Kinetic Nucleation Model Research Articles

Atomistic modeling of nucleation kinetics of Guinier–Preston zones in Al–Cu alloys: Two formation scenarios and prediction of the time-temperature-transformation diagram

Metastable precipitates of solute atoms, known as Guinier–Preston (GP) zones, play a significant role in the age hardening of Al–Cu alloys. In this study, we utilized the classical nucleation theory (CNT) to obtain time-temperature-transformation (TTT) diagrams for steady-state nucleation over a wide temperature range. The CNT model, which is based on atomistic simulations using artificial neural network potentials, was constructed to predict the nucleation kinetics of GP zones in the Al–Cu system with solute concentrations ranging from 1.3 to 2.5 at% (3.0 to 5.7 wt%). The nose temperature at which the steady-state nucleation time for GP zone formation is the shortest was calculated. The nose temperature increased and the minimum nucleation time decreased as the solute concentration increased. These predictions are comparable to previous theoretical results and are in good qualitative agreement with experimental observations. Furthermore, two formation scenarios of double-layer GP (GP2) zones, considering synchronous and asynchronous attachments of solute atoms to clusters, were compared in terms of nucleation efficiency. This provides new insights into the nucleation pathways of the GP2 zone in Al–Cu alloys.

Kinetics model of crystal nucleation and growth in supercooled water for designing ice-templating soft matter scaffold

Ice-templating technology has recently attracted extensive attention to achieve programed structure-property relationships in porous soft matter scaffolds. However, there is a huge gap existed between theoretical understanding and practical applications of nucleation kinetics and growth of ice crystals in supercooled water. This paper establishes a nucleation kinetics model of crystal growth in supercooled water, for designing ice-templating soft matter scaffolds with programmable structure-property relationship. A phase transition model was firstly formulated to characterize liquid-liquid phase transition of supercooled water, based on a two-state model and free-volume theory. Effects of diffusion coefficient and density of the supercooled water on ice nucleation kinetics and crystal growth were investigated, based on the classic nucleation theory. Analytical results showed excellent agreement with experimental data, with correlation indices of R2=90.7 % for diffusion coefficients and R2=94.0 % for densities, respectively. The model predicted a nucleation rate of 31.7 m−3∙s−1 at 200 K and peak nucleation rate and crystal growth rates appearing at 183 K and 227 K. Constitutive relationships among mechanical behaviors, ice nucleus radius, nucleation ratio, and crystallization growth rate, were developed for the ice-templating scaffolds, based on the affine model theory and verified with finite element analysis results (R2= 99.9 %) and experimental results (R2 = 95.8 %). Finally, the prediction results using the proposed model were further verified using the experimental data reported in the literature. This study provides a new methodology to describe the nucleation kinetics and growth of ice crystals in supercooled water and programmable structure-property relationships in ice-templating soft matter scaffolds.

Dynamics analysis of twin formation for InP and preparation of 6 inch InP single crystals

Twin-free InP crystals can be grown under suitable growth conditions. A kinetic model for twin nucleation is proposed.

Reaction mechanisms, kinetics, and nanostructural evolution of magnesium silicate hydrate (M-S-H) gels

M-S-H gels were synthesised via reaction of Mg(OH)2 with silica fume, cured at 35 °C for up to 112 days, and their chemical and nanostructural evolution was examined. M-S-H gels with structural similarity to the thermodynamically stable serpentine-group mineral lizardite were formed. Quantification of 25Mg and 29Si MAS and 1H29Si CPMAS NMR, electron microscopy, and thermogravimetric data showed dissolution of brucite and silica fume, and M-S-H formation, all occurred linearly with time up to 56 days. Data showed strong correlation with the Avrami-Erofeyey nucleation kinetic model, indicating M-S-H formation was governed by nucleation reactions. After 112 days, two distinct M-S-H gels were formed: a Si-rich M-S-H gel with molar Mg/Si = 0.55(±0.2), and a Mg-rich M-S-H gel with molar Mg/Si = 0.80(±0.5). Nanostructural rearrangement of M-S-H continues up to 112 days, with increased crosslinking and polymerisation. This new insight is important for application of M-S-H binders in both construction and radioactive/toxic waste immobilisation.

