82 research outputs found
Dewetting of solid films with substrate mediated evaporation
The dewetting dynamics of an ultrathin film is studied in the presence of
evaporation - or reaction - of adatoms on the substrate. KMC simulations are in
good agreement with an analytical model with diffusion, rim facetting, and
substrate sublimation. As sublimation is increased, we find a transition from
the usual dewetting regime where the front slows down with time, to a
sublimation-controlled regime where the front velocity is approximately
constant. The rim width exhibits an unexpected non-monotonous behavior, with a
maximum in time.Comment: 6 pages, 6 figure
Nonlinear wavelength selection in surface faceting under electromigration
We report on the control of the faceting of crystal surfaces by means of
surface electromigration. When electromigration reinforces the faceting
instability, we find perpetual coarsening with a wavelength increasing as
. For strongly stabilizing electromigration, the surface is stable.
For weakly stabilizing electromigration, a cellular pattern is obtained, with a
nonlinearly selected wavelength. The selection mechanism is not caused by an
instability of steady-states, as suggested by previous works in the literature.
Instead, the dynamics is found to exhibit coarsening {\it before} reaching a
continuous family of stable non-equilibrium steady-states.Comment: 5 pages, 4 figures, submitte
Atomic step motion during the dewetting of ultra-thin films
We report on three key processes involving atomic step motion during the
dewetting of thin solid films: (i) the growth of an isolated island nucleated
far from a hole, (ii) the spreading of a monolayer rim, and (iii) the zipping
of a monolayer island along a straight dewetting front. Kinetic Monte Carlo
results are in good agreement with simple analytical models assuming
diffusion-limited dynamics.Comment: 7 pages, 5 figure
Anisotropic diffusion in continuum relaxation of stepped crystal surfaces
We study the continuum limit in 2+1 dimensions of nanoscale anisotropic
diffusion processes on crystal surfaces relaxing to become flat below
roughening. Our main result is a continuum law for the surface flux in terms of
a new continuum-scale tensor mobility. The starting point is the Burton,
Cabrera and Frank (BCF) theory, which offers a discrete scheme for atomic steps
whose motion drives surface evolution. Our derivation is based on the
separation of local space variables into fast and slow. The model includes: (i)
anisotropic diffusion of adsorbed atoms (adatoms) on terraces separating steps;
(ii) diffusion of atoms along step edges; and (iii) attachment-detachment of
atoms at step edges. We derive a parabolic fourth-order, fully nonlinear
partial differential equation (PDE) for the continuum surface height profile.
An ingredient of this PDE is the surface mobility for the adatom flux, which is
a nontrivial extension of the tensor mobility for isotropic terrace diffusion
derived previously by Margetis and Kohn. Approximate, separable solutions of
the PDE are discussed.Comment: 14 pages, 1 figur
Quantal distribution functions in non-extensive statistics and an early universe test revisited
Within the context of non-extensive thermostatistics, we use the
factorization approximation to study a recently proposed early universe test. A
very restrictive bound upon the non-extensive parameter is presented: .Comment: 4 pages, prl revtex style, no figures. To appear in Physica A, 199
Continuum description of profile scaling in nanostructure decay
The relaxation of axisymmetric crystal surfaces with a single facet below the
roughening transition is studied via a continuum approach that accounts for
step energy g_1 and step-step interaction energy g_3>0. For diffusion-limited
kinetics, free-boundary and boundary-layer theories are used for self-similar
shapes close to the growing facet. For long times and g_3/g_1 < 1, (a) a
universal equation is derived for the shape profile, (b) the layer thickness
varies as (g_3/g_1)^{1/3}, (c) distinct solutions are found for different
g_3/_1, and (d) for conical shapes, the profile peak scales as
(g_3/g_1)^{-1/6}. These results compare favorably with kinetic simulations.Comment: 4 pages including 3 figure
Spontaneous magnetization of the Ising model on the Sierpinski carpet fractal, a rigorous result
We give a rigorous proof of the existence of spontaneous magnetization at
finite temperature for the Ising spin model defined on the Sierpinski carpet
fractal. The theorem is inspired by the classical Peierls argument for the two
dimensional lattice. Therefore, this exact result proves the existence of
spontaneous magnetization for the Ising model in low dimensional structures,
i.e. structures with dimension smaller than 2.Comment: 14 pages, 8 figure
Novel continuum modeling of crystal surface evolution
We propose a novel approach to continuum modeling of the dynamics of crystal
surfaces. Our model follows the evolution of an ensemble of step
configurations, which are consistent with the macroscopic surface profile.
Contrary to the usual approach where the continuum limit is achieved when
typical surface features consist of many steps, our continuum limit is
approached when the number of step configurations of the ensemble is very
large. The model can handle singular surface structures such as corners and
facets. It has a clear computational advantage over discrete models.Comment: 4 pages, 3 postscript figure
- …