654 research outputs found
Stability of strained heteroepitaxial systems in (1+1) dimensions
We present a simple analytical model for the determination of the stable
phases of strained heteroepitaxial systems in (1+1) dimensions. In order for
this model to be consistent with a subsequent dynamic treatment, all
expressions are adjusted to an atomistic Lennard-Jones system. Good agreement
is obtained when the total energy is assumed to consist of two contributions:
the surface energy and the elastic energy. As a result, we determine the stable
phases as a function of the main ``control parameters'' (binding energies,
coverage and lattice mismatch). We find that there exists no set of parameters
leading to an array of islands as a stable configuration. We however show that
a slight modification of the model can lead to the formation of stable arrays
of islands.Comment: 11 pages, 14 figures, submitted to Physical Review
Free energy of cluster formation and a new scaling relation for the nucleation rate
Recent very large molecular dynamics simulations of homogeneous nucleation
with Lennard-Jones atoms [Diemand et al. J. Chem. Phys. {\bf
139}, 074309 (2013)] allow us to accurately determine the formation free energy
of clusters over a wide range of cluster sizes. This is now possible because
such large simulations allow for very precise measurements of the cluster size
distribution in the steady state nucleation regime. The peaks of the free
energy curves give critical cluster sizes, which agree well with independent
estimates based on the nucleation theorem. Using these results, we derive an
analytical formula and a new scaling relation for nucleation rates: is scaled by , where the supersaturation ratio is ,
is the dimensionless surface energy, and is a dimensionless
nucleation rate. This relation can be derived using the free energy of cluster
formation at equilibrium which corresponds to the surface energy required to
form the vapor-liquid interface. At low temperatures (below the triple point),
we find that the surface energy divided by that of the classical nucleation
theory does not depend on temperature, which leads to the scaling relation and
implies a constant, positive Tolman length equal to half of the mean
inter-particle separation in the liquid phase.Comment: 7 figure
Systematic Improvement of Classical Nucleation Theory
We reconsider the applicability of classical nucleation theory (CNT) to the
calculation of the free energy of solid cluster formation in a liquid and its
use to the evaluation of interface free energies from nucleation barriers.
Using two different freezing transitions (hard spheres and NaCl) as test cases,
we first observe that the interface-free-energy estimates based on CNT are
generally in error. As successive refinements of nucleation-barrier theory, we
consider corrections due to a non-sharp solid-liquid interface and to a
non-spherical cluster shape. Extensive calculations for the Ising model show
that corrections due to a non-sharp and thermally fluctuating interface account
for the barrier shape with excellent accuracy. The experimental solid
nucleation rates that are measured in colloids are better accounted for by
these non-CNT terms, whose effect appears to be crucial in the interpretation
of data and in the extraction of the interface tension from them.Comment: 20 pages (text + supplementary material
Geometrical Frustration: A Study of 4d Hard Spheres
The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the
icosahedron and the tetrahedron is the smallest volume that can show up in
Delaunay tessalation. No periodic lattice is consistent with either and hence
these dense packings are geometrically frustrated. Because icosahedra can be
assembled from almost perfect tetrahedra, the terms "icosahedral" and
"polytetrahedral" packing are often used interchangeably, which leaves the true
origin of geometric frustration unclear. Here we report a computational study
of freezing of 4d hard spheres, where the densest Voronoi cluster is compatible
with the symmetry of the densest crystal, while polytetrahedral order is not.
We observe that, under otherwise comparable conditions, crystal nucleation in
4d is less facile than in 3d. This suggest that it is the geometrical
frustration of polytetrahedral structures that inhibits crystallization.Comment: 4 pages, 3 figures; revised interpretatio
Hard sphere crystallization gets rarer with increasing dimension
We recently found that crystallization of monodisperse hard spheres from the
bulk fluid faces a much higher free energy barrier in four than in three
dimensions at equivalent supersaturation, due to the increased geometrical
frustration between the simplex-based fluid order and the crystal [J.A. van
Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here,
we analyze the microscopic contributions to the fluid-crystal interfacial free
energy to understand how the barrier to crystallization changes with dimension.
We find the barrier to grow with dimension and we identify the role of
polydispersity in preventing crystal formation. The increased fluid stability
allows us to study the jamming behavior in four, five, and six dimensions and
compare our observations with two recent theories [C. Song, P. Wang, and H. A.
Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in
press (2009)].Comment: 15 pages, 5 figure
Nanosecond spin lifetimes in single- and few-layer graphene-hBN heterostructures at room temperature
We present a new fabrication method of graphene spin-valve devices which
yields enhanced spin and charge transport properties by improving both the
electrode-to-graphene and graphene-to-substrate interface. First, we prepare
Co/MgO spin injection electrodes onto Si/SiO. Thereafter, we
mechanically transfer a graphene-hBN heterostructure onto the prepatterned
electrodes. We show that room temperature spin transport in single-, bi- and
trilayer graphene devices exhibit nanosecond spin lifetimes with spin diffusion
lengths reaching 10m combined with carrier mobilities exceeding 20,000
cm/Vs.Comment: 15 pages, 5 figure
Quark model description of quasi-elastic pion knockout from the proton at JLAB
The interference term between s- and t-pole contributions to the p(e,e' pi+)n
cross section is evaluated on the basis of the constituent quark model. It is
shown that the contribution of baryon s-poles can be modeled by a nonlocal
extension of the Kroll-Rudermann contact term. This contribution is in a
destructive interference with the pion t-pole that is essential to improve the
description of recent JLab data at the invariant mass W=1.95 GeV. Some
predictions are made for a new JLab measurement at higher values W=2.1-2.3 GeV
and Q2 centered at 1.6 and 2.45 GeV2/c2.Comment: 15 pages, 4 figures, to be published in Phys. Lett.
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