Lifshitz Slyozov Wagner Theory Research Articles

Growth kinetics of [formula omitted] particles in [formula omitted]-Ti matrix studied by in situ small-angle X-ray scattering

Nucleation and growth kinetics of nanoparticles of hexagonal ω phase in a body-centered cubic β titanium matrix in single crystals of β-Ti alloys were investigated by small-angle X-ray scattering measured in situ during ageing at various temperatures up to 450°C. The experimental data were compared with numerical simulations based on a three-dimensional short-range order model of nanoparticle self-ordering. The X-ray contrast of the particles is caused by an inhomogeneous distribution of impurity atoms (Mo, Fe and Al), whose density profile around growing nanoparticles was simulated by solving the corresponding diffusion equation with moving boundary conditions. From the analysis of the experimental data we determined the mean distance and size of the nanoparticles and confirmed the validity of the ∝t1/3 growth law following from the Lifshitz–Slyozov–Wagner theory. From a detailed comparison of the experimental data with simulations we also assessed the diffusion coefficient of the impurity atoms and its activation energy.

Coarsening and Hardening Behaviors of Cu-Rich Precipitates in Super304H Austenitic Steel

The coarsening and hardening behaviors of Cu-rich precipitates in Super304H austenitic steel aged at 923 K, 973 K, and 1023 K (650 °C, 700 °C, and 750 °C), respectively, have been investigated through measuring the particle size by transmission electron microscopy and microhardness. The results showed the Cu-rich precipitates have a cubic-to-cubic crystallographic relationship and coherent interface with the austenitic matrix during long-time aging, and that the coarsening behavior of the Cu-rich particles can be predicted with the help of the Lifshitz–Slyozov–Wagner theory. The activation energy for coarsening of the Cu-rich precipitates was evaluated to be 212 ± 3 kJ/mol. The coarsening of Cu-rich precipitates is controlled mainly by the volume diffusion of copper atoms in the austenitic matrix. The contributions to the maximum microhardness occurring at different aging temperatures from precipitation strengthening range from about 17 to 25 pct. The strengthening of the Cu-rich precipitates arises mainly from the coherency strain and partially from stacking-fault strengthening.

Quantitative Phase Field Study on the Precipitation Dynamics of γ′ Phase in Ni-Based Superalloys with Different Concentration

A quantitative phase field simulation was performed on the dynamics evolution of γ′ (L12-Ni3X) phase in Ni-based superalloys, the microstructure, the volume fraction and the particle size distribution (PSD) of γ′ phase for Ni-Al alloys aged at 1173K with the Al concentration c=0.178, 0.180 and 0.182 were investigated, and the results were compared with Lifshitz-Slyozov-Wagner (LSW) theory and Brailsford-Wynblatt (BW) theory. As the Al concentration increases the γ′ phase morphology changed from the separated cuboidal shape to the connected rectangle shape, the nucleation and growth of γ′ phase became faster and the volume fraction of the γ′ phase increased. The average particle radius <r> of γ′ phase and the aging time t has a exponent relationship <r> ~ tn at the coarsening stage with the exponents n=0.313, 0.235 and 0.204 for c=0.178, 0.180 and 0.182, respectively. The peaks of the fitted PSDs are less than the predicted value from the LSW theory and the fitted PSDs are wider than that of LSW predicted, while they are similar to that of the BW theory as the Al concentration increases. The peaks appear at a smaller r/<r> than the predictions of the LSW and BW theories.

Static coarsening behavior of the lamellar alpha in Ti-17 alloy

Static coarsening behavior of Ti-17 alloy with the lamellar alpha structure has been investigated as a function of time at temperatures of 820°C and 860°C. The resultant microstructures have been characterized using scanning electron microscopy. Microstructure prior to heat treatment contained a fully lamellar alpha structure. Heat treatment at 820°C and 860°C resulted in the continuous coarsening of alpha lamellae. The coarsening rate decreases with heat treatment time. Static coarsening of Ti-17 alloy with the lamellar alpha was mainly controlled by termination migration mechanism. Solute atoms migrated from the termination or local defect positions of lamellae to the flat interface, leading to the coarsening or separation of the lamellar alpha. The coarsening behavior could be interpreted in terms of Lifshitz–Slyozov–Wagner (LSW) theory, and the kinetics equation could be established by the modified LSW theory model (d=Ktn). The coarsening coefficients n of Ti-17 alloy with the lamellar structure were determined to 0.33–0.4 for 820°C and 0.45–0.5 for 860°C, respectively. Therefore, the coarsening was more likely influenced by bulk diffusion at 820°C, and controlled by interface reaction at 860°C. In addition, a mathematical model was developed to predict static coarsening rate of the lamellar alpha of Ti-17 alloy. The results showed that the model can provide a relatively reliable prediction for static coarsening behavior of the lamellar structure of Ti-17 alloy.

