13 research outputs found
Self-Diffusion in Random-Tiling Quasicrystals
The first explicit realization of the conjecture that phason dynamics leads
to self-diffusion in quasicrystals is presented for the icosahedral Ammann
tilings. On short time scales, the transport is found to be subdiffusive with
the exponent , while on long time scales it is consistent
with normal diffusion that is up to an order of magnitude larger than in the
typical room temperature vacancy-assisted self-diffusion. No simple finite-size
scaling is found, suggesting anomalous corrections to normal diffusion, or
existence of at least two independent length scales.Comment: 11 pages + 2 figures, COMPRESSED postscript figures available by
anonymous ftp to black_hole.physics.ubc.ca directory outgoing/diffuse (use bi
for binary mode to transfer), REVTeX 3.0, CTP-TAMU 21/9
Quantum dynamics in high codimension tilings: from quasiperiodicity to disorder
We analyze the spreading of wavepackets in two-dimensional quasiperiodic and
random tilings as a function of their codimension, i.e. of their topological
complexity. In the quasiperiodic case, we show that the diffusion exponent that
characterizes the propagation decreases when the codimension increases and goes
to 1/2 in the high codimension limit. By constrast, the exponent for the random
tilings is independent of their codimension and also equals 1/2. This shows
that, in high codimension, the quasiperiodicity is irrelevant and that the
topological disorder leads in every case, to a diffusive regime, at least in
the time scale investigated here.Comment: 4 pages, 5 EPS figure
Cluster Model of Decagonal Tilings
A relaxed version of Gummelt's covering rules for the aperiodic decagon is
considered, which produces certain random-tiling-type structures. These
structures are precisely characterized, along with their relationships to
various other random tiling ensembles. The relaxed covering rule has a natural
realization in terms of a vertex cluster in the Penrose pentagon tiling. Using
Monte Carlo simulations, it is shown that the structures obtained by maximizing
the density of this cluster are the same as those produced by the corresponding
covering rules. The entropy density of the covering ensemble is determined
using the entropic sampling algorithm. If the model is extended by an
additional coupling between neighboring clusters, perfectly ordered structures
are obtained, like those produced by Gummelt's perfect covering rules.Comment: 10 pages, 20 figures, RevTeX; minor changes; to be published in Phys.
Rev.
6-dimensional properties of Al0.86Mn0.14 alloy
The general properties of the phases with the icosahedral point group and long-range orientational order are considered. 6 Goldstone modes — 3 phonons and 3 phasons — are shown to exist. A model for the microscopic structure — a 6-D crystal — is proposed, and phason modes are discussed in this framework. Bravais lattice types are determined and some physical phenomena due to the peculiar AlMn dimension 6 are listed. Simple Landau-theory type arguments for advantages of icosahedral structure are put forward.Les propriétés générales des phases présentant un groupe ponctuel icosaédrique et un ordre orientationnel à grande distance sont étudiées ici. On montre l'existence de six modes de Goldstone — 3 phonons et 3 phasons. Un modèle pour la structure microscopique, cristalline dans un espace à six dimensions est proposé et les modes phasons sont discutés dans ce cadre. Des réseaux de Bravais sont déterminés et certains phénomènes physiques de AlMn dus à cette dimension six sont soulignés. Des arguments simples, du type de la théorie de Landau, montrent pourquoi la structure icosaédrique est favorisée