Diffusion-limited Precipitation Research Articles

Growth of magnetic cobalt hexacyanoferrate nanoparticles onto bacterial cellulose nanofibers

Natural polymers templates capable to maneuver the growth and spatial distribution of functional nanoparticles have been furthering the development of a new generation of sustainable and versatile materials. Pure cellulose nanofibrils, biosynthesized by bacteria, naturally deliver a 3D interconnected network of lightweight, foldable and sustainable matrices. Cellulose membrane is an exceptional biodegradable and biocompatible and high mechanical strength substrate with a native fibrous structure that can be easily applied as a structure-directing host to produce nanosized materials with optical, electrical or magnetic properties. In this work, we investigated the preparation of magnetic membranes by using bacterial cellulose nanofibers to control the growth of molecule-based magnetic nanoparticles such as Prussian Blue analogs. Magnetic Cobalt–Prussian Blue (CoHCEFe) nanoparticles were synthesized in situ by hydrothermal method through a diffusion-limited precipitation process onto a bacterial cellulose nanofiber network. Scanning electron microscopy and atomic force microscopy clearly unveiled a homogeneous distribution of immobilized COHCEFe crystalline nanoparticles whose size ranges from 94 to 70 nm as a function of nanoparticle content (up 28 wt%). Magnetic force microscopy showed that these nanometric COHCEFe crystalline nanoparticles well dispersed in BC fibers network respond to the magnetic field applied to the MFM-tip. This nano/nano association approach can provide functionally advanced materials for application in catalysis, adsorption of radionuclides, energy generation, data storage, biosensing, optical and magnetic devices.

Experimental assessment of occurrences and stability of lead-bearing minerals in bacterial biofilms

Bio-induced precipitation of lead-bearing minerals is investigated in bacterial biofilms grown by Shewanella oneidensis MR-1 under aerobic conditions. Under the different conditions investigated, thermodynamic calculations establish that the stable mineral phases expected to precipitate are either wulfenite PbMoO4 or cerussite PbCO3. However, observations by electron microscopy show that the first solids precipitated within hours at the experimental solution/biofilm interface are crystals of about 20 nm in diameter of pyromorphite Pb5(PO4)3(OH,Cl). In Mo-bearing systems, the precipitation of the thermodynamically-predicted wulfenite phase is delayed compared to the abiotic experiment and is observed only after seven days of lead exposure. The initial lead phosphate crystals observed on the extracellular polymeric substances are assumed to result from concurrent local abundances of adsorbed Pb2+ ions and phosphate groups released by metabolically active cells. Scanning electron microscopy observations of samples milled by focused ion beam reveal effective diffusion-limited precipitation of pyromorphite within the well-preserved biofilm porosity.

Biofilm Growth and Fossil Form

Stromatolites are fossilized remains of microbial mats that stopped growing billions of years ago. A large class of them have similar conical shapes. Understanding their growth dynamics would seem like a daunting task. However, positing diffusion of calcium ions and inorganic carbon-based molecules in microbial mats and their diffusion-limited precipitation as the primary growth mechanisms, a mathematical model not only successfully predicts the conical shape but also concludes that the thickness of the ancient microbial mats was similar to that of modern-day mats.

Phase-field modeling of two-dimensional solute precipitation/dissolution: Solid fingers and diffusion-limited precipitation

Two-dimensional dendritic growth due to solute precipitation was simulated using a phase-field model reported earlier [Z. Xu and P. Meakin, J. Chem. Phys. 129, 014705 (2008)]. It was shown that diffusion-limited precipitation due to the chemical reaction at the solid-liquid interface has similarities with diffusion-limited aggregation (DLA). The diffusion-limited precipitation is attained by setting the chemical reaction rate much larger compared to the solute diffusion to eliminate the effect of the interface growth kinetics. The phase-field simulation results were in reasonable agreement with the analytical solutions. The fractal solid fingers can be formed in the diffusion-limited precipitation and have a fractal dimension measured d(f)=1.68, close to 1.64, the fractal dimensionality of large square lattice DLA clusters.

The Build-Up of Strain Fields in Czochralski-Si Observed in Real Time by High Energy X-Ray Diffraction

The build-up of strain fields caused by the precipitation of oxygen in Czochralski-silicon during annealing up to 1200°C and for process times up to 70 hours has been observed in real time by high energy x-ray diffraction. Five different processes are distinguished in the temperature evolution of the intensity and of the rocking width of the silicon 220-reflection. These features are attributed to different precipitation mechanisms. A fit to part of the data with a diffusion limited precipitation model leads to an activation energy for oxygen diffusion in silicon of 2.2 eV in the temperature range from 700°C to 950°C.

Global hydration kinetics of tricalcium silicate cement.

