Fractal structure and cluster statistics of zinc-metal trees de- posited on a line electrode

The fractal correlation between relaxation dynamics and atomic-level structures observed in metallic glasses by computer simulation

Hierarchical clustering analysis shows that the activating atoms are excited in a cooperative and avalanche-like model to form activating units. Interestingly, a fractal correlation is found between the number and size of the activating units.

Fractal structure formation from Ag nanoparticle films on insulating substrates

Two dimensional (2D) fractal structures were observed to form from fairly uniform Ag island films (equivalent mass thicknesses of 1.5 and 5 nm) on insulating silicon dioxide surfaces (thermally grown silicon oxide on Si or quartz) upon immersion in deionized water. This result is distinctly different from the previously observed three-dimensional (3D) growth of faceted Ag nanocrystals on conductive surfaces (ITO and graphite) as the result of an electrochemical Ostwald ripening process, which also occurs on native oxide covered silicon surfaces as reported here. The fractal structures formed by diffusion-limited aggregation (DLA) of Ag species on the insulating surfaces. We present the experimental observation of this phenomenon and discuss some possible mechanisms for the DLA formation.

Ballistic deposition on deterministic fractals: observation of discrete scale invariance

The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established Family-Vicsek dynamic scaling approach. Systematic deviations from that standard scaling law are observed, suggesting that significant scaling corrections have to be introduced in order to achieve a more accurate understanding of the behavior of the interface. Subsequently, we study the internal structure of the growing aggregates that can be rationalized in terms of the scaling behavior of frozen trees, i.e., structures inhibited for further growth, lying below the growing interface. It is shown that the rms height (h_{s}) and width (w_{s}) of the trees of size s obey power laws of the form h_{s} proportional, variants;{nu_{ parallel}} and w_{s} proportional, variants;{nu_{ perpendicular}} , respectively. Also, the tree-size distribution (n_{s}) behaves according to n_{s} approximately s;{-tau} . Here, nu_{ parallel} and nu_{ perpendicular} are the correlation length exponents in the directions parallel and perpendicular to the interface, respectively. Also, tau is a critical exponent. However, due to the interplay between the discrete scale invariance of the underlying fractal substrates and the dynamics of the growing process, all these power laws are modulated by logarithmic periodic oscillations. The fundamental scaling ratios, characteristic of these oscillations, can be linked to the (spatial) fundamental scaling ratio of the underlying fractal by means of relationships involving critical exponents. We argue that the interplay between the spatial discrete scale invariance of the fractal substrate and the dynamics of the physical process occurring in those media is a quite general phenomenon that leads to the observation of logarithmic-periodic modulations of physical observables.

Influence of Pinning Effects on the Electrochemical Formation of Silver Patterns in Agarose-Containing Sols and Gels

The formation of silver patterns via electrolysis from aqueous silver sulfate + x% w/v agarose sol and gel media, with and without supporting electrolyte, in a quasi-two-dimensional (2D) cylindrical cell at room temperature, is utilized as a reference system to investigate the complexity of pinning effects. From pattern morphology and electrochemical data, both delocalized and localized pinning in the bulk dominate the drift of the growth front, depending on the concentration of agarose in the heterogeneous media. Delocalized pinning results from mobile, small agarose aggregates at the growth front and from their accumulation by the front drift. For gels, localized pinning comes from their own percolated structure. A depinning/pinning transition is observed in going from sols to gels. The relative contribution of diffusion and advection in mass-transport-controlled silver electrodeposition depends on the plating bath composition. On the other hand, silver ion attachment to the cathode appears to be interfered with by some screening caused by weakly adsorbed, mobile agarose aggregates at the metal surface without slowing down the rate of the electron-transfer step at the cathode. Their relative contribution of a delocalized, localized pinning and screening effect to a great extent determines the morphology and transition in the growth mode of silver patterns in both media. The analysis of charge and current transients and the corresponding silver pattern morphologies for open and dense radial patterns is made. Results are qualitatively simulated with a novel, rather simple cellular automaton algorithm.

Aggregation process on complex networks

We study the dynamics of the aggregation of particles and the evolution of the mass distribution, on a complex network which is built following the Watts-Strogatz model. The particles perform random walks following the links on the network, and aggregate when they meet other particles. On disordered networks the density of particles decays as t(-1), while on regular networks it decays as t(-1/2). For intermediate levels of network disorder the dynamics follows that of regular networks at intermediate density, and for low density the disorder of the network becomes relevant and the density decays as t(-1). The crossover time between these two regimes scales with network disorder as t approximately p(-2). We study also an annealed model for the aggregation process, in which the quenched disorder of the network is replaced by stochastic long range jumps in the particle dynamics. The annealed model is found to obey a different scaling with network disorder, with a crossover time t approximately p(-1).

