arXiv subjects

Rodolfo Cuerno

Publications and source records attributed to Rodolfo Cuerno.

At least 37 records · Page 2Linked to original sources

arXiv2013

Strong anisotropy in two-dimensional surfaces with generic scale invariance: Non-linear effects

We expand a previous study [Phys. Rev. E 86, 051611 (2012)] on the conditions for occurrence of strong anisotropy (SA) in the scaling properties of two-dimensional surfaces displaying generic scale invariance. There, a natural Ansatz was proposed for SA, which arises naturally when analyzing data from e.g. thin-film production experiments. The Ansatz was tested in Gaussian (linear) models of surface dynamics and in non-linear models, like the Hwa-Kardar (HK) equation [Phys. Rev. Lett. 62, 1813 (1989)], which are susceptible of accurate approximations through the former. In contrast, here we analyze non-linear equations for which such type of approximations fail. Working within generically-scale-invariant situations, and as representative case studies, we formulate and study a generalization of the HK equation for conserved dynamics, and reconsider well-known systems, such as the conserved and the non-conserved anisotropic Kardar-Parisi-Zhang equations. Through the combined use of Dynamic Renormalization Group analysis and direct numerical simulations, we conclude that the occurrence of SA in two-dimensional surfaces requires dynamics to be conserved. We find that, moreover, SA is not generic in parameter space but requires, rather, specific shapes from the terms appearing in the equation of motion, whose justification needs detailed information on the dynamical process that is being modeled in each particular case.

cond-mat.stat-mech↗

arXiv2013

Dimensional fragility of the Kardar-Parisi-Zhang universality class

We assess the dependence on substrate dimensionality of the asymptotic scaling behavior of a whole family of equations that feature the basic symmetries of the Kardar-Parisi-Zhang (KPZ) equation. Even for cases in which, as expected from universality arguments, these models display KPZ values for the critical exponents and limit distributions, their behavior deviates from KPZ scaling for increasing system dimensions. Such a fragility of KPZ universality contradicts naive expectations, and questions straightforward application of universality principles for the continuum description of experimental systems.

cond-mat.stat-mech↗

arXiv2012

Strong anisotropy in surface kinetic roughening: analysis and experiments

We report an experimental assessment of surface kinetic roughening properties that are anisotropic in space. Working for two specific instances of silicon surfaces irradiated by ion-beam sputtering under diverse conditions (with and without concurrent metallic impurity codeposition), we verify the predictions and consistency of a recently proposed scaling Ansatz for surface observables like the two-dimensional (2D) height Power Spectral Density (PSD). In contrast with other formulations, this Ansatz is naturally tailored to the study of two-dimensional surfaces, and allows to readily explore the implications of anisotropic scaling for other observables, such as real-space correlation functions and PSD functions for 1D profiles of the surface. Our results confirm that there are indeed actual experimental systems whose kinetic roughening is strongly anisotropic, as consistently described by this scaling analysis. In the light of our work, some types of experimental measurements are seen to be more affected by issues like finite space resolution effects, etc. that may hinder a clear-cut assessment of strongly anisotropic scaling in the present and other practical contexts.

cond-mat.mtrl-sci↗

arXiv2012

Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models

Among systems that display generic scale invariance, those whose asymptotic properties are anisotropic in space (strong anisotropy, SA) have received a relatively smaller attention, specially in the context of kinetic roughening for two-dimensional surfaces. This is in contrast with their experimental ubiquity, e.g. in the context of thin film production by diverse techniques. Based on exact results for integrable (linear) cases, here we formulate a SA Ansatz that, albeit equivalent to existing ones borrowed from equilibrium critical phenomena, is more naturally adapted to the type of observables that are measured in experiments on the dynamics of thin films, such as one and two-dimensional height structure factors. We test our Ansatz on a paradigmatic nonlinear stochastic equation displaying strong anisotropy like the Hwa-Kardar equation [Phys. Rev. Lett. 62, 1813 (1989)], that was initially proposed to describe the interface dynamics of running sand piles. A very important role to elucidate its SA properties is played by an accurate (Gaussian) approximation through a non-local linear equation that shares the same asymptotic properties.

