arXiv subjects

T. J. Oliveira

Publications and source records attributed to T. J. Oliveira.

At least 19 recordsLinked to original sources

arXiv2021

Phase diagram and critical properties of a two-dimensional associating lattice gas

We revisit the associating lattice gas~(ALG) introduced by Henriques \textit{et al.} [PRE 71, 031504 (2005)] in its symmetric version. In this model, defined on the triangular lattice, interaction between molecules occupying nearest-neighbor sites depends on their relative orientation, mimicking the formation of hydrogen bonds in network-forming fluids. Although all previous studies of this model agree that it has a disordered fluid (DF), a low-density liquid (LDL) and a high-density liquid (HDL) phase, quite different forms have been reported for its phase diagram. Here, we present a thorough investigation of its phase behavior using both transfer matrix calculations and Monte Carlo (MC) simulations, along with finite-size scaling extrapolations. Results in striking agreement are found using these methods. The critical point associated with the DF-HDL transition at full occupancy, dentified by Furlan and coworkers [Phys.~Rev.~E~{\bf 100}, 022109 (2019)] is shown to be one terminus of a {\it critical line} separating these phases. In opposition to previous simulation studies, we find that the transition between the DF and LDL phases is always discontinuous, similar to the LDL-HDL transition. The associated coexistence lines meet at the point where the DF-HDL critical line ends, making it critical-end-point. Overall, the form of the phase diagram observed in our simulations is very similar to that found in the exact solution of the model on a Husimi lattice. Our results confirm that, despite the existence of some waterlike anomalies in this model, it is unable to reproduce key features of the phase behavior of liquid water.

cond-mat.stat-mech↗

arXiv2020

Height fluctuations in homoepitaxial thin film growth: A numerical study

We report on the investigation of height distributions (HDs) and spatial covariances of two-dimensional surfaces obtained from extensive numerical simulations of the celebrated Clarke-Vvedensky (CV) model for homoepitaxial thin film growth. In this model, the effect of temperature, deposition flux, and strengths of atom-atom interactions are encoded in two parameters: the diffusion to deposition ratio $R=D/F$ and $\varepsilon$, which is related to the probability of an adatom "breaking" a lateral bond. We demonstrate that the HDs present a strong dependence on both $R$ and $\varepsilon$, and even after the deposition of $10^5$ monolayers (MLs) they are still far from the asymptotics in some cases. For instance, the temporal evolution of the HDs' skewness (kurtosis) displays a pronounced minimum (maximum), for small $R$ and $\varepsilon$, and only at long times it passes to increase (decrease) toward its asymptotic value. However, it is hard to determine whether they converge to a single value or different nonuniversal ones. For large $R$ and/or $\varepsilon$, on the other hand, these quantities clearly converge to the values expected for the Villain-Lai-Das Sarma (VLDS) universality class. A similar behavior is observed in the spatial covariances, but with weaker finite-time effects, so that rescaled curves of them collapse quite well with the one for the VLDS class at long times. Simulations of a model with limited mobility of particles, which captures some essential features of the CV model in the limit of irreversible aggregation ($\varepsilon=0$), reveal a similar scenario. Overall, these results point out that the study of fluctuations in homoepitaxial thin films' surfaces can be a very difficult task and shall be performed very carefully, once typical experimental films have $\lesssim 10^4$ MLs, so that their HDs and covariances can be in the realm of transient regimes.

