66 research outputs found
Growing Perfect Decagonal Quasicrystals by Local Rules
A local growth algorithm for a decagonal quasicrystal is presented. We show
that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling
layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to
form on the upper layer, successive 2D PPT layers can be added on top resulting
in a perfect decagonal quasicrystalline structure in bulk with a point defect
only on the bottom surface layer. Our growth rule shows that an ideal
quasicrystal structure can be constructed by a local growth algorithm in 3D,
contrary to the necessity of non-local information for a 2D PPT growth.Comment: 4pages, 2figure
Finite-lattice expansion for Ising models on quasiperiodic tilings
Low-temperature series are calculated for the free energy, magnetisation,
susceptibility and field-derivatives of the susceptibility in the Ising model
on the quasiperiodic Penrose lattice. The series are computed to order 20 and
estimates of the critical exponents alpha, beta and gamma are obtained from
Pade approximants.Comment: 16 pages, REVTeX, 26 postscript figure
Soap Froths and Crystal Structures
We propose a physical mechanism to explain the crystal symmetries found in
macromolecular and supramolecular micellar materials. We argue that the packing
entropy of the hard micellar cores is frustrated by the entropic interaction of
their brush-like coronas. The latter interaction is treated as a surface effect
between neighboring Voronoi cells. The observed crystal structures correspond
to the Kelvin and Weaire-Phelan minimal foams. We show that these structures
are stable for reasonable areal entropy densities.Comment: 4 pages, RevTeX, 2 included eps figure
Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes
We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces
Complex crystal structures formed by the self assembly of di-tethered nanospheres
We report the results from a computational study of the self-assembly of
amphiphilic di-tethered nanospheres using molecular simulation. As a function
of the interaction strength and directionality of the tether-tether
interactions, we predict the formation of four highly ordered phases not
previously reported for nanoparticle systems. We find a double diamond
structure comprised of a zincblende (binary diamond) arrangement of spherical
micelles with a complementary diamond network of nanoparticles (ZnS/D); a phase
of alternating spherical micelles in a NaCl structure with a complementary
simple cubic network of nanoparticles to form an overall crystal structure
identical to that of AlCu_2Mn (NaCl/SC); an alternating tetragonal ordered
cylinder phase with a tetragonal mesh of nanoparticles described by the [8,8,4]
Archimedean tiling (TC/T); and an alternating diamond phase in which both
diamond networks are formed by the tethers (AD) within a nanoparticle matrix.
We compare these structures with those observed in linear and star triblock
copolymer systems
Q-Dependent Susceptibility in Z-Invariant Pentagrid Ising Model
We study the q-dependent susceptibility chi(q) of a Z-invariant ferromagnetic
Ising model on a Penrose tiling, as first introduced by Korepin using de
Bruijn's pentagrid for the rapidity lines. The pair-correlation function for
this model can be calculated exactly using the quadratic difference equations
from our previous papers. Its Fourier transform chi(q) is studied using a novel
way to calculate the joint probability for the pentagrid neighborhoods of the
two spins, reducing this calculation to linear programming. Since the lattice
is quasiperiodic, we find that chi(q) is aperiodic and has everywhere dense
peaks, which are not all visible at very low or high temperatures. More and
more peaks become visible as the correlation length increases--that is, as the
temperature approaches the critical temperature.Comment: LaTeX2e, 52 pages, 12 figures (45 eps files), uses rotating.sty
(choose right rotdriver). v2: Quality of figures has been much enhanced. v3:
Misprints correcte
Surface structure of Al-Pd-Mn quasicrystals: Existence of supersaturated bulk vacancy concentrations
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