cond-mat.stat-mech↗

arXiv2012

Universality of cauliflower-like fronts: from nanoscale thin films to macroscopic plants

Chemical vapor deposition (CVD) is a widely used technique to grow solid materials with accurate control of layer thickness and composition. Under mass-transport-limited conditions, the surface of thin films thus produced grows in an unstable fashion, developing a typical motif that resembles the familiar surface of a cauliflower plant. Through experiments on CVD production of amorphous hydrogenated carbon films leading to cauliflower-like fronts, we provide a quantitative assessment of a continuum description of CVD interface growth. As a result, we identify non-locality, non-conservation, and randomness as the main general mechanisms controlling the formation of these ubiquitous shapes. We also show that the surfaces of actual cauliflower plants and combustion fronts obey the same scaling laws, proving the validity of the theory over seven orders of magnitude in length scales. Thus, a theoretical justification is provided, that had remained elusive thus far, for the remarkable similarity between the textures of surfaces found for systems that differ widely in physical nature and typical scales.

cond-mat.stat-mech↗

arXiv2012

Kardar-Parisi-Zhang asymptotics for the two-dimensional noisy Kuramoto-Sivashinsky equation

We study numerically the Kuramoto-Sivashinsky (KS) equation forced by external white noise in two space dimensions, that is a generic model for e.g. surface kinetic roughening in the presence of morphological instabilities. Large scale simulations using a pseudospectral numerical scheme allow us to retrieve Kardar-Parisi-Zhang (KPZ) scaling as the asymptotic state of the system, as in the 1D case. However, this is only the case for sufficiently large values of the coupling and/or system size, so that previous conclusions on non-KPZ asymptotics are demonstrated as finite size effects. Crossover effects are comparatively stronger for the 2D case than for the 1D system.

cond-mat.stat-mech↗

arXiv2012

Dynamic effects induced by renormalization in anisotropic pattern forming systems

The dynamics of patterns in large two-dimensional domains remains a challenge in non-equilibrium phenomena. Often it is addressed through mild extensions of one-dimensional equations. We show that full 2D generalizations of the latter can lead to unexpected dynamical behavior. As an example we consider the anisotropic Kuramoto-Sivashinsky equation, that is a generic model of anisotropic pattern forming systems and has been derived in different instances of thin film dynamics. A rotation of a ripple pattern by $90^{\circ}$ occurs in the system evolution when nonlinearities are strongly suppressed along one direction. This effect originates in non-linear parameter renormalization at different rates in the two system dimensions, showing a dynamical interplay between scale invariance and wavelength selection. Potential experimental realizations of this phenomenon are identified.

cond-mat.stat-mech↗

arXiv2011

Dynamical Renormalization Group Study for a Class of Non-local Interface Equations

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and the less studied case in which pattern formation occurs, for which flat surfaces are linearly unstable to periodic perturbations. We show that the latter leads to non-trivial scaling behavior in an appropriate parameter range when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that nevertheless does not correspond to the KPZ universality class. This novel asymptotic behavior is characterized by two scaling laws that fix the critical exponents to dimension-independent values, that agree with previous reports from numerical simulations and experimental systems. We show that the precise form of the linear stabilizing terms does not modify the hydrodynamic behavior of these equations. One of the scaling laws, usually associated with Galilean invariance, is shown to derive from a vertex cancellation that occurs (at least to one loop order) for any choice of linear terms in the equation of motion and is independent on the morphological stability of the surface, hence generalizing this well-known property of the KPZ equation. Moreover, the argument carries over to other systems like the Lai-Das Sarma-Villain equation, in which vertex cancellation is known {\em not to} imply an associated symmetry of the equation.

