Characteristic growth of chemical gardens from mixtures of two salts (original) (raw)
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Journal of colloid and …, 2002
Chemical gardens are the plant-like structures formed upon placing together a soluble metal salt, often in the form of a seed crystal, and an aqueous solution of one of many anions, often sodium silicate. We have observed the development of chemical gardens with Mach-Zehnder interferometry. We show that a combination of forced convection from osmosis and free convection from buoyancy, together with chemical reaction, is responsible for their morphogenesis. C 2002 Elsevier Science (USA)
Spiral precipitation patterns in confined chemical gardens
Proceedings of the National Academy of Sciences, 2014
Chemical gardens are mineral aggregates that grow in three dimensions with plant-like forms and share properties with self-assembled structures like nanoscale tubes, brinicles or chimneys at hydrothermal vents. The analysis of their shapes remains a challenge, as their growth is influenced by osmosis, buoyancy and reaction-diffusion processes. Here we show that chemical gardens grown by injection of one reactant into the other in confined conditions feature a wealth of new patterns including spirals, flowers, and filaments. The confinement decreases the influence of buoyancy, reduces the spatial degrees of freedom and allows analysis of the patterns by tools classically used to analyze two-dimensional patterns. Injection moreover allows the study in controlled conditions of the effects of variable concentrations on the selected morphology. We illustrate these innovative aspects by characterizing quantitatively, with a simple geometrical model, a new class of self-similar logarithmic spirals observed in a large zone of the parameter space.
Genericity of confined chemical garden patterns with regard to changes in the reactants
The growth of chemical gardens is studied experimentally in a horizontal confined geometry when a solution of metallic salt is injected into an alkaline solution at a fixed flow rate. Various precipitate patterns are observed—spirals, flowers, worms or filaments—depending on the reactant concentrations. In order to determine the relative importance of the chemical nature of the reactants and physical processes in the pattern selection, we compare the structures obtained by performing the same experiment using different pairs of reactants of varying concentrations with cations of calcium, cobalt, copper, and nickel, and anions of silicate and carbonate. We show that although the transition zones between different patterns are not sharply defined, the morphological phase diagrams are similar in the various cases. We deduce that the nature of the chemical reactants is not a key factor for the pattern selection in the confined chemical gardens studied here and that the observed morphologies are generic patterns for precipitates possessing a given level of cohesiveness when grown under certain flow conditions.
On evaluation of the equations for the growth kinetics of ellipsoidal precipitates
Scripta Metallurgica, 1984
Grain boundary allotriomorphs are probably most accurately modeled as double spherical caps (1). However, a solution to the diffusional growth problem for this morphology has not yet been reported, A reasonable approximation of the double spherical cap model is provided by the oblate ellipsoid of revolution.
Journal of Materials Science, 2007
We present a mathematical model to describe competitive growth of spherical precipitates in reactioncontrolled systems. In this model the flux of solute atoms through the interface depends on the interface migration velocity and on the differences of chemical potential at the interface. The growth-rate obtained is dependent on the precipitate radius, much like in the diffusion-controlled case. Numerical simulations were performed using a modified finite-difference approach where the time-step increase changes during evolution to avoid dissolution of more than one precipitate each step. By using the continuity equation we obtained an analytical function that represents the self-similar shape of the precipitate-size distribution dependent of the growth-parameter m. The effect of m on the coarsening evolution was investigated. Our results show that the precipitate size distribution obtained from the numerical simulations agrees well with the analytical solution. As predicted by the theory, we obtained the growth parameter (m = 4) and the temporal dependence of the mean-radius (t 1/2) different of the diffusion case, m = 6.75 and t 1/3. We also show that the self-similarity of the PSD is independent of the initial PSD.
Oscillations of a chemical garden
Physical Review E, 2008
When soluble metal salts are placed in a silicate solution, chemical gardens grow. These gardens are treelike structures formed of long, thin, hollow tubes. Here we study one particular case: a calcium nitrate pellet in a solution of sodium trisilicate. We observe that tube growth results from a relaxation oscillation. The average period and the average growth rate are approximately constant for most of the structures growth. The period does fluctuate from cycle to cycle, with the oscillation amplitude proportional to the period. Based on our observations, we develop a model of the relaxation oscillations which calculates the average oscillation period and the average tube radius in terms of fundamental membrane parameters. We also propose a model for the average tube growth rate. Predictions are made for future experiments.
Growth kinetics and morphological stability of precipitates in 3-D: a phase field study
arXiv: Materials Science, 2014
We have studied the growth kinetics of isolated precipitates growing from a supersaturated matrix in 3-dimensions (3-D) using phase field models; we assume isotropic interfacial energy consider both constant and variable diffusivity. We report and compare our numerical growth rates with the classic analytical solutions of Zener and Frank (ZF). The numerical results deviate from the analytical ones. These deviations can be understood in terms of the generalised Gibbs-Thomson effect. Specifically, due to the higher capillary contribution in 3-D (curvature is twice for a sphere compared to a circle), the precipitate growth kinetics deviates more from ZF in 3-D as compared to 2-D. In addition, the kinetic parameter associated with the normal velocity of the precipitate-matrix interface also modifies the deviation of the precipitate composition from its equilibrium value and hence its growth kinetics. In phase field models (such as the one used by us) which use a combination of Allen-Cah...
Chemical-Garden Formation, Morphology, and Composition. I. Effect of the Nature of the Cations
Langmuir, 2011
We have grown chemical gardens in different sodium silicate solutions from several metal-ion salts-calcium chloride, manganese chloride, cobalt chloride, and nickel sulfate-with cations from period 4 of the periodic table. We have studied their formation process using photography, examined the morphologies produced using scanning electron microscopy (SEM), and analyzed chemical compositions using X-ray powder diffraction (XRD) and energy dispersive X-ray analysis (EDX) to understand better the physical and chemical processes involved in the chemical-garden reaction. We have identified different growth regimes in these salts that are dependent on the concentration of silicate solution and the nature of the cations involved.
Analytical treatment of diffusion during precipitate growth in multicomponent systems
Acta Materialia, 2008
We propose an approximate growth rate equation that takes into account both cross-diffusion and high supersaturations for modeling precipitation in multicomponent systems. We then apply it to an Fe-alloy in which interstitial C atoms diffuse much faster than substitutional solutes, and predict a spontaneous transition from slow growth under ortho-equilibrium to fast growth under the non-partitioning local equilibrium condition. The transition is caused by the decrease in the Gibbs-Thomson effect as the growing particle becomes larger. The results agree with DICTRA simulations where full diffusion fields are calculated.
Mixed-mode growth of a multicomponent precipitate in the quasi-steady state regime
Materials Theory, 2018
An exact analytical solution of the Fick's second law was developed and applied to the mixed-mode growth of a multicomponent ellipsoidal precipitate growing with constant eccentricities in the quasi-stationary regime. The solution is exact if the nominal composition, equilibrium concentrations and material properties are assumed constant, and can be applied to compounds having no limitations in the number of components. The solution was compared to the solution calculated by a diffusion-controlled application software and it was found that the solute concentrations at the interface can be determined knowing only the nominal composition, the full equilibrium concentrations and the coefficients of diffusion. The thermodynamic calculations owing to find alternative tie-lines are proven to be useless in the mixed-mode model. From this, it appears that the search of alternative tie-lines is computationally counterproductive, even when the interface has a very high mobility. A more efficient computational scheme is possible by considering that a moving interface is not at equilibrium.