816 research outputs found
Elastic properties of cubic crystals: Every's versus Blackman's diagram
Blackman's diagram of two dimensionless ratios of elastic constants is
frequently used to correlate elastic properties of cubic crystals with
interatomic bondings. Every's diagram of a different set of two dimensionless
variables was used by us for classification of various properties of such
crystals. We compare these two ways of characterization of elastic properties
of cubic materials and consider the description of various groups of materials,
e.g. simple metals, oxides, and alkali halides. With exception of intermediate
valent compounds, the correlation coefficients for Every's diagrams of various
groups of materials are greater than for Blackaman's diagrams, revealing the
existence of a linear relationship between two dimensionless Every's variables.
Alignment of elements and compounds along lines of constant Poisson's ratio
, ( arbitrary perpendicular to ) is
observed. Division of the stability region in Blackman's diagram into region of
complete auxetics, auxetics and non-auxetics is introduced. Correlations of a
scaling and an acoustic anisotropy parameter are considered.Comment: 8 pages, 9 figures, presented on The Ninth International School on
Theoretical Physics "Symmetry and Structural Properties of Condensed Matter",
5 - 12 September 2007, Myczkowce, Polan
Tetratic Order in the Phase Behavior of a Hard-Rectangle System
Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have found
two unusual phases in two-dimensional systems of anisotropic hard particles: a
tetratic phase of four-fold symmetry for hard squares [Comp. Methods in Science
and Tech., 10: 235-255, 2004], and a nonperiodic degenerate solid phase for
hard-disk dimers [Phys. Rev. Lett., 66: 3168-3171, 1991]. In this work, we
study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers
(or dominos), and demonstrate that it exhibits a solid phase with both of these
unusual properties. The solid shows tetratic, but not nematic, order, and it is
nonperiodic having the structure of a random tiling of the square lattice with
dominos. We obtain similar results with both a classical Monte Carlo method
using true rectangles and a novel molecular dynamics algorithm employing
rectangles with rounded corners. It is remarkable that such simple convex
two-dimensional shapes can produce such rich phase behavior. Although we have
not performed exact free-energy calculations, we expect that the random domino
tiling is thermodynamically stabilized by its degeneracy entropy, well-known to
be per particle from previous studies of the dimer problem on the
square lattice. Our observations are consistent with a KTHNY two-stage phase
transition scenario with two continuous phase transitions, the first from
isotropic to tetratic liquid, and the second from tetratic liquid to solid.Comment: Submitted for publicatio
Novel Features Arising in the Maximally Random Jammed Packings of Superballs
Dense random packings of hard particles are useful models of granular media
and are closely related to the structure of nonequilibrium low-temperature
amorphous phases of matter. Most work has been done for random jammed packings
of spheres, and it is only recently that corresponding packings of nonspherical
particles (e.g., ellipsoids) have received attention. Here we report a study of
the maximally random jammed (MRJ) packings of binary superdisks and
monodispersed superballs whose shapes are defined by |x_1|^2p+...+|x_2|^2p<=1
with d = 2 and 3, respectively, where p is the deformation parameter with
values in the interval (0, infinity). We find that the MRJ densities of such
packings increase dramatically and nonanalytically as one moves away from the
circular-disk and sphere point. Moreover, the disordered packings are
hypostatic and the local arrangements of particles are necessarily nontrivially
correlated to achieve jamming. We term such correlated structures "nongeneric".
The degree of "nongenericity" of the packings is quantitatively characterized
by determining the fraction of local coordination structures in which the
central particles have fewer contacting neighbors than average. We also show
that such seemingly special packing configurations are counterintuitively not
rare. As the anisotropy of the particles increases, the fraction of rattlers
decreases while the minimal orientational order increases. These novel
characteristics result from the unique rotational symmetry breaking manner of
the particles.Comment: 20 pages, 8 figure
Charge Ordering in alpha-(BEDT-TTF)2I3 by synchrotron x-ray diffraction
The spatial charge arrangement of a typical quasi-two-dimensional organic
conductor alpha-(BEDT-TTF)2I3 is revealed by single crystal structure analysis
using synchrotron radiation. The results show that the horizontal stripe type
structure, which was suggested by mean field theory, is established. We also
find the charge disproportion above the metal-insulator transition temperature
and a significant change in transfer integrals caused by the phase transition.
Our result elucidates the insulating phase of this material as a 2k_F charge
density localization.Comment: 8 pages, 5 figures, 1 tabl
Possible Verification of Tilted Anisotropic Dirac Cone in \alpha-(BEDT-TTF)_2 I_3 Using Interlayer Magnetoresistance
It is proposed that the presence of a tilted and anisotropic Dirac cone can
be verified using the interlayer magnetoresistance in the layered Dirac fermion
system, which is realized in quasi-two-dimensional organic compound
\alpha-(BEDT-TTF)_2 I_3. Theoretical formula is derived using the analytic
Landau level wave functions and assuming local tunneling of electrons. It is
shown that the resistivity takes the maximum in the direction of the tilt if
anisotropy of the Fermi velocity of the Dirac cone is small. The procedure is
described to determine the parameters of the tilt and anisotropy.Comment: 4 pages, 4 figures, corrected Fig.