Electrochemical growth of iron and cobalt arborescences under a magnetic field

Pattern formation in the electrochemical deposition of the magnetic Fe and Co metals from thin layers of Fe(SO4) or Co(SO4) aqueous solutions were investigated in circular geometry and under magnetic field. Sparse arborescences with few thick branches and dense arborescences with many thin branches can be generated when no magnetic field is applied. Unlike for nonmagnetic metals, no tendency towards growth spiraling or asymmetric branching is found out in magnetic field normal to the plane of the growth. The morphology of the deposits appears instead to become more sparse. Under in-plane magnetic field, the sparse arborescences get into a needle morphology, oriented along the field, while the dense arborescences show a circular to rectangular morphology symmetry breaking, one edge of the rectangle being parallel to the field. Unexpected in most instances, these magnetic field effects cannot be understood without invoking the magnetic dipolar interaction inside the magnetized growing aggregate together with its interaction with the applied field.

Formation of nanostructured copper filaments in electrochemical deposition

In this paper, we report in detail the studies of a different self-organized copper electrodeposition carried out in an ultrathin layer of CuSO4 electrolyte. On a macroscopic scale, the morphology of the electrodeposit is fingerlike. Microscopically, each fingering branch consists of long, straight copper filaments with periodic corrugated nanostructures. Branching rate of the electrodeposit is significantly decreased, compared with the patterns grown in conventional systems. Detailed information of the growth environment in the ultrathin electrodeposition system is provided, the formation mechanism of the periodic nanostructures on the deposit filaments is explored, and the origin of the significant descent of branching rate of the electrodeposit is discussed.

Stability analysis of branched silver electrodeposits: solid phase growth under a marginally stable regime

The mass-transport controlled growth of silver deposits at the early stage of multiple bump formation, and when a silver single needle growth regime is attained, are investigated. Linear stability analysis as proposed by Barkey, Muller, and Tobias [J. Electrochem. Soc. 136, 2199 (1989)] is applied to kinetic mesoscale data. A reasonable correlation between the current density and the average amplitude of unstable perturbation is established.

Pattern selection induced by electroconvection in the electrodeposition of iron

The morphology of iron electrodeposit is shown to relate closely to the pH of the electrolyte solution. Macroscopically, depending on the strength of the interbranch convection, which is associated with the concentration of H3O+ in the electrolyte, the deposit morphology varies from treelike pattern to meshlike pattern and dense-branching morphology. Microscopically the deposit is ramified and dense-branching at lower concentration of H3O+, while it becomes relatively smooth and stringy at higher H3O+ concentration. The symmetry of the convective vortices on the two sides of the growing tip is observed to decide the growth behavior of the tip. We suggest that H3O+ influences the pattern formation and pattern selection in the electrodeposition of iron from FeSO4 solution by either initiating interbranch convection or changing the effective interfacial energy of the deposit and the electrolyte.

Stromatolites in Precambrian carbonates: evolutionary mileposts or environmental dipsticks?

Stromatolites are attached, lithified sedimentary growth structures, accretionary away from a point or limited surface of initiation. Though the accretion process is commonly regarded to result from the sediment trapping or precipitation-inducing activities of microbial mats, little evidence of this process is preserved in most Precambrian stromatolites. The successful study and interpretation of stromatolites requires a process-based approach, oriented toward deconvolving the replacement textures of ancient stromatolites. The effects of diagenetic recrystallization first must be accounted for, followed by analysis of lamination textures and deduction of possible accretion mechanisms. Accretion hypotheses can be tested using numerical simulations based on modem stromatolite growth processes. Application of this approach has shown that stromatolites were originally formed largely through in situ precipitation of laminae during Archean and older Proterozoic times, but that younger Proterozoic stromatolites grew largely through the accretion of carbonate sediments, most likely through the physical process of microbial trapping and binding. This trend most likely reflects long-term evolution of the earth's environment rather than microbial communities.

Electrodeposition in support: concentration gradients, an ohmic model and the genesis of branching fractals

The technique of paper-supported copper electrodeposition provides examples of well-presented fractal and dense radial structures. The growths may be developed to reveal concentration gradients around the growths at low cell overpotential. Measurements for current and length scale against time, within a mid-range of cell overpotentials, fit an ohmic model of the growth conditions. To examine the relation of growth morphology to the micrometre-scale structure, we grew first at one overpotential and then continued at a lower overpotential. Electron microscope observations of this growth reveal a distinct change in microstructure from irregular to dentritic microcrystalline from the high to low potential respectively. The interface between the growths is a distinctive compact granular deposit. The granular deposit is unstable to branching and dendrite growth.