arXiv subjects

F. D. A. Aarao Reis

Publications and source records attributed to F. D. A. Aarao Reis.

At least 19 recordsLinked to original sources

arXiv2017

Scaling relations in the diffusive infiltration in fractals

In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as F~t^n, with n<1/2, thus providing a macroscopic realization of anomalous diffusion [Filipovitch et al, Water Resour. Res. 52 5167 (2016)]. The results agree with simulations of a diffusion equation with constant pressure at one of the borders of those fractals, but the exponent n is very different from the anomalous exponent nu=1/D_W of single particle diffusion in the same fractals (D_W is the random walk dimension). Here we use a scaling approach to show that those exponents are related as n=nu(D_F-D_B), where D_F and D_B are the fractal dimensions of the bulk and of the border from which diffusing particles come, respectively. This relation is supported by accurate numerical estimates in two SCs and in two generalized Menger sponges (MSs), in which we performed simulations of single particle random walks (RWs) with a rigid impermeable border and of a diffusive infiltration model in which that border is permanently filled with diffusing particles. This study includes one MS whose external border is also fractal. The exponent relation is also consistent with the recent simulational and experimental results on fluid infiltration in SCs, and explains the approximate quadratic dependence of n on D_F in these fractals. We also show that the mean-square displacement of single particle RWs has log-periodic oscillations, whose periods are similar for fractals with the same scaling factor in the generator (even with different embedding dimensions), which is consistent with the discrete scale invariance scenario. The roughness of a diffusion front defined in the infiltration problem also shows this type of oscillation, which is enhanced in fractals with narrow channels between large lacunas.

cond-mat.stat-mech↗

arXiv2015

Transition from compact to porous films in deposition with temperature activated diffusion

We study a thin film growth model with temperature activated diffusion of adsorbed particles, allowing for the formation of overhangs and pores, but without detachment of adatoms or clusters from the deposit. Simulations in one-dimensional substrates are performed for several values of the diffusion-to-deposition ratio R of adatoms with a single bond and of the detachment probability epsilon per additional nearest neighbor (NN), respectively with activation energies are Es and Eb. If R and epsilon independently vary, regimes of low and high porosity are separated at 0.075 < epsilon_c < 0.09, with vanishingly small porosity below that point and finite porosity for larger epsilon. Alternatively, for fixed values of Es and Eb and varying temperature, the porosity has a minimum at Tc, and a nontrivial regime in which it increases with temperature is observe above that point. This is related to the large mobility of adatoms, resembling features of equilibrium surface roughening. In this high-temperature region, the deposit has the structure of a critical percolation cluster due to the non-desorption condition. The pores are regions enclosed by blobs of the corresponding percolating backbone, thus the distribution of pore size s is expected to scale as s^{-tau} with tau ~ 1.45, in reasonable agreement with numerical estimates. Roughening of the outer interface of the deposits suggests Villain-Lai-Das Sarma scaling below the transition. Above the transition, the roughness exponent alpha ~ 0.35 is consistent with the percolation backbone structure via the relation alpha = 2-d_B, where d_B is the backbone fractal dimension.

cond-mat.stat-mech↗

arXiv2015

Substrate effects and diffusion dominated roughening in Cu2O electrodeposition

Cuprous oxide (Cu2O) films from 25 nm to 1500 nm were electrodeposited on n-Si(100) and Ni/n-Si(100) substrates from aqueous solution at room temperature. X-ray diffraction and transmission electron microscopy imaging show that the Cu2O structure and morphology is strongly affected by the substrate choice, with V shape and U shape columnar growth on n-Si(100) and Ni/n-Si(100), respectively. Atomic force microscopy reveals the presence of rounded grains at the surface in both cases. Anomalous and normal roughening are observed in films grown on n-Si and Ni, respectively, but estimates of scaling exponents are not conclusive. On the other hand, the distributions of local heights, roughness, and extremal heights show good agreement with those of the fourth order linear stochastic equation of Mullins and Herring (MH). Thus, surface dynamics in both systems is dominated by diffusion of adsorbed molecules, with no large scale effect of possible inhomogeneities in mass flux from the solution or in reaction and adsorption rates. In growth on n-Si substrates, the noise amplitude of the MH equation increases in time as t^{0.8}, while the coefficient of the curvature-related term is time-independent. Step edge energy barriers restrict the mass flux across grain boundaries, thus a broad size distribution of initial grains leads to coarsening of the larger ones. This explains their V shape in the thickest films and establishes a connection with the anomalous roughening. These effects are reduced in films grown on Ni/n-Si, which initially have much larger grains with narrower size distributions and, consequently, smaller fluctuations in coarse grained growth rates.

