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

Nicoli, Matteo; Castro, Mario; Cuerno, Rodolfo

doi:10.1088/1742-5468/2009/02/p02036

Cited by 17 publications

(45 citation statements)

References 48 publications

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“…From the data in table 1 and equation (5), we can estimate k D 0.75 cm s −1 , which is considerably higher than V = 2.4 × 10 −8 cm s −1 . Hence, the system can be assumed to be in the fast kinetics regime for which equation (1) is expected to hold [7][8][9]. In spite of the previous assessment of parameter values, still many microscopic details of the experimental setup cannot be measured or even estimated from data, mainly due to the limited resolution of the experimental measurements and also due to the coexistence of species both in the vapor phase and at the very same aggregate surface: to cite a few, the mean atomic volume of aggregating species at the surface, surface tension, or the capillarity length.…”

Section: Comparison With Experimentsmentioning

confidence: 99%

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

et al. 2012

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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 6 2 over seven orders of magnitude in length scales. Thus, a theoretical justification is provided, which had remained elusive so far, for the remarkable similarity between the textures of surfaces found for systems that differ widely in physical nature and typical scales. Contents

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Section: Comparison With Experimentsmentioning

confidence: 99%

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

et al. 2012

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“…Beyond their role as realistic descriptions of experimental interfaces (additional examples exist for electrodeposition [14] and for unstable flame propagation [29]), these equations are interesting for their combination of nonlocality and fluctuations, having remained poorly understood to date [7]. Moreover, they may account for similarities between diffusive and ballistic surface growth [8,11].…”

Section: Prl 102 256102 (2009) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

“…Moreover, unstable dispersion relations of the same form as in Eq. (1) have been seen to describe effectively (for 0 <<2, m ¼ 2) experiments of surface growth by electrodeposition [14]. While the stable version of Eq.…”

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confidence: 97%

Unstable Nonlocal Interface Dynamics

2009

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Nonlocal effects occur in many nonequilibrium interfaces, due to diverse physical mechanisms like diffusive, ballistic, or anomalous transport, with examples from flame fronts to thin films. While dimen sional analysis describes stable nonlocal interfaces, we show the morphologically unstable condition to be nontrivial. This is the case for a family of stochastic equations of experimental relevance, paradigmatically including the Michelson Sivashinsky system. For a whole parameter range, the asymptotic dynamics is scale invariant with dimension independent exponents reflecting a hidden Galilean symmetry. The usual Kardar Parisi Zhang nonlinearity, albeit irrelevant in that parameter range, plays a key role in this behavior. DOI: 10.1103/PhysRevLett.102.256102 PACS numbers: 68.35.Ct, 05.45. a, 47.54. r The interface dynamics of many nonequilibrium systems arises from the interplay between nonlocal interactions and morphological instabilities. Examples range from flame front propagation to thin film growth [1]. Often, although the basic physical interactions are short-ranged and local, the evolution is driven by nonlocal effects implicitly (via projection of the overall dynamics on the interface) or explicitly (as in elastic media or viscous flow) [1]. These nonlocalities appear in many fields, diffusion-limited growth being a prominent example. Here, although diffusion events of aggregating units are local, the morphology of a growing cluster is dominated by shadowing of the most prominent surface features over less exposed ones. Hence, the local growth velocity depends on the global surface shape. This moreover leads to the classic Mullins-Sekerka (MS) morphological instability [1], whereby prominent features grow faster. Still, nonlocality and morphological stability are independent properties. Thus, we may consider diffusion-limited erosion (DLE) [2,3], qualitatively relevant to experiments on, e.g., ion irradiation smoothing [4]. Here the most exposed surface features are eroded faster, leading to nonlocal stable interface evolution in which differences in surface height are smoothed out.Often [3], the nonequilibrium dynamics of these interfaces can be cast into a stochastic equation for the surface height hðr; tÞ at time t and point r on a d-dimensional substrate. Assuming translational and rotational symmetry, we propose the following equation (after space Fourier transform F )Here, , m, n, K, and N are positive constants (0 < 2, m ! 2, and n > m; see below), the linear dispersionproviding the amplification rate for periodic disturbances (with wave vector k) of a planar interface. The term proportional to is the Kardar-Parisi-Zhang (KPZ) nonlinearity, generically expected whenever the interface evolves in the absence of conservation laws [3], while k ðtÞ is Gaussian uncorrelated noise. Indeed, equations like (1) have been derived from constitutive laws, and from symmetry arguments, as weakly nonlinear, long wavelength (k ¼ jkj ( 1) descriptions of a variety of systems [1,3,6]. Locality holds whenever ! ...

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“…However, those works did not analyze this crossover in detail because their focus were long time growth properties, such as surface instability and anomalous scaling of the roughness. Most theoretical approaches for electrodeposition have the same focus; for instance, in systems with instability control mechanisms, a transition from initial unstable growth to standard kinetic roughening may be observed [10,11]. Instead, the short time crossover analyzed here occurs in the opposite direction: from initial kinetic roughening dominated by surface diffusion [36,37] to long time instability developement.…”

Section: Introductionmentioning

confidence: 99%

Crossover from compact to branched films in electrodeposition with surface diffusion

2017

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We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute activated surface diffusion, which is represented by a sequence of random hops to neighboring lattice sites with a maximum of G hop attempts (G≫1), a detachment probability ε<1 per neighboring particle, and a no-desorption condition. Computer simulations show the formation of a compact wetting layer followed by the growth of branched deposits. The maximal thickness z_{c} of that layer increases with G but is weakly affected by ε. A scaling approach describes the crossover from smooth film growth to unstable growth and predicts z_{c}∼G^{γ}, with γ=1/[2(1-ν)]≈0.43, where ν≈0.30 is the inverse of the dynamical exponent of the Villain-Lai-Das Sarma equation that describes the initial roughening. Using previous results for related deposition models, the thickness z_{c} can be predicted as a function of an activation energy for terrace surface diffusion and the temperature, and the small effects of the parameter ε are justified. These predictions are confirmed by the numerical results with good accuracy. We discuss possible applications, with a particular focus on the growth of multifuncional structures with stacking layers of different porosity.

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

Cited by 17 publications

References 48 publications

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

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

Unstable Nonlocal Interface Dynamics

Crossover from compact to branched films in electrodeposition with surface diffusion

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