tight binding model on simple tilings. We focus on spectral properties, which
we compare with those of other complex systems, in particular, the Anderson
model of a disordered metal.Comment: 15 pages including 19 figures. Review article, submitted to Phil. Ma
A Tale of Two Tilings
What do you get when you cross a crystal with a quasicrystal? The surprising
answer stretches from Fibonacci to Kepler, who nearly 400 years ago showed how
the ancient tiles of Archimedes form periodic patterns.Comment: 3 pages, 1 figur
Formes du fer des sols rouges et bruns fersiallitiques : application de la spectrométrie Mössbauer
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