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 $\Phi$ of P sites is an estimate of the porosity, and the ratio between anion diffusion coefficients in those regions is $D_{\text r}<1$. Simulation results without the large pores ($\Phi =0$) are similar to those of a formerly studied model of corrosion and passivation and are explained by a scaling approach. If $\Phi >0$ and $D_{\text r}\ll 1$, significant changes are observed in passive layer growth and corrosion front roughness. For small $\Phi$, 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

Phase diagram of a 2D Ising model within a nonextensive approach

In this work we report Monte Carlo simulations of a 2D Ising model, in which the statistics of the Metropolis algorithm is replaced by the nonextensive one. We compute the magnetization and show that phase transitions are present for $q\neq 1$. A $q -$ phase diagram (critical temperature vs. the entropic parameter $q$) is built and exhibits some interesting features, such as phases which are governed by the value of the entropic index $q$. It is shown that such phases favors some energy levels of magnetization states. It is also showed that the contribution of the Tsallis cutoff is essential to the existence of phase transitions

Interface Collisions

We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form rough domain boundaries, which defines collision interfaces in time and space. We show that statistical properties of such interfaces depend on the kinetics of the growing interfaces before collision, but are independent of the details of their interaction and of their fluctuations during the collision. Those properties exhibit dynamic scaling with exponents related to the growth kinetics, but their distributions may be non-universal. These results are supported by simulations of lattice models with irreversible dynamics and local interactions. Relations to first passage processes are discussed and a possible application to grain boundary formation in two-dimensional materials is suggested.Comment: Paper with 12 pages and 2 figures; supplemental material with 4 pages and 3 figure

Scaling in reversible submonolayer deposition

The scaling of island and monomer density, capture zone distributions (CZDs), and island size distributions (ISDs) in reversible submonolayer growth was studied using the Clarke-Vvedensky model. An approach based on rate-equation results for irreversible aggregation (IA) models is extended to predict several scaling regimes in square and triangular lattices, in agreement with simulation results. Consistently with previous works, a regime I with fractal islands is observed at low temperatures, corresponding to IA with critical island size i=1, and a crossover to a second regime appears as the temperature is increased to \epsilon R^{2/3} ~ 1, where \epsilon is the single bond detachment probability and R is the diffusion-to-deposition ratio. In the square (triangular) lattice, a regime with scaling similar to IA with i=3 (i=2) is observed after that crossover. In the triangular lattice, a subsequent crossover to an IA regime with i=3 is observed, which is explained by the recurrence properties of random walks in two dimensional lattices, which is beyond the mean-field approaches. At high temperatures, a crossover to a fully reversible regime is observed, characterized by a large density of small islands, a small density of very large islands, and total island and monomer densities increasing with temperature, in contrast to IA models. CZDs and ISDs with Gaussian right tails appear in all regimes for R ~ 10^7 or larger, including the fully reversible regime, where the CZDs are bimodal. This shows that the Pimpinelli-Einstein (PE) approach for IA explains the main mechanisms for the large islands to compete for free adatom aggregation in the reversible model, and may be the reason for its successful application to a variety of materials and growth conditions.Comment: 10 pages, 7 figure

Crystallization of a quasi-two-dimensional granular fluid

We experimentally investigate the crystallization of a uniformly heated quasi-2D granular fluid as a function of filling fraction. Our experimental results for the Lindemann melting criterion, the radial distribution function, the bond order parameter and the statistics of topological changes at the particle level are the same as those found in simulations of equilibrium hard disks. This direct mapping suggests that the study of equilibrium systems can be effectively applied to study non-equilibrium steady states like those found in our driven and dissipative granular system.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Langevin equations for competitive growth models

Langevin equations for several competitive growth models in one dimension are derived. For models with crossover from random deposition (RD) to some correlated deposition (CD) dynamics, with small probability p of CD, the surface tension \nu and the nonlinear coefficient \lambda of the associated equations have linear dependence on p due solely to this random choice. However, they also depend on the regularized step functions present in the analytical representations of the CD, whose expansion coefficients scale with p according to the divergence of local height differences when p->0. The superposition of those scaling factors gives \nu ~ p^2 for random deposition with surface relaxation (RDSR) as the CD, and \nu ~ p, \lambda ~ p^{3/2} for ballistic deposition (BD) as the CD, in agreement with simulation and other scaling approaches. For bidisperse ballistic deposition (BBD), the same scaling of RD-BD model is found. The Langevin equation for the model with competing RDSR and BD, with probability p for the latter, is also constructed. It shows linear p-dependence of \lambda, while the quadratic dependence observed in previous simulations is explained by an additional crossover before the asymptotic regime. The results highlight the relevance of scaling of the coefficients of step function expansions in systems with steep surfaces, which is responsible for noninteger exponents in some p-dependent stochastic equations, and the importance of the physical correspondence of aggregation rules and equation coefficients.Comment: 8 pages with 1 figure include