Green synthesis and growth kinetics of nanosilver under bio-diversified plant extracts influence

In this report, synthesis, growth and formation kinetics of silver nanoparticles mediated by various plant extracts in their biodiversity have been monitored using UV–Vis spectrophotometer by sampling at time intervals during bioreduction process. Plasmon band resonance of the silver nanoparticles was observed as the reaction progresses indicating nucleation and particle formation. There were cases of red shifting indicating particle size increase. In the bioreduction process, onset of nanoparticle nucleation and growth were observed within 2, 5, 10 or 30 min and eventual formation of spherical or quazi-spherical amidst twinned morphology as determined by transmission electron microscope (TEM). The nanosilver growth kinetics mechanism has been probed using a time-resolved UV–Vis in conjunction with TEM following existing Lifshitz–Slyozov–Wagner theory. For some biological extract-mediated synthesis, a single-stage mechanism that is diffusion controlled following Ostwald ripening (OR) is proposed. Whereas, for other bioreduction process, a double stage involving (1) initial OR followed by (2) surface adsorption-oriented attachment is proposed for temporal evolution of the nanosilver in green environment.

Coherent precipitation of copper in Super304H austenite steel

The precipitation behavior of copper-rich phase in an austenitic stainless steel and the interface structure between the precipitates and the matrix have been investigated combining transmission electron microscopy and coarsening analysis. The fine dispersed Cu precipitates were spherical and highly stable in the austenite matrix, with the size being only 32nm in diameter even after a long time 10,000h aging at 650°C. The average size of Cu precipitate was increasing with aging time, as predicted by the Lifshitz–Slyozov–Wagner theory. The coherent relationship between the precipitates and the matrix was preserved during the whole aging process, even at the later stage. The interfacial energy of Cu in the austenitic matrix has been independently derived from the data on coarsening experiment based on two kinds of approximations: γ-Fe and Fe–18Cr–9Ni–3Cu matrix were considered separately instead of complex austenite in this study. It was 0.086J/m2 for Cu/γ-Fe and 0.017J/m2 for Cu/Fe–18Cr–9Ni–3Cu. Both values are satisfied with the range of coherent interfacial energy. The coherent interfacial structure and highly stable microstructure play a key role on strengthening materials.

Microstructural evolution of Cr–Cu composites in liquid-phase sintering

The paper examines the effect of temperature and volume fraction of refractory particles on the kinetics of their growth during liquid-phase sintering of Cr–Cu composites in the temperature range 1150–1350°C under a vacuum of (2–4)∙10–3 Pa. It is established that the growth kinetics of average-size particles is described by a near-cubic law and the decrease in their number is determined by a near-inverse dependence: the apparent activation energy (Q = 113 ± 10 kJ/mol) is of the order of magnitude comparable to that of diffusion in liquid metals. According to the Lifshitz–Slyozov–Wagner theory (LSW theory), diffusion coalescence is indicative of diffusion-controlled particle growth. Experimental growth constants are one order of magnitude higher than those calculated within the classical LSW theory. The increase in the growth rate constant with volume fraction of refractory particles varying from 0.4 to 0.7 and the change in the particle size distribution function after sintering for 90 min at 1200°C agree with the Ardell model, which modifies the LSW theory considering the effect of volume fraction of particles on their growth kinetics.

