52 research outputs found
Effects of porosity in a model of corrosion and passive layer growth
We introduce a stochastic lattice model to investigate the effects of pore
formation in a passive layer grown with products of metal corrosion. It
considers that an anionic species diffuses across that layer and reacts at the
corrosion front (metal-oxide interface), producing a random distribution of
compact regions and large pores, respectively represented by O (oxide) and P
(pore) sites. O sites are assumed to have very small pores, so that the
fraction of P sites is an estimate of the porosity, and the ratio
between anion diffusion coefficients in those regions is .
Simulation results without the large pores () are similar to those of
a formerly studied model of corrosion and passivation and are explained by a
scaling approach. If and , significant changes are
observed in passive layer growth and corrosion front roughness. For small
, a slowdown of the growth rate is observed, which is interpreted as a
consequence of the confinement of anions in isolated pores for long times.
However, the presence of large pores near the corrosion front increases the
frequency of reactions at those regions, which leads to an increase in the
roughness of that front. This model may be a first step to represent defects in
a passive layer which favor pitting corrosion.Comment: 8 pages, 6 figure
Scaling in the crossover from random to correlated growth
In systems where deposition rates are high compared to diffusion, desorption
and other mechanisms that generate correlations, a crossover from random to
correlated growth of surface roughness is expected at a characteristic time
t_0. This crossover is analyzed in lattice models via scaling arguments, with
support from simulation results presented here and in other authors works. We
argue that the amplitudes of the saturation roughness and of the saturation
time scale as {t_0}^{1/2} and t_0, respectively. For models with lateral
aggregation, which typically are in the Kardar-Parisi-Zhang (KPZ) class, we
show that t_0 ~ 1/p, where p is the probability of the correlated aggregation
mechanism to take place. However, t_0 ~ 1/p^2 is obtained in solid-on-solid
models with single particle deposition attempts. This group includes models in
various universality classes, with numerical examples being provided in the
Edwards-Wilkinson (EW), KPZ and Villain-Lai-Das Sarma (nonlinear molecular-beam
epitaxy) classes. Most applications are for two-component models in which
random deposition, with probability 1-p, competes with a correlated aggregation
process with probability p. However, our approach can be extended to other
systems with the same crossover, such as the generalized restricted
solid-on-solid model with maximum height difference S, for large S. Moreover,
the scaling approach applies to all dimensions. In the particular case of
one-dimensional KPZ processes with this crossover, we show that t_0 ~ nu^{-1}
and nu ~ lambda^{2/3}, where nu and lambda are the coefficients of the linear
and nonlinear terms of the associated KPZ equations. The applicability of
previous results on models in the EW and KPZ classes is discussed.Comment: 14 pages + 5 figures, minor changes, version accepted in Phys. Rev.
Non-universal coarsening and universal distributions in far-from equilibrium systems
Anomalous coarsening in far-from equilibrium one-dimensional systems is
investigated by simulation and analytic techniques. The minimal hard core
particle (exclusion) models contain mechanisms of aggregated particle
diffusion, with rates epsilon<<1, particle deposition into cluster gaps, but
suppressed for the smallest gaps, and breakup of clusters which are adjacent to
large gaps. Cluster breakup rates vary with the cluster length x as kx^alpha.
The domain growth law x ~ (epsilon t)^z, with z=1/(2+alpha) for alpha>0, is
explained by a scaling picture, as well as the scaling of the density of double
vacancies (at which deposition and cluster breakup are allowed) as 1/[t(epsilon
t)^z]. Numerical simulations for several values of alpha and epsilon confirm
these results. An approximate factorization of the cluster configuration
probability is performed within the master equation resulting from the mapping
to a column picture. The equation for a one-variable scaling function explains
the above results. The probability distributions of cluster lengths scale as
P(x)= 1/(epsilon t)^z g(y), with y=x/(epsilon t)^z. However, those
distributions show a universal tail with the form g(y) ~ exp(-y^{3/2}), which
disagrees with the prediction of the independent cluster approximation. This
result is explained by the connection of the vacancy dynamics with the problem
of particle trapping in an infinite sea of traps and is confirmed by
simulation.Comment: 30 pages (10 figures included), to appear in Phys. Rev.