cond-mat.mtrl-sci↗

arXiv2015

Crossover from anomalous to normal diffusion in porous media

Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores, in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover to long time normal diffusion is observed in most samples. The anomalous concentration profile remains at long times in very porous solids if the walker steps are restricted to nearest neighbors and is accompanied with subdiffusion features. These findings are correlated with a decay of the explored area with z. The study of RW of tracer particles left at the internal part of the solid rules out an interpretation by diffusion equations with position-dependent coefficients. A model of RW in a tube of decreasing cross section explains those results by showing long crossovers from an effective subdiffusion regime to an asymptotic normal diffusion. The crossover position and density are analytically calculated for a tube with area decreasing exponentially with z and show good agreement with numerical data. The anomalous decay of the concentration profile is interpreted as a templating effect of the tube shape on the total number of diffusing particles at each depth, while the volumetric concentration in the actually explored porous region may not have significant decay. These results may explain the anomalous diffusion of metal atoms in porous deposits observed in recent works. They also confirm the difficulty in interpreting experimental or computational data on anomalous transport reported in recent works, particularly if only the concentration profiles are measured.

cond-mat.stat-mech↗

arXiv2014

Simulating the initial growth of a deposit from colloidal suspensions

We study the short time properties of a two-dimensional film growth model in which incident particles execute advective-diffusive motion with a vertical step followed by $D$ horizontal steps. The model represents some features of the deposition of anisotropic colloidal particles of the experiment in Phys. Rev. Lett. {\bf 110}, 035501 (2013), in which wandering particles are attracted to particle-rich regions in the deposit. Height profiles changing from rough to columnar structure are observed as $D$ increases from $0$ (ballistic deposition) to $8$, with striking similarity to the experimental ones. The effective growth exponents matches the experimental estimates and the scaling of those exponents on $D$ show a remarkable effect of the range of the particle-deposit interaction. The nearly ellipsoidal shape of colloidal particles is represented for the calculation of roughness exponents in conditions that parallel the experimental ones, giving a range of estimates that also include the experimental values. The effective dynamic exponents calculated from the autocorrelation function are shown to be suitable to decide between a true dynamic scaling or transient behavior, particularly because the latter leads to deviations in an exponent relation. These results are consistent with arguments on short time unstable (columnar) growth of Phys. Rev. Lett {\bf 111}, 209601 (2013), indicating that critical quenched KPZ dynamics does not explain that colloidal particle deposition problem.

cond-mat.stat-mech↗

arXiv2013

Universal fluctuations in the growth of semiconductor thin films

Scaling of surface fluctuations of polycrystalline CdTe/Si(100) films grown by hot wall epitaxy are studied. The growth exponent of surface roughness and the dynamic exponent of the auto-correlation function in the mound growth regime agree with the values of the Kardar-Parisi-Zhang (KPZ) class. The scaled distributions of heights, local roughness, and extremal heights show remarkable collapse with those of the KPZ class, giving the first experimental observation of KPZ distributions in $2+1$ dimensions. Deviations from KPZ values in the long-time estimates of dynamic and roughness exponents are explained by spurious effects of multi-peaked coalescing mounds and by effects of grain shapes. Thus, this scheme for investigating universality classes of growing films advances over the simple comparison of scaling exponents.

cond-mat.stat-mech↗

arXiv2013

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 εR^{2/3} ~ 1, where εis 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.

cond-mat.stat-mech↗

arXiv2013

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 νand the nonlinear coefficient λof 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 ν~ p^2 for random deposition with surface relaxation (RDSR) as the CD, and ν~ p, λ~ 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 λ, 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.

cond-mat.stat-mech↗

arXiv2012

Crossover in the scaling of island size and capture zone distributions

Simulations of irreversible growth of extended (fractal and square) islands with critical island sizes i=1 and 2 are performed in broad ranges of coverage θand diffusion-to-deposition ratios R in order to investigate scaling of island size and capture zone area distributions (ISD, CZD). Large θand small R lead to a crossover from the CZD predicted by the theory of Pimpinelli and Einstein (PE), with Gaussian right tail, to CZD with simple exponential decays. The corresponding ISD also cross over from Gaussian or faster decays to simple exponential ones. For fractal islands, these features are explained by changes in the island growth kinetics, from a competition for capture of diffusing adatoms (PE scaling) to aggregation of adatoms with effectively irrelevant diffusion, which is characteristic of random sequential adsorption (RSA) without surface diffusion. This interpretation is confirmed by studying the crossover with similar CZ areas (of order 100 sites) in a model with freezing of diffusing adatoms that corresponds to i=0. For square islands, deviations from PE predictions appear for coverages near θ=0.2 and are mainly related to island coalescence. Our results show that the range of applicability of the PE theory is narrow, thus observing the predicted Gaussian tail of CZD may be difficult in real systems.

