2,986 research outputs found
Low temperature shape relaxation of 2-d islands by edge diffusion
We present a precise microscopic description of the limiting step for low
temperature shape relaxation of two dimensional islands in which activated
diffusion of particles along the boundary is the only mechanism of transport
allowed. In particular, we are able to explain why the system is driven
irreversibly towards equilibrium. Based on this description, we present a
scheme for calculating the duration of the limiting step at each stage of the
relaxation process. Finally, we calculate numerically the total relaxation time
as predicted by our results and compare it with simulations of the relaxation
process.Comment: 11 pages, 5 figures, to appear in Phys. Rev.
Profile scaling in decay of nanostructures
The flattening of a crystal cone below its roughening transition is studied
by means of a step flow model. Numerical and analytical analyses show that the
height profile, h(r,t), obeys the scaling scenario dh/dr = F(r t^{-1/4}). The
scaling function is flat at radii r<R(t) \sim t^{1/4}. We find a one parameter
family of solutions for the scaling function, and propose a selection criterion
for the unique solution the system reaches.Comment: 4 pages, RevTex, 3 eps figure
Multiscale Mass-Spring Models of Carbon Nanotube Arrays Accounting for Mullins-like Behavior and Permanent Deformation
Changing shapes in the nanoworld
What are the mechanisms leading to the shape relaxation of three dimensional
crystallites ? Kinetic Monte Carlo simulations of fcc clusters show that the
usual theories of equilibration, via atomic surface diffusion driven by
curvature, are verified only at high temperatures. Below the roughening
temperature, the relaxation is much slower, kinetics being governed by the
nucleation of a critical germ on a facet. We show that the energy barrier for
this step linearly increases with the size of the crystallite, leading to an
exponential dependence of the relaxation time.Comment: 4 pages, 5 figures. Accepted by Phys Rev Let
Phase Separation of Crystal Surfaces: A Lattice Gas Approach
We consider both equilibrium and kinetic aspects of the phase separation
(``thermal faceting") of thermodynamically unstable crystal surfaces into a
hill--valley structure. The model we study is an Ising lattice gas for a simple
cubic crystal with nearest--neighbor attractive interactions and weak
next--nearest--neighbor repulsive interactions. It is likely applicable to
alkali halides with the sodium chloride structure. Emphasis is placed on the
fact that the equilibrium crystal shape can be interpreted as a phase diagram
and that the details of its structure tell us into which surface orientations
an unstable surface will decompose. We find that, depending on the temperature
and growth conditions, a number of interesting behaviors are expected. For a
crystal in equilibrium with its vapor, these include a low temperature regime
with logarithmically--slow separation into three symmetrically--equivalent
facets, and a higher temperature regime where separation proceeds as a power
law in time into an entire one--parameter family of surface orientations. For a
crystal slightly out of equilibrium with its vapor (slow crystal growth or
etching), power--law growth should be the rule at late enough times. However,
in the low temperature regime, the rate of separation rapidly decreases as the
chemical potential difference between crystal and vapor phases goes to zero.Comment: 16 pages (RevTex 3.0); 12 postscript figures available on request
([email protected]). Submitted to Physical Review E. SFU-JDSDJB-94-0
Fluctuations, line tensions, and correlation times of nanoscale islands on surfaces
We analyze in detail the fluctuations and correlations of the (spatial)
Fourier modes of nano-scale single-layer islands on (111) fcc crystal surfaces.
We analytically show that the Fourier modes of the fluctuations couple due to
the anisotropy of the crystal, changing the power spectrum of the fluctuations,
and that the actual eigenmodes of the fluctuations are the appropriate linear
combinations of the Fourier modes. Using kinetic Monte Carlo simulations with
bond-counting parameters that best match realistic energy barriers for hopping
rates, we deduce absolute line tensions as a function of azimuthal orientation
from the analyses of the fluctuation of each individual mode. The
autocorrelation functions of these modes give the scaling of the correlation
times with wavelength, providing us with the rate-limiting kinetics driving the
fluctuations, here step-edge diffusion. The results for the energetic
parameters are in reasonable agreement with available experimental data for
Pb(111) surfaces, and we compare the correlation times of island-edge
fluctuations to relaxation times of quenched Pb crystallites.Comment: 11 pages, 8 figures; to appear in PRB 70, xxx (15 Dec 2004), changes
in MC and its implication
The profile of a decaying crystalline cone
The decay of a crystalline cone below the roughening transition is studied.