Insights into direct reduction iron using bamboo biomass as a green and renewable reducer: Reduction behavior study and kinetics analysis

Biochar is a renewable, carbon-neutral energy source that can replace traditional fossil fuels for iron and steel production, so it is of great significance to reduce carbon emissions and reduce pollution. In this paper, the reaction characteristics and kinetics between biomass (bamboo powder) pyrolysis gas, biochar, and iron ore powder are studied by a thermogravimetric analyzer (TG). Comparing the samples with four different C/O ratios (C/O = 0.375, 0.5, 1, 3), it is found that the sample with C/O = 1 can completely reduce hematite. The mass loss process is divided into the following four stages: de-crystal water, hematite to magnetite, magnetite to wustite, and wustite to metallic iron. Among them, the latter three stages are following the kinetic model of random nucleation (n = 1, 2) and three-dimensional diffusion, and the activation energy of the three stages increases and then decreases. Through scanning electron microscopy (SEM), the surface of hematite particles changed from relatively flat to porous and finally the reduced metal iron aggregated, and connected into large pieces. By using online Thermogravimetry-Fourier Transform Infrared Reflection (TG-FTIR), when the reduction temperature is lower than 700 °C, biochar plays a leading role. On the contrary, the CO produced by biochar gasification plays a leading role.

The effect of thermal non-equilibrium on kinetic nucleation

Context. Nucleation is considered to be the first step in dust and cloud formation in the atmospheres of asymptotic giant branch (AGB) stars, exoplanets, and brown dwarfs. In these environments dust and cloud particles grow to macroscopic sizes when gas phase species condense onto cloud condensation nuclei (CCNs). Understanding the formation processes of CCNs and dust in AGB stars is important because the species that formed in their outflows enrich the interstellar medium. Although widely used, the validity of chemical and thermal equilibrium conditions is debatable in some of these highly dynamical astrophysical environments. Aims. We aim to derive a kinetic nucleation model that includes the effects of thermal non-equilibrium by adopting different temperatures for nucleating species, and to quantify the impact of thermal non-equilibrium on kinetic nucleation. Methods. Forward and backward rate coefficients are derived as part of a collisional kinetic nucleation theory ansatz. The endother-mic backward rates are derived from the law of mass action in thermal non-equilibrium. We consider elastic collisions as thermal equilibrium drivers. Results. For homogeneous TiO2 nucleation and a gas temperature of 1250 K, we find that differences in the kinetic cluster temperatures as small as 20 K increase the formation of larger TiO2 clusters by over an order of magnitude. Conversely, an increase in cluster temperature of around 20 K at gas temperatures of 1000 K can reduce the formation of a larger TiO2 cluster by over an order of magnitude. Conclusions. Our results confirm and quantify the prediction of previous thermal non-equilibrium studies. Small thermal non-equilibria can cause a significant change in the synthesis of larger clusters. Therefore, it is important to use kinetic nucleation models that include thermal non-equilibrium to describe the formation of clusters in environments where even small thermal non-equilibria can be present.

Nucleation kinetics model for primary crystallization in Al-Y-Fe metallic glass.

The high density of aluminum nanocrystals (>1021m-3) that develop during the primary crystallization in Al-based metallic glasses indicates a high nucleation rate (∼1018m-3s-1). Several studies have been advanced to account for the primary crystallization behavior, but none have been developed to completely describe the reaction kinetics. Recently, structural analysis by fluctuation electron microscopy has demonstrated the presence of the Al-like medium range order (MRO) regions as a spatial heterogeneity in as-spun Al88Y7Fe5 metallic glass that is representative for the class of Al-based amorphous alloys that develop Al nanocrystals during primary crystallization. From the structural characterization, an MRO seeded nucleation configuration is established, whereby the Al nanocrystals are catalyzed by the MRO core to decrease the nucleation barrier. The MRO seeded nucleation model and the kinetic data from the delay time (τ) measurement provide a full accounting of the evolution of the Al nanocrystal density (Nv) during the primary crystallization under isothermal annealing treatments. Moreover, the calculated values of the steady state nucleation rates (Jss) predicted by the nucleation model agree with the experimental results. Moreover, the model satisfies constraints on the structural, thermodynamic, and kinetic parameters, such as the critical nucleus size, the interface energy, and the volume-free energy driving force that are essential for a fully self-consistent nucleation kinetics analysis. The nucleation kinetics model can be applied more broadly to materials that are characterized by the presence of spatial heterogeneities.