cond-mat.stat-mech↗

arXiv2011

Scaling of island size and capture zone distributions in submonolayer growth

Island size and capture zone distributions (ISDs, CZDs) are studied numerically in submonolayer growth with various critical island sizes and shapes. CZDs scaled by the variance show excellent agreement with the Wigner surmise, confirming the Pimpinelli-Einstein approach for large CZs / large island dynamics. The ISD decay as exp(-s^x), with x=4, x approx 2.4 and 2 for point, fractal, and square islands, respectively. A scaling approach explains the values of x from the Gaussian decay of CZD and the efficiency of islands to capture diffusing adatoms.

cond-mat.stat-mech↗

arXiv2011

Roughness exponents and grain shapes

In surfaces with grainy features, the local roughness $w$ shows a crossover at a characteristic length $r_c$, with roughness exponent changing from $α_1\approx 1$ to a smaller $α_2$. The grain shape, the choice of $w$ or height-height correlation function (HHCF) $C$, and the procedure to calculate root mean-square averages are shown to have remarkable effects on $α_1$. With grains of pyramidal shape, $α_1$ can be as low as 0.71, which is much lower than the previous prediction 0.85 for rounded grains. The same crossover is observed in the HHCF, but with initial exponent $χ_1\approx 0.5$ for flat grains, while for some conical grains it may increase to $χ_1\approx 0.7$. The universality class of the growth process determines the exponents $α_2=χ_2$ after the crossover, but has no effect on the initial exponents $α_1$ and $χ_1$, supporting the geometric interpretation of their values. For all grain shapes and different definitions of surface roughness or HHCF, we still observe that the crossover length $r_c$ is an accurate estimate of the grain size. The exponents obtained in several recent experimental works on different materials are explained by those models, with some surface images qualitatively similar to our model films.

cond-mat.stat-mech↗

arXiv2008

Unusual features of coarsening with detachment rates decreasing with cluster mass

We study conserved one-dimensional models of particle diffusion, attachment and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) ~ m^{-k}, k>0. Heuristic scaling arguments based on random walk properties show that the typical cluster size scales as (t/ln(t))^z, with z=1/(k+2). The initial symmetric flux of particles between neighboring clusters is followed by an effectively assymmetric flux due to the unbalanced detachement rates, which leads to the above logarithmic correction. Small clusters have densities of order t^{-mz(1)}, with z(1) = k/(k+2). Thus, for k<1, the small clusters (mass of order unity) are statistically dominant and the average cluster size does not scale as the size of typically large clusters does. We also solve the Master equation of the model under an independent interval approximation, which yields cluster distributions and exponent relations and gives the correct dominant coarsening exponent after accounting for the effects of correlations. The coarsening of large clusters is described by the distribution P_t(m) ~ 1/t^y f(m/t^z), with y=2z. All results are confirmed by simulation, which also illustrates the unusual features of cluster size distributions, with a power law decay for small masses and a negatively skewed peak in the scaling region. The detachment rates considered here can apply in the presence of strong attractive interactions, and recent applications suggest that even more rapid rate decays are also physically realistic.

cond-mat.stat-mech↗

arXiv2008

Numerical study of the Kardar-Parisi-Zhang equation

We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in 1+1 and 2+1 dimensions using an Euler discretization scheme and the replacement of ${(\nabla h)}^2$ by exponentially decreasing functions of that quantity to suppress instabilities. When applied to the equation in 1+1 dimensions, the method of instability control provides values of scaling amplitudes consistent with exactly known results, in contrast to the deviations generated by the original scheme. In 2+1 dimensions, we spanned a range of the model parameters where transients with Edwards-Wilkinson or random growth are not bserved, in box sizes $8\leq L\leq 128$. We obtain roughness exponent $0.37\leq α\leq 0.40$ and steady state height distributions with skewness $S= 0.25\pm 0.01$ and kurtosis $Q= 0.15\pm 0.1$. These estimates are obtained after extrapolations to the large $L$ limit, which is necessary due to significant finite-size effects in the estimates of effective exponents and height distributions. On the other hand, the steady state roughness distributions show weak scaling corrections and evidence of stretched exponentials tails. These results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class.

cond-mat.stat-mech↗

arXiv2008

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 $ $ as scaling factor, is not obeyed in the steady states of a group of ballistic-like models in 2+1 dimensions, even when very large system sizes are considered. On the other hand, good collapse of the same data is obtained with a scaling relation that involves the root mean square fluctuation of the roughness, which can be explained by finite-size effects on second moments of the scaling functions. We also obtain data collapse with an alternative scaling relation that accounts for the effect of the intrinsic width, which is a constant correction term previously proposed for the scaling of $ $. 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.