cond-mat.stat-mech↗

arXiv2011

Intrinsic geometry approach to surface kinetic roughening

A model for kinetic roughening of one-dimensional interfaces is presented within an intrinsic geometry framework that is free from the standard small-slope and no-overhang approximations. The model is meant to probe the consequences of the latter on the Kardar-Parisi-Zhang (KPZ) description of non-conserved, irreversible growth. Thus, growth always occurs along the local normal direction to the interface, with a rate that is subject to fluctuations and depends on the local curvature. Adaptive numerical techniques have been designed that are specially suited to the study of fractal morphologies and can support interfaces with large slopes and overhangs. Interface self-intersections are detected, and the ensuing cavities removed. After appropriate generalization of observables such as the global and local surface roughness functions, the interface scaling is seen in our simulations to be of the Family-Vicsek type for arbitrary curvature dependence of the growth rate, KPZ scaling appearing for large sytems sizes and sufficiently large noise amplitudes.

cond-mat.stat-mech↗

arXiv2010

Ion induced solid flow

Amorphous solids can flow over very long periods of time. Solid flow can also be artificially enhanced by creating defects, as by Ion Beam Sputtering (IBS) in which collimated ions with energies in the 0.1 to 10 keV range impact a solid target, eroding its surface and inducing formation of nanometric structures. Recent experiments have challenged knowledge accumulated during the last two decades so that a basic understanding of self-organized nano-pattern formation under IBS is still lacking. We show that considering the irradiated solid to flow like a highly viscous liquids can account for the complex IBS morphological phase diagram, relegating erosion to a subsidiary role and demonstrating a controllable instance of solid flow at the nanoscale. This new perspective can allow for a full harnessing of this bottom-up route to nanostructuring.

cond-mat.stat-mech↗

arXiv2008

Kinetic roughening in a realistic model of non-conserved interface growth

We provide a quantitative picture of non-conserved interface growth from a diffusive field making special emphasis on two main issues, the range of validity of the effective small-slopes (interfacial) theories and the interplay between the emergence of morphologically instabilities in the aggregate dynamics, and its kinetic roughening properties. Taking for definiteness electrochemical deposition as our experimental field of reference, our theoretical approach makes use of two complementary approaches: interfacial effective equations and a phase-field formulation of the electrodeposition process. Both descriptions allow us to establish a close quantitative connection between theory and experiments. Moreover, we are able to correlate the anomalous scaling properties seen in some experiments with the failure of the small slope approximation, and to assess the effective re-emergence of standard kinetic roughening properties at very long times under appropriate experimental conditions.

cond-mat.stat-mech↗

arXiv2008

Unified moving boundary model with fluctuations for unstable diffusive growth

We study a moving boundary model of non-conserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin film production by chemical vapor deposition and electrochemical deposition. The model also incorporates noise terms that account for fluctuations in the diffusive and in the attachment processes. A small slope approximation allows us to derive effective interface evolution equations (IEE) in which parameters are related to those of the full moving boundary problem. In particular, the form of the linear dispersion relation of the IEE changes drastically for slow or for instantaneous attachment kinetics. In the former case the IEE takes the form of the well-known (noisy) Kuramoto-Sivashinsky equation, showing a morphological instability at short times that evolves into kinetic roughening of the Kardar-Parisi-Zhang class. In the instantaneous kinetics limit, the IEE combines Mullins-Sekerka linear dispersion relation with a KPZ nonlinearity, and we provide a numerical study of the ensuing dynamics. In all cases, the long preasymptotic transients can account for the experimental difficulties to observe KPZ scaling. We also compare our results with relevant data from experiments and discrete models.

cond-mat.stat-mech↗

arXiv2008

Coupling of morphology to surface transport in ion-beam irradiated surfaces. I. Oblique incidence

We propose and study a continuum model for the dynamics of amorphizable surfaces undergoing ion-beam sputtering (IBS) at intermediate energies and oblique incidence. After considering the current limitations of more standard descriptions in which a single evolution equation is posed for the surface height, we overcome (some of) them by explicitly formulating the dynamics of the species that transport along the surface, and by coupling it to that of the surface height proper. In this we follow recent proposals inspired by ``hydrodynamic'' descriptions of pattern formation in aeolian sand dunes and ion-sputtered systems. From this enlarged model, and by exploiting the time-scale separation among various dynamical processes in the system, we derive a single height equation in which coefficients can be related to experimental parameters. This equation generalizes those obtained by previous continuum models and is able to account for many experimental features of pattern formation by IBS at oblique incidence, such as the evolution of the irradiation-induced amorphous layer, transverse ripple motion with non-uniform velocity, ripple coarsening, onset of kinetic roughening and other. Additionally, the dynamics of the full two-field model is compared with that of the effective interface equation.