We reconsider a number of measurements for the overall hydration kinetics of tricalcium silicate pastes having an initial water to cement weight ratio close to 0.5. We find that the time dependent ratio of hydrated and unhydrated silica mole numbers can be well characterized by two power laws in time, x/(1-x) approximately (t/t(x))(psi). For early times t<t(x) we find an "accelerated" hydration (psi=5/2) and for later times t>t(x) a parabolic behavior (psi=1/2). The crossover time is estimated as t(x) approximately 16 h. We interpret these results in terms of a global second-order rate equation indicating that (a) hydrates catalyze the hydration process for t<t(x), (b) they inhibit further hydration for t>t(x), and (c) the value of the associated rate constant is of magnitude 6 x 10(-7) - 7 x 10(-6) l mol(-1) s(-1). We argue, by considering that the hydration process actually occurs via diffusion limited precipitation, that the exponents psi=5/2 and psi=1/2 directly indicate a preferentially plate-like hydrate microstructure. This is essentially in agreement with experimental observations of cellular hydrate microstructures for this class of materials.

Diffusion limited oxygen precipitation in silicon: Precipitate growth kinetics and phase formation

Published experimental data on silicon oxide precipitate growth kinetics are interpreted in the framework of the theory of Ham for diffusion limited precipitation. A growth law for plate-like, octahedral and spherical precipitates is derived showing a size dependence which varies as the square root of time. Using well accepted data for the solubility and the diffusion constant of oxygen in silicon, the calculations suggest that the precipitated phase is closer to SiO than to SiO2.

Long-term processes in a stabilized coal-waste block exposed to seawater

A stabilized waste block, formed by cementation of coal combustion wastes with portland cement and lime, was retrieved after 8-years exposure to a marine environment. The block was analyzed to obtain concentration profiles for major and minor elements. Combination of the major element profiles with semiquantitative X-ray diffraction results allowed identification of diffusion-limited precipitation and dissolution processes. The precipitation and dissolution processes moved as a sharp boundary from the surface toward the center of the block, penetrating about 10-20 mm in the 8 years

ON SQUARE HOLES IN PENNATE DIATOMS

Square holes observed in the walls of the pennate diatoms may be due to cubic crystals inside the silicalemma that interfere with silica deposition, or cause its dissolution shortly after deposition. Their presence is consistent with models of valve morphogenesis by diffusion limited precipitation of amorphous silica without any pre-pattern.

The precipitation of oxygen in silicon

The precipitation of oxygen in silicon has been studied over a wide temperature range, using a number of experimental methods including: kinetic rate data from infra red absorption in the 9 μm band at 4.2 K, Particle densities by optical scattering between 1.5-3.0 μm (large precipitates), chemical etching of defects (medium precipitates) and small angle neutron scattering (small precipitates). From the Ham theory of diffusion limited precipitation, a direct relation between the kinetic time constants and the equilibrium numbers and sizes of particles is predicted - which is confirmed by the results. This places emphasis on the need for precise diffusion data over a wide range. This has been explored by extending the above work with classical oxygen in-diffusion measurements up to 1250°C and stress dichroism in the range 350ȁ400°C, from which a value of D is obtained over 12 orders of magnitude with a single activation energy ȲE = 2.50 ± 0.15 eV. Recent results throw some light on the basic diffusion mechanism and the role of supersaturation and other impurities in the nucleation stage of this process.

Internal friction and thermal losses in Zn-Al eutectoid alloy

A Kê pendulum was used to determine the internal friction, Q -1, of Zn-Al eutectoid alloy (22 wt% Al) in relation to its microstructure. The internal friction for the as-quenched and slowly cooled samples from above the eutectoid temperature, showed an exponential rise with temperature, characteristic to existing phases and microstructure of the samples. The internal-friction value at any particular temperature decreased as the quenched, metastable state α'-phase transformed to (α + β) phases in thermodynamic equilibrium below the eutectoid temperature. The phase transformation was made by giving the prescribed heat-pulses to the as quenched samples. The energy activating the process responsible for the rise of Q -1 with temperature decreased from 0.544 × 10 -19 J for the α'-phase to 0.448 × 10 -19 J for the (α + β) phases at temperatures below the eutectoid temperature. This decrease was attributed to the role of the different phases in the relaxation mechanism responsible for this effect. The internal friction was used to assess the degree of transformation from the high-temperature phase to the low-temperature phase. Results were discussed in terms of Ham's theory of diffusion-limited precipitation of supersaturated solid solutions.

Precipitation of lithium in germanium

The precipitation of lithium in solid germanium has been measured: Li is diffused into Ge from an external phase consisting of a molten LiPb alloy; diffusion temperatures extend from 250 to 420°C. Precipitation is measured at 60°C. Results are consistent with Morin and Reiss' theory about the nature of precipitation sites and with Ham's theory of diffusion limited precipitation. Measurements of the rate of nuclei generation are in rough agreement with Lothe's theory of vacancy generation by dislocation climb, but are in substantial disagreement with earlier measurements of Morin and Reiss.

