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Register a new userPattern formation during diffusion limited transformations in solids
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We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase equilibrium conditions. We formulate equations for the interface kinetics similar to dendritic growth and study the growth of a stable phase from a metastable solid in both a channel geometry and in free space. We perform sharp interface calculations based on Greens function methods and phase field simulations, supplemented by analytical investigations. For pure dilatational transformations we find a single growing finger with symmetry breaking at higher driving forces, whereas for shear transformations the emergence of twin structures can be favorable. We predict the steady state shapes and propagation velocities, which can be higher than in conventional dendritic growth.
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A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and qualitative behavior of some admissible patterns, namely traveling wave solutions, to this singular reaction-difusion equation. We show the existence and qualitative behavior of different types of traveling waves: classical profiles for wave speeds high enough, and discontinuous waves that are reminiscent of hyperbolic shock waves when the wave speed lowers below a certain threshold. Some of these solutions are of particular relevance as they provide models by which the whole solution (and not just the bulk of it, as it is the case with classical traveling waves) spreads through the medium with finite speed.
We present a model for the interplay between the fundamental phenomena responsible for the formation of nanostructures by metalorganic vapour phase epitaxy on patterned (001)/(111)B GaAs substrates. Experiments have demonstrated that V-groove quantum wires and pyramidal quantum dots form as a consequence of a self-limiting profile that develops, respectively, at the bottom of V-grooves and inverted pyramids. Our model is based on a system of reaction-diffusion equations, one for each crystallographic facet that defines the pattern, and include the group III precursors, their decomposition and diffusion kinetics (for which we discuss the experimental evidence), and the subsequent diffusion and incorporation kinetics of the group-III atoms released by the precursors. This approach can be applied to any facet configuration, including pyramidal quantum dots, but we focus on the particular case of V-groove templates and offer an explanation for the self-limited profile and the Ga segregation observed in the V-groove. The explicit inclusion of the precursor decomposition kinetics and the diffusion of the atomic species revises and generalizes the earlier work of Basiol et al. [Phys. Rev. Lett. 81, 2962 (1998); Phys. Rev. B 65, 205306 (2002)] and is shown to be essential for obtaining a complete description of self-limiting growth. The solution of the system of equations yields spatially resolved adatom concentrations, from which average facet growth rates are calculated. This provides the basis for determining the conditions that yield selflimiting growth. The foregoing scenario, previously used to account for the growth modes of vicinal GaAs(001) during MOVPE and the step-edge profiles on the ridges of vicinal surfaces patterned with V-grooves, can be used to describe the morphological evolution of any template composed of distinct facets.
Polymeric nanoparticles (NPs) have a great application potential in science and technology. Their functionality strongly depends on their size. We present a theory for the size of NPs formed by precipitation of polymers into a bad solvent in the presence of a stabilizing surfactant. The analytical theory is based upon diffusion-limited coalescence kinetics of the polymers. Two relevant time scales, a mixing and a coalescence time, are identified and their ratio is shown to determine the final NP diameter. The size is found to scale in a universal manner and is predominantly sensitive to the mixing time and the polymer concentration if the surfactant concentration is sufficiently high. The model predictions are in good agreement with experimental data. Hence the theory provides a solid framework for tailoring nanoparticles with a priori determined size.
We develop continuum theory of self-assembly and pattern formation in metallic microparticles immersed in a poorly conducting liquid in DC electric field. The theory is formulated in terms of two conservation laws for the densities of immobile particles (precipitate) and bouncing particles (gas) coupled to the Navier-Stokes equation for the liquid. This theory successfully reproduces correct topology of the phase diagram and primary patterns observed in the experiment [Sapozhnikov et al, Phys. Rev. Lett. v. 90, 114301 (2003)]: static crystals and honeycombs and dynamic pulsating rings and rotating multi-petal vortices.
A microscopic model of the effect of unbinding in diffusion limited aggregation based on a cellular automata approach is presented. The geometry resembles electrochemical deposition - ``ions diffuse at random from the top of a container until encountering a cluster in contact with the bottom, to which they stick. The model exhibits dendritic (fractal) growth in the diffusion limited case. The addition of a field eliminates the fractal nature but the density remains low. The addition of molecules which unbind atoms from the aggregate transforms the deposit to a 100% dense one (in 3D). The molecules are remarkably adept at avoiding being trapped. This mimics the effect of so-called ``leveller molecules which are used in electrochemical deposition.
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