cond-mat.stat-mech↗

arXiv2019

Geometry dependence in linear interface growth

The effect of geometry in the statistics of \textit{nonlinear} universality classes for interface growth has been widely investigated in recent years and it is well known to yield a split of them into subclasses. In this work, we investigate this for the \textit{linear} classes of Edwards-Wilkinson (EW) and of Mullins-Herring (MH) in one- and two-dimensions. From comparison of analytical results with extensive numerical simulations of several discrete models belonging to these classes, as well as numerical integrations of the growth equations on substrates of fixed size (flat geometry) or expanding linearly in time (radial geometry), we verify that the height distributions (HDs), the spatial and the temporal covariances are universal, but geometry-dependent. In fact, the HDs are always Gaussian and, when defined in terms of the so-called "KPZ ansatz" $[h \simeq v_{\infty} t + (Γt)^β χ]$, their probability density functions $P(χ)$ have mean null, so that all their cumulants are null, except by their variances, which assume different values in the flat and radial cases. The shape of the (rescaled) covariance curves is analyzed in detail and compared with some existing analytical results for them. Overall, these results demonstrate that the splitting of such university classes is quite general, being not restricted to the nonlinear ones.

cond-mat.stat-mech↗

arXiv2018

Circular Kardar-Parisi-Zhang interfaces evolving out of the plane

Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy$_2$ spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as a bowl, a cup, or any surface of revolution? To give an answer to this, we report here extensive numerical analyses of several one-dimensional KPZ models on substrates whose size enlarges as $\langle L(t) \rangle = L_0+ωt^γ$, while their mean height $\langle h \rangle$ increases as usual [$\langle h \rangle\sim t$]. We show that the competition between the $L$ enlargement and the correlation length ($ξ\simeq c t^{1/z}$) plays a key role in the asymptotic statistics of the interfaces. While systems with $γ>1/z$ have HDs given by GUE and the interface width increasing as $w \sim t^β$, for $γ<1/z$ the HDs are Gaussian, in a correlated regime where $w \sim t^{αγ}$. For the special case $γ=1/z$, a continuous class of distributions exists, which interpolate between Gaussian (for small $ω/c$) and GUE (for $ω/c \gg 1$). Interestingly, the HD seems to agree with the Gaussian symplectic ensemble (GSE) TW distribution for $ω/c \approx 10$. Despite the GUE HDs for $γ>1/z$, the spatial covariances present a strong dependence on the parameters $ω$ and $γ$, agreeing with Airy$_2$ only for $ω\gg 1$, for a given $γ$, or when $γ=1$, for a fixed $ω$. These results considerably generalize our knowledge on the 1D KPZ systems, unveiling the importance of the background space in their statistics.

cond-mat.stat-mech↗

arXiv2017

Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition

The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its short-time behavior. We tackle such issues by analyzing surface fluctuations of CdTe films deposited on polymeric substrates, based on a huge spatio-temporal surface sampling acquired through atomic force microscopy. A \textit{pseudo}-steady state (where average surface roughness and spatial correlations stay constant in time) is observed at initial times, persisting up to deposition of $\sim 10^{4}$ monolayers. This state results from a fine balance between roughening and smoothening, as supported by a phenomenological growth model. KPZ statistics arises at long times, thoroughly verified by universal exponents, spatial covariance and several distributions. Recent theoretical generalizations of the Family-Vicsek scaling and the emergence of log-normal distributions during interface growth are experimentally confirmed. These results confirm that high vacuum vapor deposition of CdTe constitutes a genuine 2D-KPZ system, and expand our knowledge about possible substrate-induced short-time behaviors.

cond-mat.stat-mech↗

arXiv2016

Grand-canonical solution of semi-flexible self-avoiding trails on the Bethe lattice

We consider a model of semi-flexible interacting self-avoiding trails (sISAT's) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting self-avoiding walks (SASAW) to investigate the collapse transition of polymers, with the attractive interactions being on site, as opposed to nearest-neighbor interactions in SASAW. The grand-canonical version of the sISAT model is solved on a four-coordinated Bethe lattice, and four phases appear: non-polymerized (NP), regular polymerized (P), dense polymerized (DP) and anisotropic nematic (AN), the last one present in the phase diagram only for sufficiently stiff chains. The last two phases are dense, in the sense that all lattice sites are visited once in AN phase and twice in DP phase. In general, critical NP-P and DP-P transition surfaces meet with a NP-DP coexistence surface at a line of bicritical points. The region in which the AN phase is stable is limited by a discontinuous critical transition to the P phase, and we study this somewhat unusual transition in some detail. In the limit of rods, where the chains are totally rigid, the P phase is absent and the three coexistence lines (NP-AN, AN-DP, and NP-DP) meet at a triple point, which is the endpoint of the bicritical line.