Thermodynamics and Nucleation Kinetics Model of Nonalloyed Carbon Deoxidation of Bearing Steel

Non alloyed carbon deoxidation can fundamentally solve the technical difficulty of fatigue failure of high‐quality bearing steel caused by inclusions. Herein, nonalloyed carbon deoxidation is presented with CO as a product, which can avoid the problem of residual inclusions. The thermodynamic and kinetic nucleation models of [C] deoxidation are constructed. The results suggest that a decrease in strengthens the deoxidation ability of [C], and the [%O] balanced with [%C] shows multiple decreases. When = 0.1 atm and [%C] = 0.5%, [%O] can be reduced to less than 10 ppm. However, from the results of the nucleation kinetic model, as decreases, the critical radius increases, and the resistance of CO nucleation also increases. This results in difficulty of nucleation. Based on the nucleation kinetic model, the following C–O reaction mechanism is proposed: 1) [C] and [O] move to the reaction interface, 2) [C] + [O] = CO, forming a critical bubble nucleus, and 3) the newly formed CO diffuses continuously into the critical bubble, causing the bubble to grow and float away. Alternatively, the CO separates from the gas–liquid interface and enters the bubble, which floats away.

Effects of composition and magnetism on interfacial energy in Cu-Co alloys

The composition and magnetic dependent interfacial energy in Cu-Co immiscible alloys is investigated within a coherent interface model using ab initio calculations. We translate the composition dependence of the interfacial energy to the temperature dependence considering the variations of the equilibrium compositions of precipitate and matrix with respect to temperature. The obtained results are in reasonable agreement with those obtained by experiments and thermodynamic calculations. Reviewing the experimental methods for determining the interfacial energy based on kinetic models for precipitate nucleation and coarsening, as well the thermodynamic models based on broken-bond models, we point out that the temperature effect on the interfacial energy in the above models is primarily due to the composition change of the interface. The present work emphasizes the effort to understand the meaning of the speciously same quantity in different methods.

Brewer’s spent grains as biofuels in combustion-based energy recovery processes: Evaluation of thermo-oxidative decomposition

The high global generation of wastes and side streams from agri-food production has led to environmental impact and causes nature degradation due to their uncontrolled management. These wastes are profitable materials with significant economic value that could otherwise be exploited as new sources in the feed industry or the production of bioenergy. Among them, brewer’s spent grain (BSG) is a solid by-product generated in the beer-brewing process that consists of the barley grain husks together with parts of the pericarp and seed coat layer. Although it is rich in fibres and proteins, its main use is currently limited to animal feed or simply deposition to landfills. This study pursues the evaluation of BSGs as biofuels in energy recovery processes. For this purpose, the elemental composition, the higher heating value, the content of volatiles, fixed carbon, moisture, and ash yield along with the kinetic analysis of its decomposition during thermo-oxidative combustion were assessed. The thermo-oxidative decomposition of hemicellulose, cellulose, lignin, and char occurred in two main stages. The average apparent activation energy for Stage I was 190–200 kJ·mol−1, significantly higher than that of Stage II (100–150 kJ·mol−1). Stage I revealed a random nucleation kinetic model (Fn) and involved the volatilisation of hemicellulose and cellulose and partially lignin. Stage II, described by a three-dimensional diffusion kinetic model (D4), comprised the completion of lignin and the decomposition of char. The environmental advantage of using such residues was demonstrated with the low ash yield (in the range of 1.7–5.4%) and high calorific value between 17.8 and 19.1 MJ·kg−1. The obtained results serve as the baseline for describing the energy recovery process in a reactor that uses BSG residues as feedstock under oxidative conditions. Altogether it is pointed out the feasibility of using pelletised BSGs regardless of the malt type or mixture as a renewable source of energy in incineration plants above 500 °C.

Hierarchical mesoscale assembly of PbO2 on 3D titanium felt/TiO2 nanotubular array electrode for anodic decolourisation of RB-5 dye

Hierarchical PbO2 nanoparticles (NPs) were grown by hydrothermal method on TiO2 nanotubes (NTs) at 3D titanium felt, which is simple and scalable method. TiO2 NTs were formed on titanium felt by anodising at 25 °C in environmentally friendly methanesulphonic acid solution. The growth of PbO2 on the TiO2 NTs depended on immersion time during hydrothermal synthesis and followed a LaMer-Dinegar burst kinetic model of nucleation and growth. PbO2 formation began with rapid nucleation, followed by mesoscale assembly due to organic capping of poly(vinylpyrrolidinone). The electrochemical performance of 3D electrode was recorded in pH 3 sodium sulphate solutions containing Reactive Black 5 (RB-5) azo dye at 25 °C. The resulting hierarchical 3D electrode achieved 98% decolourisation after 50 min of anodic oxidation with a first order batch decay rate of 0.0875 min−1.

