6,535 research outputs found
Microscopic theory for the glass transition in a system without static correlations
We study the orientational dynamics of infinitely thin hard rods of length L,
with the centers-of-mass fixed on a simple cubic lattice with lattice constant
a.We approximate the influence of the surrounding rods onto dynamics of a pair
of rods by introducing an effective rotational diffusion constant D(l),l=L/a.
We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a
time-dependent torque-torque correlator of an isolated pair of rods. A glass
transition occurs at l_c, if v(l_c)=1. We present a variational and a
numerically exact evaluation of v(l).Close to l_c the diffusion constant
decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a
glass transition in the absence of any static correlations, in contrast to
present form of mode coupling theory.Comment: 6 pages, 3 figure
Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model
We investigate the potential energy surface of a phi^4 model with infinite
range interactions. All stationary points can be uniquely characterized by
three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_-
= 1, provided that the interaction strength mu is smaller than a critical
value. The saddle index n_s is equal to alpha_0 and its distribution function
has a maximum at n_s^max = 1/3. The density p(e) of stationary points with
energy per particle e, as well as the Euler characteristic chi(e), are singular
at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu)
\neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per
particle at the thermodynamic phase transition point T_c. This proves that
previous claims that the topological and thermodynamic transition points
coincide is not valid, in general. Both types of singularities disappear for H
\neq 0. The average saddle index bar{n}_s as function of e decreases
monotonically with e and vanishes at the ground state energy, only. In
contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is
given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 >
upsilon_0, the ground state energy.Comment: 9 PR pages, 6 figure
Microscopic theory of glassy dynamics and glass transition for molecular crystals
We derive a microscopic equation of motion for the dynamical orientational
correlators of molecular crystals. Our approach is based upon mode coupling
theory. Compared to liquids we find four main differences: (i) the memory
kernel contains Umklapp processes, (ii) besides the static two-molecule
orientational correlators one also needs the static one-molecule orientational
density as an input, where the latter is nontrivial, (iii) the static
orientational current density correlator does contribute an anisotropic,
inertia-independent part to the memory kernel, (iv) if the molecules are
assumed to be fixed on a rigid lattice, the tensorial orientational correlators
and the memory kernel have vanishing l,l'=0 components. The resulting mode
coupling equations are solved for hard ellipsoids of revolution on a rigid
sc-lattice. Using the static orientational correlators from Percus-Yevick
theory we find an ideal glass transition generated due to precursors of
orientational order which depend on X and p, the aspect ratio and packing
fraction of the ellipsoids. The glass formation of oblate ellipsoids is
enhanced compared to that for prolate ones. For oblate ellipsoids with X <~ 0.7
and prolate ellipsoids with X >~ 4, the critical diagonal nonergodicity
parameters in reciprocal space exhibit more or less sharp maxima at the zone
center with very small values elsewhere, while for prolate ellipsoids with 2 <~
X <~ 2.5 we have maxima at the zone edge. The off-diagonal nonergodicity
parameters are not restricted to positive values and show similar behavior. For
0.7 <~ X <~ 2, no glass transition is found. In the glass phase, the
nonergodicity parameters show a pronounced q-dependence.Comment: 17 pages, 12 figures, accepted at Phys. Rev. E. v4 is almost
identical to the final paper version. It includes, compared to former
versions v2/v3, no new physical content, but only some corrected formulas in
the appendices and corrected typos in text. In comparison to version v1, in
v2-v4 some new results have been included and text has been change
Glass transition of hard spheres in high dimensions
We have investigated analytically and numerically the liquid-glass transition
of hard spheres for dimensions in the framework of mode-coupling
theory. The numerical results for the critical collective and self
nonergodicity parameters and exhibit
non-Gaussian -dependence even up to . and
differ for , but become identical on a scale
, which is proven analytically. The critical packing fraction
is above the corresponding Kauzmann packing
fraction derived by a small cage expansion. Its quadratic
pre-exponential factor is different from the linear one found earlier. The
numerical values for the exponent parameter and therefore the critical