Modeling one-dimensional island growth with mass-dependent detachment rates
We study one-dimensional models of particle diffusion and
attachment/detachment from islands where the detachment rates gamma(m) of
particles at the cluster edges increase with cluster mass m. They are expected
to mimic the effects of lattice mismatch with the substrate and/or long-range
repulsive interactions that work against the formation of long islands.
Short-range attraction is represented by an overall factor epsilon<<1 in the
detachment rates relatively to isolated particle hopping rates [epsilon ~
exp(-E/T), with binding energy E and temperature T]. We consider various
gamma(m), from rapidly increasing forms such as gamma(m) ~ m to slowly
increasing ones, such as gamma(m) ~ [m/(m+1)]^b. A mapping onto a column
problem shows that these systems are zero-range processes, whose steady states
properties are exactly calculated under the assumption of independent column
heights in the Master equation. Simulation provides island size distributions
which confirm analytic reductions and are useful whenever the analytical tools
cannot provide results in closed form. The shape of island size distributions
can be changed from monomodal to monotonically decreasing by tuning the
temperature or changing the particle density rho. Small values of the scaling
variable X=epsilon^{-1}rho/(1-rho) favour the monotonically decreasing ones.
However, for large X, rapidly increasing gamma(m) lead to distributions with
peaks very close to and rapidly decreasing tails, while slowly increasing
gamma(m) provide peaks close to /2$ and fat right tails.Comment: 16 pages, 6 figure
Finite-size effects in roughness distribution scaling
We study numerically finite-size corrections in scaling relations for
roughness distributions of various interface growth models. The most common
relation, which considers the average roughness . This illustrates how
finite-size corrections can be obtained from roughness distributions scaling.
However, we discard the usual interpretation that the intrinsic width is a
consequence of high surface steps by analyzing data of restricted
solid-on-solid models with various maximal height differences between
neighboring columns. We also observe that large finite-size corrections in the
roughness distributions are usually accompanied by huge corrections in height
distributions and average local slopes, as well as in estimates of scaling
exponents. The molecular-beam epitaxy model of Das Sarma and Tamborenea in 1+1
dimensions is a case example in which none of the proposed scaling relations
works properly, while the other measured quantities do not converge to the
expected asymptotic values. Thus, although roughness distributions are clearly
better than other quantities to determine the universality class of a growing
system, it is not the final solution for this task.Comment: 25 pages, including 9 figures and 1 tabl
Phase transitions and crossovers in reaction-diffusion models with catalyst deactivation
The activity of catalytic materials is reduced during operation by several
mechanisms, one of them being poisoning of catalytic sites by chemisorbed
impurities or products. Here we study the effects of poisoning in two
reaction-diffusion models in one-dimensional lattices with randomly distributed
catalytic sites. Unimolecular and bimolecular single-species reactions are
considered, without reactant input during the operation. The models show
transitions between a phase with continuous decay of reactant concentration and
a phase with asymptotic non-zero reactant concentration and complete poisoning
of the catalyst. The transition boundary depends on the initial reactant and
catalyst concentrations and on the poisoning probability. The critical system
behaves as in the two-species annihilation reaction, with reactant
concentration decaying as t^{-1/4} and the catalytic sites playing the role of
the second species. In the unimolecular reaction, a significant crossover to
the asymptotic scaling is observed even when one of those parameters is 10% far
from criticality. Consequently, an effective power-law decay of concentration
may persist up to long times and lead to an apparent change in the reaction
kinetics. In the bimolecular single-species reaction, the critical scaling is
followed by a two-dimensional rapid decay, thus two crossovers are found.Comment: 8 pages, 7 figure
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