Growth Dynamics of Photoinduced Domains in Two-Dimensional Charge-Ordered Conductors Depending on Stabilization Mechanisms
Photoinduced melting of horizontal-stripe charge orders in
quasi-two-dimensional organic conductors
\theta-(BEDT-TTF)2RbZn(SCN)4[BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene]
and
\alpha-(BEDT-TTF)2I3 is investigated theoretically. By numerically solving
the time-dependent Schr\"odinger equation, we study the photoinduced dynamics
in extended Peierls-Hubbard models on anisotropic triangular lattices within
the
Hartree-Fock approximation. The melting of the charge order needs more energy
for \theta-(BEDT-TTF)2RbZn(SCN)4 than for \alpha-(BEDT-TTF)2I3, which is a
consequence of the larger stabilization energy in \theta-(BEDT-TTF)2RbZn(SCN)4.
After local photoexcitation in the charge ordered states, the growth of a
photoinduced domain shows anisotropy. In \theta-(BEDT-TTF)2RbZn(SCN)4, the
domain hardly expands to the direction perpendicular to the horizontal-stripes.
This is because all the molecules on the hole-rich stripe are rotated in one
direction and those on the hole-poor stripe in the other direction. They
modulate horizontally connected transfer integrals homogeneously, stabilizing
the charge order stripe by stripe. In \alpha-(BEDT-TTF)2I3, lattice distortions
locally stabilize the charge order so that it is easily weakened by local
photoexcitation. The photoinduced domain indeed expands in the plane. These
results are consistent with recent observation by femtosecond reflection
spectroscopy.Comment: 9 pages, 8 figures, to appear in J. Phys. Soc. Jpn. Vol. 79 (2010)
No.
Phase Transitions of Hard Disks in External Periodic Potentials: A Monte Carlo Study
The nature of freezing and melting transitions for a system of hard disks in
a spatially periodic external potential is studied using extensive Monte Carlo
simulations. Detailed finite size scaling analysis of various thermodynamic
quantities like the order parameter, its cumulants etc. are used to map the
phase diagram of the system for various values of the density and the amplitude
of the external potential. We find clear indication of a re-entrant liquid
phase over a significant region of the parameter space. Our simulations
therefore show that the system of hard disks behaves in a fashion similar to
charge stabilized colloids which are known to undergo an initial freezing,
followed by a re-melting transition as the amplitude of the imposed, modulating
field produced by crossed laser beams is steadily increased. Detailed analysis
of our data shows several features consistent with a recent dislocation
unbinding theory of laser induced melting.Comment: 36 pages, 16 figure
Optimal Packings of Superballs
Dense hard-particle packings are intimately related to the structure of
low-temperature phases of matter and are useful models of heterogeneous
materials and granular media. Most studies of the densest packings in three
dimensions have considered spherical shapes, and it is only more recently that
nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs
(whose shapes are defined by |x1|^2p + |x2|^2p + |x3|^2p <= 1) provide a
versatile family of convex particles (p >= 0.5) with both cubic- and
octahedral-like shapes as well as concave particles (0 < p < 0.5) with
octahedral-like shapes. In this paper, we provide analytical constructions for
the densest known superball packings for all convex and concave cases. The
candidate maximally dense packings are certain families of Bravais lattice
packings. The maximal packing density as a function of p is nonanalytic at the
sphere-point (p = 1) and increases dramatically as p moves away from unity. The
packing characteristics determined by the broken rotational symmetry of
superballs are similar to but richer than their two-dimensional "superdisk"
counterparts, and are distinctly different from that of ellipsoid packings. Our
candidate optimal superball packings provide a starting point to quantify the
equilibrium phase behavior of superball systems, which should deepen our
understanding of the statistical thermodynamics of nonspherical-particle
systems.Comment: 28 pages, 16 figure
New boundary conditions for integrable lattices
New boundary conditions for integrable nonlinear lattices of the XXX type,
such as the Heisenberg chain and the Toda lattice are presented. These
integrable extensions are formulated in terms of a generic XXX Heisenberg
magnet interacting with two additional spins at each end of the chain. The
construction uses the most general rank 1 ansatz for the 2x2 L-operator
satisfying the reflection equation algebra with rational r-matrix. The
associated quadratic algebra is shown to be the one of dynamical symmetry for
the A1 and BC2 Calogero-Moser problems. Other physical realizations of our
quadratic algebra are also considered.Comment: 22 pages, latex, no figure
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