An Experimental and Theoretical Evaluation of Microstructure Coarsening in Duplex Stainless Steels

The coarsening of duplex stainless steel microstructures at temperatures above 1000°C was investigated experimentally and theoretically. Hot-rolled duplex 2205 and superduplex 2507 samples were heat treated isothermally at 1100°C up to 700 h, and also between 1000 and 1250°C for 24 h. The ferrite content and the microstructure coarseness, quantified by the measured austenite spacing, AS, were evaluated. It was found that the observed coarsening could be described using Ostwald ripening theory expressed as , where AS0 is austenite spacing of the as-delivered material, k the rate constant, n the exponent, and t the heat treatment time. Using regression analysis, n and k were evaluated and the resulting predictions compared with literature theories and results. The results were also calculated according to the original Lifshitz, Slyozov, Wagner (LSW) theory with parameters taken from literature, as well as with the Dictra software for diffusion and growth in multicomponent systems. The calculations indicated that while the classical LSW theory failed to give a good description of the experimental results, the Dictra simulations proved very accurate, even though systems of equal ferrite and austenite content are considerably outside the intended range of applicability of the software.

Microstructure Formation and Evolution in Composites during Liquid-Phase Sintering

The paper presents a brief literature review on microstructure development in composites during liquid-phase sintering. Two mechanisms of microstructure coarsening in liquid-phase sintered systems are considered: dissolution–reprecipitation and coalescence. The data are systematized in the context of the Lifshitz–Slyozov–Wagner theory and the theory of coalescence at the final stages of liquid-phase sintering. The effect of various physicochemical factors, such as temperature, volume fraction, and time on microstructure development is explained in terms of quasichemical kinetics.

Influence of interfacial properties on Ostwald ripening in crosslinked multilayered oil-in-water emulsions

The influence of interfacial crosslinking, layer thickness and layer density on the kinetics of Ostwald ripening in multilayered emulsions at different temperatures was investigated. Growth rates of droplets were measured by monitoring changes in the droplet size distributions of 0.5% (w/w) n-octane, n-decane, and n-dodecane oil-in-water emulsions using static light scattering. Lifshitz–Slyozov–Wagner theory was used to calculate Ostwald ripening rates. A sequential two step process, based on electrostatic deposition of sugar beet pectin onto fish gelatin or whey protein isolate (WPI) interfacial membranes, was used to manipulate the interfacial properties of the oil droplets. Laccase was added to the fish gelatin–beet pectin emulsions to promote crosslinking of adsorbed pectin molecules via ferulic acid groups, whereas heat was induced to promote crosslinking of WPI and helix coil transitions of fish gelatin. Ripening rates of single-layered, double-layered and crosslinked emulsions increased as the chain length of the n-alkanes decreased. Emulsions containing crosslinked fish gelatin–beet pectin coated droplets had lower droplet growth rates (3.1±0.3×10−26m3/s) than fish gelatin-stabilized droplets (7.3±0.2×10−26m3/s), which was attributed to the formation of a protective network. Results suggest that physical or enzymatic biopolymer-crosslinking of interfaces may reduce the molecular transport of alkanes between the droplets in the continuous phase.

An investigation on the coarsening behavior of γ′ precipitate in GTD-111 Ni-base superalloy

Morphology of γ′ precipitates affects mechanical properties of Ni-base superalloys. In this research study, the coarsening behavior of γ′ precipitates in Ni-base superalloy GTD-111 was investigated. The alloy was solution-treated at 1200°C for 4 h and water quenched to obtain single size distribution of the precipitates. Aging at 1000°C up to 200 h was carried out to examine the effect of aging time on the growth of γ′ precipitates. The shape of γ′ precipitates changed from sphere to oval and then to cube as the aging time was increased. Moreover, the coarsening of γ′ precipitates started fast initially, whereas it slowed down as the growth continued, contrary to the Lifshitz–Slyozov–Wagner theory. The decelerated coarsening of γ′ precipitates was attributed to the effect of elastic interaction energy and decrease in driving force. Finally, the activation energy for diffusion of solute atoms or the growth of γ′ precipitates in GTD-111 alloy was calculated.