We consider local mass transport through surface diffusion, focusing on the two
cases of diffusion limited and attachment-detachment limited step kinetics. In
both cases, we describe the decay kinetics in terms of step flow models.
Numerical simulations of the models indicate that in the attachment-detachment
limited case the system undergoes a step bunching instability if the repulsive
interactions between steps are weak. Such an instability does not occur in the
diffusion limited case. In stable cases the height profile, h(r,t), is flat at
radii r<R(t)\sim t^{1/4}. Outside this flat region the height profile obeys the
scaling scenario \partial h/\partial r = {\cal F}(r t^{-1/4}). A scaling ansatz
for the time-dependent profile of the cone yields analytical values for the
scaling exponents and a differential equation for the scaling function. In the
long time limit this equation provides an exact description of the discrete
step dynamics. It admits a family of solutions and the mechanism responsible
for the selection of a unique scaling function is discussed in detail. Finally
we generalize the model and consider permeable steps by allowing direct adatom
hops between neighboring terraces. We argue that step permeability does not
change the scaling behavior of the system, and its only effect is a
renormalization of some of the parameters.Comment: 25 pages, 18 postscript figure
Re-expansion of balloon-expandable stents after growth
AbstractObjectives. The purpose of this study was to evaluate the feasibility of re-expansion of balloon expandable intravascular stents and to examine the gross and histologic effects of re-expansion on vascular integrity.Background. Intravascular stents have been used successfully as an adjunct to balloon dilation of congenital pulmonary artery branch stenosis and postoperative stenosis of the pulmonary arteries in children. However, use of rigid stents in children could result in development of relative stenosis at the site of stent implantation with subsequent growth of the child.Methods. Stainless steel “iliac” stents were placed in the thoracic aorta of 10 normal juvenile swine by a transcatheter technique. Angiography and re-expansion were performed at a mean of 11 weeks (n = 9) and again at 18 weeks (n = 5). After euthanasia, the aortic specimens were removed for gross and histologic examination.Results. Stents were successfully implanted in 10 swine. Re-expansion was successfully performed in each animal at 11 weeks and at 18 weeks. Aortic growth produced a relative constriction of the aorta of 20% ± 10% (mean ± SD) at the site of stent implantation at both 11 and 18 weeks. Re-expansion produced a significant increase in mean stent diameter from 10.1 ± 1 mm to 12.3 ± 1.2 mm at 11 weeks and from 11.2 ± 0.7 to 13.5 ± 1.1 mm at 18 weeks after implantation (p < 0.001). Balloon dilation produced a relative increase in stent diameter of 21% ± 7% at 11 weeks and 18% ± 4% at 18 weeks. Stent re-expansion was accompanied by plastic deformation of the neointima without neointimal dissection. Where neointima was thick, there was no evidence of neointimal abrasion, but where neointima was thin, areas of localized neointimal abrasion were observed with focal fibrin and platelet adherence to the stent struts. There was no evidence of medial or adventitial hemorrhage or dissection produced by re-expansion.Conclusions. Re-expansion of intravascular stents is feasible after growth in juvenile swine without significant injury to neointima, media or adventitia. The results of this study support careful and selective use of intravascular stents as an adjunct to balloon dilation of congenital stenoses in children
Decay of one dimensional surface modulations
The relaxation process of one dimensional surface modulations is re-examined.
Surface evolution is described in terms of a standard step flow model.
Numerical evidence that the surface slope, D(x,t), obeys the scaling ansatz
D(x,t)=alpha(t)F(x) is provided. We use the scaling ansatz to transform the
discrete step model into a continuum model for surface dynamics. The model
consists of differential equations for the functions alpha(t) and F(x). The
solutions of these equations agree with simulation results of the discrete step
model. We identify two types of possible scaling solutions. Solutions of the
first type have facets at the extremum points, while in solutions of the second
type the facets are replaced by cusps. Interactions between steps of opposite
signs determine whether a system is of the first or second type. Finally, we
relate our model to an actual experiment and find good agreement between a
measured AFM snapshot and a solution of our continuum model.Comment: 18 pages, 6 figures in 9 eps file
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