exponents and depend on , even for the largest values of .Comment: 11 pages, 8 figures, Phys. Rev. E (in print
Anomalous He-Gas High-Pressure Studies on Superconducting LaO1-xFxFeAs
AC susceptibility measurements have been carried out on superconducting
LaO1-xFxFeAs for x=0.07 and 0.14 under He-gas pressures to about 0.8 GPa. Not
only do the measured values of dTc/dP differ substantially from those obtained
in previous studies using other pressure media, but the Tc(P) dependences
observed depend on the detailed pressure/temperature history of the sample. A
sizeable sensitivity of Tc(P) to shear stresses provides a possible
explanation
Dynamic Glass Transition in Two Dimensions
The question about the existence of a structural glass transition in two
dimensions is studied using mode coupling theory (MCT). We determine the
explicit d-dependence of the memory functional of mode coupling for
one-component systems. Applied to two dimensions we solve the MCT equations
numerically for monodisperse hard discs. A dynamic glass transition is found at
a critical packing fraction phi_c^{d=2} = 0.697 which is above phi_c^{d=3} =
0.516 by about 35%. phi^d_c scales approximately with phi^d_{\rm rcp} the value
for random close packing, at least for d=2, 3. Quantities characterizing the
local, cooperative 'cage motion' do not differ much for d=2 and d=3, and we
e.g. find the Lindemann criterion for the localization length at the glass
transition. The final relaxation obeys the superposition principle, collapsing
remarkably well onto a Kohlrausch law. The d=2 MCT results are in qualitative
agreement with existing results from MC and MD simulations. The mean squared
displacements measured experimentally for a quasi-two-dimensional binary system
of dipolar hard spheres can be described satisfactorily by MCT for monodisperse
hard discs over four decades in time provided the experimental control
parameter Gamma (which measures the strength of dipolar interactions) and the
packing fraction phi are properly related to each other.Comment: 14 pages, 15 figure
Effect of mixing and spatial dimension on the glass transition
We study the influence of composition changes on the glass transition of
binary hard disc and hard sphere mixtures in the framework of mode coupling
theory. We derive a general expression for the slope of a glass transition
line. Applied to the binary mixture in the low concentration limits, this new
method allows a fast prediction of some properties of the glass transition
lines. The glass transition diagram we find for binary hard discs strongly
resembles the random close packing diagram. Compared to 3D from previous
studies, the extension of the glass regime due to mixing is much more
pronounced in 2D where plasticization only sets in at larger size disparities.
For small size disparities we find a stabilization of the glass phase quadratic
in the deviation of the size disparity from unity.Comment: 13 pages, 8 figures, Phys. Rev. E (in print
Dynamics of uniaxial hard ellipsoids
We study the dynamics of monodisperse hard ellipsoids via a new event-driven
molecular dynamics algorithm as a function of volume fraction and aspect
ratio . We evaluate the translational and the rotational
diffusion coefficient and the associated isodiffusivity lines in the
plane. We observe a decoupling of the translational and rotational
dynamics which generates an almost perpendicular crossing of the
and isodiffusivity lines. While the self intermediate scattering
function exhibits stretched relaxation, i.e. glassy dynamics, only for large
and , the second order orientational correlator
shows stretching only for large and small values. We discuss these
findings in the context of a possible pre-nematic order driven glass
transition.Comment: accepted by Phys. Rev. Let
Analogy of the slow dynamics between the supercooled liquid and the supercooled plastic crystal states of difluorotetrachloroethane
Slow dynamics of difluorotetrachloroethane in both supercooled plastic
crystal and supercooled liquid states have been investigated from Molecular
Dynamics simulations. The temperature and wave-vector dependence of collective
dynamics in both states are probed using coherent dynamical scattering
functions . Our results confirm the strong analogy between molecular
liquids and plastic crystals for which -relaxation times and
non-ergodicity parameters are controlled by the non trivial static correlations
as predicted by the Mode Coupling Theory. The use of infinitely thin
needles distributed on a lattice as model of plastic crystals is discussed
Research on mechanisms of alloy strengthening. Part 1 - Strengthening through fine particle dispersion. Part 2 - Control of structure and properties by means of rapid quenching of liquid metals /splat cooling/ Semiannual report
Alloy strengthening mechanisms - strengthening by fine particle dispersion, and structure and properties control by rapid quenching or splat cooling of liquid metal
- …