Evolution of the semi-solid microstructure of ADC12 alloy in a modified SIMA process

Abstract Semi-solid metal processing is a new developing technology. This processing has a more advanced technology than traditional ones such as forming and casting. The quasi-spherical grain has been formed by recrystallization of the dendrites during reheating in semi-solid state. The strain-induced melt activation is simple and does not need expensive equipment for preparing semi-solid billets. In this paper a modified method was proposed based on the strain-induced melt activation process. The microstructure and mechanical properties of ADC12 aluminum alloys prepared by the modified strain-induced melt activation process were studied. Different levels of heating temperatures and holding times were used in this investigation. The results of heating experiment revealed that the optimum heating temperature, isothermal holding time and average size of particles were 828 K, 1800 s and 70 μm, respectively. The results of isothermal treatment showed that the size of spherical particles increased linearly with extending the holding time at the 828 K. In the meantime the quantity of particles showed the parabola descent. These phenomena are in accordance with the Lifshitz–Slyozov–Wagner theory and Ostwald ripening.

Size control of Sb 2Te 3 Widmanstätten precipitates in thermoelectric PbTe

The number density and area per unit volume of Sb 2Te 3 Widmanstätten plates in thermoelectric PbTe were controlled through two types of heat treatments of (PbTe) 1− x –(Sb 2Te 3) x , where x = 0.04 and 0.06: isothermal annealing at various temperatures and cooling from a solid-solution regime to a two-phase region with various rates. The microstructure was quantified by image analysis of scanning electron micrographs and Rietveld refinements of X-ray diffraction profiles. Isothermal annealing of (PbTe) 0.94–(Sb 2Te 3) 0.06, results in increasing number density and area per volume of precipitates with decreasing temperature. In controlled cooling rate experiments, faster cooling rates or smaller x result in higher number density and area per volume. These trends are discussed using phase transformation theories. Overall the number density and area per volume of precipitates were controlled in the ranges from 0.4 to 44 μm −3 and from 0.5 to 1.8 μm −1, respectively. Isothermal annealing was performed for time periods from 10 to 166 h at 723 K to check the stability of the microstructure at the (PbTe) 0.94–(Sb 2Te 3) 0.06 composition. While the Boyd and Nicholson model of the Greenwood–Lifshitz–Slyozov–Wagner theory for the average diameter of plates gives a reasonable value for peripheral interfacial energy, the time dependence was found to decelerate more than the t 1/3 rule. It has also been found that the coarsening mechanism involves the elongation of plates.

Ostwald ripening of binary alloy particles

Classical Lifshitz-Slyozov-Wagner theory is generalized for Ostwald ripening of particles composed of random binary alloy. We show that the steady state ripening process is characterized by self-similar particle size and composition distributions. The shape of particle size distribution depends on whether the process is diffusion controlled (Lifshitz-Slyozov) or reaction controlled (Wagner) and is consistent with the predictions of classical theory for one-component materials. The steady state composition distribution, in contrast, has the same functional form in both extreme cases featuring a universal dependence of the composition upon particle size. We also found that transients in particle's composition can be very quick resulting in a steady state distribution well before it is reached by particles sizes. These transients involve significant changes in particle sizes and open an opportunity for producing metastable particle size distributions of required shape.

Solution-processed ZnO nanocrystals in thin-film light-emitting diodes for printed electronics

Thin-film light-emitting diodes (LEDs) containing solution-processed ZnO nanocrystals (NCs) were prepared as printed electronics. The electroluminescent (EL) properties of thin-film LEDs were investigated along with the structural and photoluminescence (PL) properties of the ZnO NCs. Scanning electron microscope and x-ray diffraction studies revealed that the crystal sizes D were ranged from 5–11 nm, and can be controlled by varying growth time tG in the Zn2+/OH− solution at 40 °C. The time evolution of D was analyzed using Lifshitz–Slyozov–Wagner theory, showing that growth is limited by diffusion. The results of PL studies indicated that increases in the peak energies in the ultraviolet (UV) region could be attributed to the quantum-size effects on the exciton emission in the NCs with a small D, the ZnO surfaces became sufficiently passivated as D increases. Printed layers containing well-passivated ZnO NCs with different D of 8–11 nm were used as emission layers in thin-film LEDs together with pentacene hole transport layers. The current-voltage characteristics were analyzed using the trapped-charge-limited current mechanism. EL spectral measurements revealed the presence of weak UV emission that increased slightly as D decreased.