cond-mat.stat-mech↗

arXiv2016

Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation

We report extensive numerical simulations of growth models belonging to the nonlinear molecular beam epitaxy (nMBE) class, on flat (fixed-size) and expanding substrates (ES). In both $d=1+1$ and $2+1$, we find that growth regime height distributions (HDs), and spatial and temporal covariances are universal, but are dependent on the initial conditions, while the critical exponents are the same for flat and ES systems. Thus, the nMBE class does split into subclasses, as does the Kardar-Parisi-Zhang (KPZ) class. Applying the "KPZ ansatz" to nMBE models, we estimate the cumulants of the $1+1$ HDs. Spatial covariance for the flat subclass is hallmarked by a minimum, which is not present in the ES one. Temporal correlations are shown to decay following well-known conjectures.

cond-mat.stat-mech↗

arXiv2016

Point Island Models for Nucleation and Growth of Supported Nanoclusters during Surface Deposition

Point island models (PIMs) are presented for the formation of supported nanoclusters (or islands) during deposition on flat crystalline substrates at lower submonolayer coverages. These models treat islands as occupying a single adsorption site, although carrying a label to track their size (i.e., they suppress island structure). However, they are particularly effective in describing the island size and spatial distributions. In fact, these PIMs provide fundamental insight into the key features for homogeneous nucleation and growth processes on surfaces. PIMs are also versatile being readily adapted to treat both diffusion-limited and attachment-limited growth, and also a variety of other nucleation processes with modified mechanisms. Their behavior is readily and precisely assessed by kinetic Monte Carlo simulation.

cond-mat.mes-hall↗

arXiv2016

Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: discrete 2D deposition-diffusion equation analysis

A discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating kinks along the step edges. Model energetics and kinetics appropriately account for binding of adatoms at steps and kinks, distinct terrace and edge diffusion rates, and possibly asymmetric barriers for attachment to steps. Analysis of adatom attachment fluxes as well as limiting values of adatom densities at step edges for non-uniform deposition scenarios allows determination of both permeability and kinetic coefficients. Behavior of these quantities is assessed as a function of key system parameters including kink density, step attachment barriers, and the step edge diffusion rate.

cond-mat.mes-hall↗

arXiv2015

Width and extremal height distributions of fluctuating interfaces with window boundary conditions

We present a detailed study of squared local roughness (SLRDs) and local extremal height distributions (LEHDs), calculated in windows of lateral size $l$, for interfaces in several universality classes, in substrate dimensions $d_s = 1$ and $d_s = 2$. We show that their cumulants follow a Family-Vicsek type scaling, and, at early times, when $ξ\ll l$ ($ξ$ is the correlation length), the rescaled SLRDs are given by log-normal distributions, with their $n$th cumulant scaling as $(ξ/l)^{(n-1)d_s}$. This give rise to an interesting temporal scaling for such cumulants $\left\langle w_n \right\rangle_c \sim t^{γ_n}$, with $γ_n = 2 n β+ {(n-1)d_s}/{z} = \left[ 2 n + {(n-1)d_s}/α \right] β$. This scaling is analytically proved for the Edwards-Wilkinson (EW) and Random Deposition interfaces, and numerically confirmed for other classes. In general, it is featured by small corrections and, thus, it yields exponents $γ_n$'s (and, consequently, $α$, $β$ and $z$) in nice agreement with their respective universality class. Thus, it is an useful framework for numerical and experimental investigations, where it is, usually, hard to estimate the dynamic $z$ and mainly the (global) roughness $α$ exponents. The stationary (for $ξ\gg l$) SLRDs and LEHDs of Kardar-Parisi-Zhang (KPZ) class are also investigated and, for some models, strong finite-size corrections are found. However, we demonstrate that good evidences of their universality can be obtained through successive extrapolations of their cumulant ratios for long times and large $l$'s. We also show that SLRDs and LEHDs are the same for flat and curved KPZ interfaces.