cond-mat.stat-mech↗

arXiv2007

Maximal and minimal height distributions of fluctuating interfaces

We study numerically the maximal and minimal height distributions (MAHD, MIHD) of the nonlinear interface growth equations of second and fourth order and of related lattice models in two dimensions. MAHD and MIHD are different due to the asymmetry of the local height distribution, so that, in each class, the sign of the relevant nonlinear term determines which one of two universal curves is the MAHD and the MIHD. The average maximal and minimal heights scale as the average roughness, in contrast to Edwards-Wilkinson (EW) growth. All extreme height distributions, including the EW ones, have tails that cannot be fit by generalized Gumbel distributions.

cond-mat.stat-mech↗

arXiv2007

Effects of grains' features in surface roughness scaling

We study the local and global roughness scaling in growth models with grains at the film surfaces. The local roughness, measured as a function of window size r, shows a crossover at a characteristic length r_c, from a rapid increase with exponent α_1 to a slower increase with exponent α_2. The result α_1\approx 1 is explained by the large height differences in the borders of the grains when compared to intragrain roughness, and must not be interpreted as a consequence of a diffusion dominated intragrain dynamics. This exponent shows a weak dependence on the shape and size distribution of the grains, and typically ranges from 0.85 for rounded grain surfaces to 1 for the sharpest ones. The scaling corrections of exactly solvable models suggest the possibility of slightly smaller values due to other smoothing effects of the surface images. The crossover length r_c provides a reasonable estimate of the average grain size in all model systems, including the cases of wide grain size distributions. In Kardar-Parisi-Zhang growth, very different values of α_2 are obtained, ranging from 0.4 for the films with smoothest surfaces to values in the range 0.1\lesssim α_2 \lesssim 0.2 for systems with large cliffs separating the grains. Possible applications to real systems which show this crossover with similar exponents are discussed.

cond-mat.stat-mech↗

arXiv2007

Height and roughness distributions in thin films with Kardar-Parisi-Zhang scaling

We study height and roughness distributions of films grown with discrete Kardar-Parisi-Zhang (KPZ) models in a small time regime which is expected to parallel the typical experimental conditions. Those distributions are measured with square windows of sizes $8\leq r\leq 128$ gliding through a much larger surface. Results for models with weak finite-size corrections indicate that the absolute value of the skewness and the value of the kurtosis of height distributions converge to $0.2\leq |S|\leq 0.3$ and $0\leq Q\leq 0.5$, respectively. Despite the low accuracy of these results, they give additional support to a recent claim of KPZ scaling in oligomer films. However, there are significant finite-size effects in the scaled height distributions of models with large local slopes, such as ballistic deposition, which suggests that comparison of height distributions must not be used to rule out KPZ scaling. On the other hand, roughness distributions of the same models show good data collapse, with negligible dependence on time and window size. The estimates of skewness and kurtosis for roughness distributions are $1.7\leq S\leq 2$ and $3\leq Q\leq 7$. A stretched exponential tail was found, which seems to be a particular feature of KPZ systems in 2+1 dimensions. Moreover, the KPZ roughness distributions cannot be fitted by those of $1/f^α$ noise. This study suggests that the roughness distribution is the best option to test KPZ scaling in the growth regime, and provides quantitative data for future comparison with other models or experiments.

cond-mat.stat-mech↗

arXiv2006

Island coarsening in one-dimensional models with partially and completely reversible aggregation

Using computer simulations and scaling ideas, we study one-dimensional models of diffusion, aggregation and detachment of particles from islands in the post-deposition regime, i. e. without flux. The diffusion of isolated particles takes place with unit rate, aggregation occurs immediately upon contact with another particle or island, and detachment from an island occurs with rate epsilon = exp(-E/kT), where E is the related energy barrier. In the partially reversible model, dissociation is limited to islands of size larger than a critical value i, while in the completely reversible model there is no restriction to that process (infinite i). Extending previous simulation results for the completely reversible case, we observe that a peaked island size distribution in the intermediate time regime, in which the mean island size is increasing, crosses over to the theoretically predicted exponentially decreasing distribution at long times. It contrasts with the partially reversible model, in which peaked distributions are obtained until the long time frozen state, which is attained with a crossover time $τ\sim \frac{i^3}ε$. The mean island size at saturation varies as $S_{sat}\approx 2i+Cε$ (C constant), while the completely reversible case shows an Ahrrenius dependence of the mean island size, $S\sim ε^{-1/2}$. Thus, for different coverages, the effect of the critical size i on the geometric features is much stronger than that of epsilon, which may be used to infer the relevance of size-dependent detachment rates in real systems and other models.

cond-mat.stat-mech↗