Precipitation studies of lead and selenium in single-crystal PbSe

The kinetics of precipitation in PbSe was studied as a function of the species precipitating and the precipitation temperature. This was accomplished by performing Hall effect measurements as a function of time and temperature. According to Ham's theory of diffusion-limited precipitation, the kinetics are described by: $$f(t) = 1 - \exp [ - (t/\tau )]^n $$ where the time constant τ and the power dependencen provide useful information about the rate-limiting process involved and the size, shape, and density of the precipitate particles. For the initial stage of precipitation of lead in PbSe an average value ofn=1.12 was experimentally determined. This value is indicative of spheroidally shaped precipitate particles, especially if preprecipitation exists. After approximately 50 pct of the lead precipitates, a longer τ process becomes rate-controlling andn in the above equation equzls 1/3. With respect to the size, which was on the order of 1000A in radius, and the shape of the lead precipitates, the kinetic predictions were found to be in good agreement with evidence provided by extraction replica techniques and electron microscopy. For the precipitation of selenium in PbSe an average value ofn=0.9 was experimentally determined. This value is indicative of cylindrically shaped precipitate particles, especially if preprecipitation exists. Utilizing the experimentally determined value for τ, an approximate size for the precipitate particles at equilibrium was calculated as being about 40A in radius and 3000A in length. Values obtained for the activation energy of precipitation, 0.84 ev for Pb, 1.23 ev for Se, agree very closely with those for the activation energy of diffusion, 0.83 ev for Pb, 1.20 ev for Se. This indicates that diffusion plays an important role in the precipitation of lead and selenium in PbSe.

Electron microscopic study of precipitates and defects in germanium and silicon

The precipitate particles and defects formed during precipitation of lithium from solid solution in germanium and silicon have been studied by transmission electron microscopy. Kinetic studies on the same systems have been reported previously. From the microscopic investigation, it has been determined that the precipitate particles in germanium are spherical, maintain a coherent interface with the parent phase, and are randomly distributed. The experimental evidence obtained from microscopy has been interpreted through the application of the theoretical work of Ashby and Brown on diffraction contrast of coherent, spherical precipitate particles. Various contrast effects in silicon have been noted. The number density of precipitate particles in germanium has been determined from electron micrographs. This number density has been compared to the number density obtained from precipitation experiments on the same sample, the precipitation number density determined using the theory of Ham on diffusion limited precipitation for spherical precipitate particles. The agreement is found to be quite good, covering a range of number densities 8 × 10 11 cm −3 to approximately 10 14 cm −3.

Diffusion-Limited Growth of Precipitate Particles

Diffusion-limited precipitation rates are calculated, using theoretical methods derived previously, for systems of precipitate particles which may change shape as they grow. General formulas are presented, including suitable short- and long-time approximations. Explicit growth laws are derived for systems in which particles are disks and rods subjected to various constraints. The growth exponent n in the short-time approximation is found to be 2 for disks of constant thickness. Rods of constant radius that capture atoms only near their ends have n=1. Both disks and rods of constant ratio of their long and short dimensions have n=3/2. These values contrast with growth laws suggested by Wert and Zener for disks and rods, for which they found n=5/2 and 2, respectively. It is shown that growth conditions at the edge of a growing particle are not constant in diffusion-limited circumstances if the entire surface of the particle acts as a sink.

Precipitation in Semiconductors

A brief review is given of the present status of precipitation phenomena in semiconductors. Recent theoretical advances in the analysis of diffusion-limited precipitation are described. The precipitation of Li and Si is discussed as an example of diffusion-limited precipitation in which metastable centers are observed, and the precipitation of Cu as an example to which formal nucleation theory appears to apply. A recent theory of the clustering of oxygen in Si is described and its significance in terms of the nucleation process is indicated. It is emphasized that a number of techniques are now available for the observation of tiny aggregates of impurities in semiconductors, and the need for a consistently microscopic theory of nucleation is pointed out.

Precipitation of Cu in Ge. II. Supersaturation Effects

Studies have been made on the precipitation kinetics of Cu from supersaturated solid solution in Ge crystals with dislocation densities 100/${\mathrm{cm}}^{2}$. We found that the precipitation rates are very strongly dependent upon the degree of supersation. We believe this is evidence for the nucleation of the precipitate particles upon a single type of nucleation site, whose identity has not been established. An attempt is made to fit the experimental data to the simple theory of nucleation in which $\ensuremath{\sigma}$, the surface tension in the phase boundary between precipitate and host lattice, and ${E}_{p}$, the structure-sensitive increase in strain energy in the crystal upon formation of the precipitate, are parameters. We find that the data can be fit by $\ensuremath{\sigma}\ensuremath{\approx}500\ifmmode\pm\else\textpm\fi{}50$ ergs/${\mathrm{cm}}^{2}$, and ${E}_{p}\ensuremath{\approx}(1\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ erg/atom, assuming spherical precipitates. No other information about these quantities is available for comparison. An appendix gives a simplified treatment of Ham's derivation of the kinetic law for diffusion-limited precipitation upon spherical precipitate particles, which relates the observed precipitation rate to the number of precipitate particles. Theory and experiment are in reasonable agreement.