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

Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly

Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition between these phases is continuous at small concentrations of the small particles and discontinuous at larger concentrations, both transitions are separated by a tricritical point. Estimates of the central charge suggest that the critical line is in the Ising universality class, while the tricritical point has tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the total density as functions of the fugacity of small or large particles display a minimum in the disordered phase.

cond-mat.stat-mech↗

arXiv2015

Temperature effect on (2+1) experimental Kardar-Parisi-Zhang growth

We report on the effect of substrate temperature (T) on both local structure and long-wavelength fluctuations of polycrystalline CdTe thin films deposited on Si(001). A strong T-dependent mound evolution is observed and explained in terms of the energy barrier to inter-grain diffusion at grain boundaries, as corroborated by Monte Carlo simulations. This leads to transitions from uncorrelated growth to a crossover from random-to-correlated growth and transient anomalous scaling as T increases. Due to these finite-time effects, we were not able to determine the universality class of the system through the critical exponents. Nevertheless, we demonstrate that this can be circumvented by analyzing height, roughness and maximal height distributions, which allow us to prove that CdTe grows asymptotically according to the Kardar-Parisi-Zhang (KPZ) equation in a broad range of T. More important, one finds positive (negative) velocity excess in the growth at low (high) T, indicating that it is possible to control the KPZ non-linearity by adjusting the temperature.

cond-mat.stat-mech↗

arXiv2014

Interface fluctuations for deposition on enlarging flat substrates

We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all investigated models have asymptotic height distributions and spatial covariances in agreement with those expected for the KPZ subclass for curved surfaces. In $1+1$ dimensions, the height distribution and covariance are given by the GUE Tracy-Widom distribution and the Airy$_2$ process, instead of the GOE and Airy$_1$ foreseen for flat interfaces. These results imply that, when the KPZ class splits into the curved and flat subclasses, as conventionally considered, the expanding substrate may play a role equivalent to, or perhaps more important than the global curvature. Moreover, the translational invariance of the interfaces evolving on growing domains allowed us to accurately determine, in $2+1$ dimensions, the analogue of the GUE Tracy-Widom distribution for height distribution and that of the Airy$_2$ process for spatial covariance. Temporal covariance is also calculated and shown to be universal in each dimension and in each of the two subclasses. A logarithmic correction associated to the duplication of column is observed and theoretically elucidated. Finally, crossover between regimes with fixed-size and enlarging substrates is also investigated.

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

Surface and bulk properties of ballistic deposition models with bond breaking

We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is controlled through a probability $p$. These systems present a crossover, for small values of $p$, from random to correlated (KPZ) growth of surface roughness, which is studied through scaling arguments and Monte Carlo simulations on one- and two-dimensional substrates. We show that the crossover characteristic time $t_{\times}$ scales with $p$ according to $t_{\times}\sim p^{-y}$ with $y=(n+1)$ and that the interface width at saturation $W_{sat}$ scales as $W_{sat}\sim p^{-δ}$ with $δ= (n+1)/2$, where $n$ is either the maximal number of broken bonds or of dislodged suspended particles. This result shows that the sets of exponents $y=1$ and $δ=1/2$ or $y=2$ and $δ=1$ found in all previous works focusing on systems with this same type of crossover are not universal. Using scaling arguments, we show that the bulk porosity $P$ of the deposits scales as $P\sim p^{y-δ}$ for small values of $p$. This general scaling relation is confirmed by our numerical simulations and explains previous results present in literature.

cond-mat.stat-mech↗