Influence of surfactant structure on the contribution of micelles to Ostwald ripening in oil-in-water emulsions

The rate of Ostwald ripening was measured, using light scattering, in 2 wt.% and 10 wt.% decane-in-water and dodecane-in-water emulsions. Sodium dodecyl sulfate and several nonionic ethylene oxide dodecyl ethers—surfactants with tails containing 12 carbons, but with various headgroups—were used to form the emulsions. Emulsions were formed with sufficient quantities of the surfactant to saturate the droplet interfaces. The influence of surfactant micelles in the continuous phase was then explored by adding 1–5 wt.% surfactant to the water. The increase in the average droplet radius in the absence of micelles was found to agree qualitatively with Lifshitz–Slyozov–Wagner theory for the different surfactant types. The addition of micelles increased the rate of Ostwald ripening, by factors between 2 and 50, depending on the type and concentration of surfactant. However, there was no systematic correspondence between the increased rate and the equilibrium solubilization capacity of the micelles, nor was the rate decreased with increased strength of repulsive interactions between micelle and the droplet interface. It is proposed that the complex influence of surfactant on Ostwald ripening kinetics may depend on the ability of micelles to become supersaturated with oil—i.e., to incorporate solute temporarily above their equilibrium solubilization capacity.

Particle size distributions during diffusion controlled growth and coarsening

Theoretical analysis of particle growth and coarsening conducted in the present work, which includes stochastic (random) flux of a solute inside/from the growing particles, predicts normal distribution of the particle sizes, independent of the particle volume fraction. This result agrees well with the numerous experimental data and it solves a long-time problem related with a non-symmetrical size distribution in earlier Lifshitz–Slyozov–Wagner theory.

Unified model equations for microstructure evolution

Unified model equations hidden in microstructure evolution are discovered in this paper. The governing equations in Lifshitz–Slyozov–Wagner theory, and diffusion screening theory are derived with some approximations from the unified model equations. The governing equations in multiparticle diffusion simulation and phase-field simulation in microstructure evolution are also derived from the unified model equations. The advantages and limitations for different theories and simulations in microstructure evolution are compared in detail. This comparison can guide scientists to select computational tools for their needs in microstructure evolution. The unified model equations can be applied in many new technological fields, such as self-assembly in nanoscience.

Preparation and optical properties of blue-emitting colloidal CdS nanocrystallines by the solvothermal process using poly (ethylene oxide) as the stabilizer

Blue-emitting colloidal CdS nanocrystals have been synthesized through the solvothermal reaction of cadmium acetate and thiourea in N,N-dimethylformamide using poly(ethylene oxide; PEO) as the stabilizing polymer. The as-prepared CdS colloids were stable at ambient conditions for several weeks. The PEO-stabilized CdS colloids showed a narrow fluorescence band with the maximum at about 420 nm and thus emitting blue fluorescence under the ultraviolet (UV) lamp. A common red shift of fluorescence band is not detected for the prepared CdS colloids in the study, indicating that PEO-stabilized CdS NCs possess few crystalline defects on their surface. In addition, transmission electron microscope micrographs reveal that the sizes of CdS NCs are between 4.4 to 5.4 nm with small standard deviations from 0.5 to 0.7 nm. The particle growth kinetics was studied by monitoring UV-visible absorption onsets versus the reaction time and was found to nearly follow the Lifshitz–Slyozov–Wagner theory for the Ostwald ripening mechanism.

Ostwald Ripening ofβ-Carotene Nanoparticles

Ostwald ripening, the interfacial-energy-driven dissolution and reprecipitation of solutes, becomes an increasingly significant problem for nanoparticle formulations. We present the first quantitative study of Ostwald ripening for nanoparticle dispersions. The Lifshitz-Slyozov-Wagner (LSW) theory of particle growth driven by diffusion is applied to study beta-carotene nanoparticles with sizes of O(100 nm) formed by our block-copolymer protected Flash Nanoprecipitation process. A numerical implementation of the LSW theory that accounts for the original particle size distribution is presented. The predicted particle sizes from the numerical simulation are compared with the experimental results measured by dynamical light scattering. The results show quantitative agreement with no adjustable parameters. The addition of antisolvent results in the reduction of the ripening rate by dramatically decreasing bulk solubility.