cond-mat.mtrl-sci↗

arXiv2007

Self-organized surface nanopatterning by ion beam sputtering

The production of nanopatterns on the surfaces of targets irradiated by ion beams at low and intermediate energies has developed during the present decade to a salient degree of control over the main pattern features. However, there is still a wide experimental scatter in the type and relevance of various dynamic interfacial properties induced by this technique as a function of system type and parameters. In parallel, diverse theoretical models exist that differ in their capabilities to reproduce such a wide range of experimental features. We provide an overview of the most recent studies of nanoripple and dot production by ion-beam sputtering, with special attention to the comparison between experiments and (continuum) models, and with a focus on those issues that remain open or, at least, ambiguous. These are perhaps more evident for the case of nanodot patterns on amorphizable targets than for the case of nanoripples due, possibly, to the relative novelty of the former. The pattern properties to be considered are those of potential increased technological importance, such as the variation of nanodot size with parameters like ion energy, target temperature and sputtering time (i.e., fluence), as well as the conditions under which the quality of the pattern order is enhanced, issues such as wavelength coarsening and order enhancement becoming relevant.

cond-mat.mtrl-sci↗

arXiv2007

Short-range stationary patterns and long-range disorder in an evolution equation for one-dimensional interfaces

A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell pattern develops with constant wavelength and amplitude at intermediate distances, while the profile is disordered and rough at larger distances. Moreover, for a wide range of parameters the lateral extent of ordered domains ranges up to tens of cells. This behavior is new in the context of dynamics of surfaces or interfaces with morphological instabilities. We also provide analytical estimates for the stationary pattern wavelength and mean growth velocity.

cond-mat.stat-mech↗

arXiv2006

Non-linear ripple dynamics on amorphous surfaces patterned by ion-beam sputtering

Erosion by ion-beam sputtering (IBS) of amorphous targets at off-normal incidence frequently produces a (nanometric) rippled surface pattern, strongly resembling macroscopic ripples on aeolian sand dunes. Suitable generalization of continuum descriptions of the latter allows us to describe theoretically for the first time the main nonlinear features of ripple dynamics by IBS, namely, wavelength coarsening and non-uniform propagation velocity, that agree with similar results in experiments and discrete models. These properties are seen to be the anisotropic counterparts of in-plane ordering and (interrupted) pattern coarsening in IBS experiments on rotating substrates and at normal incidence.

cond-mat.stat-mech↗

arXiv2006

Single tensionless transition in the Laplacian roughening model

We report large scale Monte Carlo simulations of the equilibrium discrete Laplacian roughening (dLr) model, originally introduced as the simplest one accommodating the hexatic phase in two-dimensional melting. The dLr model is also relevant to surface roughening in molecular beam epitaxy (MBE). Our data suggest a single phase transition, possibly of the Kosterlitz-Thouless type, between a flat low-temperature phase and a rough, tensionless, high-temperature phase. Thus, earlier conclusions on the order of the phase transition and on the existence of a hexatic phase are seen as due to finite size effects, the phase diagram of the dLr model being similar to that of a continuum analog previously formulated in the context of surface growth by MBE.

cond-mat.stat-mech↗

arXiv2005

Self-Organized Ordering of Nanostructures Produced by Ion-Beam Sputtering

We study the self-organized ordering of nanostructures produced by ion-beam sputtering (IBS) of targets amorphizing under irradiation. By introducing a model akin to models of pattern formation in aeolian sand dunes, we extend consistently the current continuum theory of erosion by IBS. We obtain new non-linear effects responsible for the in-plane ordering of the structures, whose strength correlates with the degree of ordering found in experiments. Our results highlight the importance of redeposition and surface viscous flow to this nanopattern formation process.

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