1,094 research outputs found
Nanoscale periodicity in stripe-forming systems at high temperature: Au/W(110)
We observe using low-energy electron microscopy the self-assembly of
monolayer-thick stripes of Au on W(110) near the transition temperature between
stripes and the non-patterned (homogeneous) phase. We demonstrate that the
amplitude of this Au stripe phase decreases with increasing temperature and
vanishes at the order-disorder transition (ODT). The wavelength varies much
more slowly with temperature and coverage than theories of stress-domain
patterns with sharp phase boundaries would predict, and maintains a finite
value of about 100 nm at the ODT. We argue that such nanometer-scale stripes
should often appear near the ODT.Comment: 5 page
Anomalous Dimension and Spatial Correlations in a Point-Island Model
We examine the island size distribution function and spatial correlation
function of a model for island growth in the submonolayer regime in both 1 and
2 dimensions. In our model the islands do not grow in shape, and a fixed number
of adatoms are added, nucleate, and are trapped at islands as they diffuse.
We study the cases of various critical island sizes for nucleation as a
function of initial coverage. We found anomalous scaling of the island size
distribution for large . Using scaling, random walk theory, a version of
mean-field theory we obtain a closed form for the spatial correlation function.
Our analytic results are verified by Monte Carlo simulations
Effects of Impurities in Random Sequential Adsorption on a One-Dimensional Substrate
We have solved the kinetics of random sequential adsorption of linear
-mers on a one-dimensional disordered substrate for the random sequential
adsorption initial condition and for the random initial condition. The jamming
limits at fixed length of linear -mers have a
minimum point at a particular density of the linear -mers impurity for both
cases. The coverage of the surface and the jamming limits are compared to the
results for Monte Carlo simulation. The Monte Carlo results for the jamming
limits are in good agreement with the analytical results. The continuum limits
are derived from the analytical results on lattice substrates.Comment: 9 pages, latex, 1 figure not included, accepted in Phys. Rev.
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
Factors influencing graphene growth on metal surfaces
Graphene forms from a relatively dense, tightly-bound C-adatom gas, when
elemental C is deposited on or segregates to the Ru(0001) surface. Nonlinearity
of the graphene growth rate with C adatom density suggests that growth proceeds
by addition of C atom clusters to the graphene edge. The generality of this
picture has now been studied by use of low-energy electron microscopy (LEEM) to
observe graphene formation when Ru(0001) and Ir(111) surfaces are exposed to
ethylene. The finding that graphene growth velocities and nucleation rates on
Ru have precisely the same dependence on adatom concentration as for elemental
C deposition implies that hydrocarbon decomposition only affects graphene
growth through the rate of adatom formation; for ethylene, that rate decreases
with increasing adatom concentration and graphene coverage. Initially, graphene
growth on Ir(111) is like that on Ru: the growth velocity is the same nonlinear
function of adatom concentration (albeit with much smaller equilibrium adatom
concentrations, as we explain with DFT calculations of adatom formation
energies). In the later stages of growth, graphene crystals that are rotated
relative to the initial nuclei nucleate and grow. The rotated nuclei grow much
faster. This difference suggests first, that the edge-orientation of the
graphene sheets relative to the substrate plays an important role in the growth
mechanism, and second, that attachment of the clusters to the graphene is the
slowest step in cluster addition, rather than formation of clusters on the
terraces
A quantitative theory of current-induced step bunching on Si(111)
We use a one-dimensional step model to study quantitatively the growth of
step bunches on Si(111) surfaces induced by a direct heating current.
Parameters in the model are fixed from experimental measurements near 900 deg C
under the assumption that there is local mass transport through surface
diffusion and that step motion is limited by the attachment rate of adatoms to
step edges. The direct heating current is treated as an external driving force
acting on each adatom. Numerical calculations show both qualitative and
quantitative agreement with experiment. A force in the step down direction will
destabilize the uniform step train towards step bunching. The average size of
the step bunches grows with electromigration time as t^beta, with beta = 0.5,
in agreement with experiment and with an analytical treatment of the steady
states. The model is extended to include the effect of direct hopping of
adatoms between different terraces. Monte-Carlo simulations of a solid-on-solid
model, using physically motivated assumptions about the dynamics of surface
diffusion and attachment at step edges, are carried out to study two
dimensional features that are left out of the present step model and to test
its validity. These simulations give much better agreement with experiment than
previous work. We find a new step bending instability when the driving force is
along the step edge direction. This instability causes the formation of step
bunches and antisteps that is similar to that observed in experiment.Comment: 11 pages, 7 figure
Exact Solution of a Drop-push Model for Percolation
Motivated by a computer science algorithm known as `linear probing with
hashing' we study a new type of percolation model whose basic features include
a sequential `dropping' of particles on a substrate followed by their transport
via a `pushing' mechanism. Our exact solution in one dimension shows that,
unlike the ordinary random percolation model, the drop-push model has
nontrivial spatial correlations generated by the dynamics itself. The critical
exponents in the drop-push model are also different from that of the ordinary
percolation. The relevance of our results to computer science is pointed out.Comment: 4 pages revtex, 2 eps figure
Coarsening Dynamics of Crystalline Thin Films
The formation of pyramid-like structures in thin-film growth on substrates
with a quadratic symmetry, e.g., {001} surfaces, is shown to exhibit
anisotropic scaling as there exist two length scales with different time
dependences. Analytical and numerical results indicate that for most
realizations coarsening of mounds is described by an exponent n=0.2357.
However, depending on material parameters, n may lie between 0 (logarithmic
coarsening) and 1/3. In contrast, growth on substrates with triangular
symmetries ({111} surfaces) is dominated by a single length scale and an
exponent n=1/3.Comment: RevTeX, 4 pages, 3 figure
Adsorption of Line Segments on a Square Lattice
We study the deposition of line segments on a two-dimensional square lattice.
The estimates for the coverage at jamming obtained by Monte-Carlo simulations
and by -order time-series expansion are successfully compared. The
non-trivial limit of adsorption of infinitely long segments is studied, and the
lattice coverage is consistently obtained using these two approaches.Comment: 19 pages in Latex+5 postscript files sent upon request ; PTB93_
- …