Effect of shear on nucleation of carbon fiber reinforced polymer composites: Experiments and modeling

AbstractIn this study, shear‐induced crystallization of short carbon fiber (SCF)‐reinforced isotactic polypropylene (iPP) composite was investigated using polarized optical microscopy (POM) and rheometry. Although the SCF exhibited no nucleation ability to iPP in the quiescent melt under the chosen conditions, different interfacial morphologies were observed after shear was applied. The POM results revealed that the crystallite morphologies along the SCF strongly depended on the shear rate () and shear duration. A nucleation kinetics model was proposed to determine how shear affects the fraction of SCF covered with transcrystalline. The nucleation rate on the SCF was proportional to . The dependence of the nucleation rate corresponded well with the change in the shear‐induced free energy of the melt, indicating that the interactions between SCF and iPP were insignificant. The rheological results demonstrated that conformational ordering directly affected the nucleation rate. The helical content near the SCF increased rapidly owing to the enhancement of shear. Therefore, the nucleation kinetics on the SCF surface accelerated significantly.

Off-stoichiometry effects on crystal nucleation and growth kinetics in soda-lime-silicate glasses. The combeite (Na2O•2CaO•3SiO2) – devitrite (Na2O•3CaO•6SiO2) joint

To the present date, the vast majority of fundamental studies on glass crystallization has been carried out using stoichiometric compositions, whereas by far, the most common cases in glass technology are off-stoichiometric. In this work, we performed a comprehensive study on the nucleation and growth kinetics of combeite crystals in non-stoichiometric glasses of the combeite (Na2O•2CaO•3SiO2) – devitrite (Na2O•3CaO•6SiO2) system. Using cluster-size distribution functions based on a previously developed kinetic model of nucleation, we constructed the dependencies of the number N(T) of nucleated and grown crystals on the nucleation time, t, and estimated the nucleation rates, I(T)=dN(T)/dt. We then cross-checked the theoretical calculations versus experimental data. In these calculations, the critical nucleus-supercooled liquid specific interfacial energy, σ, and the effective diffusion coefficient,D, were left as fitting parameters for the best possible description of experimental data. We show that as the precursor glass composition shifts from combeite to devitrite, and thus the difference of composition between the initial glass and the precipitated crystals increases, the interfacial energy increases, and the maximum steady-state nucleation rate, Ist(Tmax), of combeite strongly drops. On the other hand, as a consequence of the composition shift, depending on the glass-forming system, the diffusion coefficient may increase or decrease. We also show a significant difference between D estimated from the nucleation experiments and Du calculated from the growth rates. These results corroborate our previous studies on other systems and are relevant to elucidate the complex mechanisms of crystallization of non-stoichiometric glasses.

Effect of non-stoichiometry on the crystal nucleation and growth in oxide glasses

Non-stoichiometric glasses (NSG) are much more common than stoichiometric compositions. However, due to inherent difficulties, fundamental studies of crystallization kinetics of NSG are much less frequent. To shed light on the crystal nucleation and growth kinetics of NSG, we adopted a nucleation kinetics model, leaving the interfacial energy and diffusion coefficient as free parameters, to explain experimental nucleation data of glasses of three compositions in the pseudo-binary Li2O·2SiO2–BaO·2SiO2 model system. We show that, as the glass composition approaches the eutectic, the nucleation rates drop drastically, mainly due to an increase in the interfacial energy. This result corroborates the common empirical observation that eutectic compositions tend to show good glass-forming ability. We also found that the structural relaxation times are significantly shorter than the characteristic nucleation times, validating the widely used and scarcely tested assumption that relaxation does not play a noticeable role in crystal nucleation. For a stoichiometric glass the fitted diffusion coefficient determining nucleation, D, is lower than that determining the growth of macro crystals, DU, and this difference significantly increases with decreasing temperature. On the other hand, the diffusion coefficient calculated from viscosity, Dη, is close to DU at high temperatures and approaches D in the glass transition range. Finally, after crystallization of the primary phase (lithium disilicate), barium disilicate and more lithium disilicate crystals precipitate in the diffusion zone existing in the residual glass.

Coupling of Contact Nucleation Kinetics with Breakage Model for Crystallization of Sodium Chloride Crystal in Fluidized Bed Crystallizer

There are many nucleation theory-based different mechanisms. These theories mainly focused on production parameters in the crystallization and less on physical properties of crystals. In this research, a new model of contact nucleation theory coupled with the breakage mechanism of crystals is applied to describe the collision process in sodium chloride crystallization. This coupling nucleation model is presented here which relates the number of contact-collision site in nucleation owing to collision rate and the interfacial energy. F2 in the expression of the classic contact nucleation rate is redefined as a power function with the physical properties of crystals and breakage propensity. The experiment results indicate that crystal breakage propensity has a significant influence on the nucleation rate. Finally, analysis of the contact nucleation kinetic model and comparison with experiments reveal that the new nucleation model results are in better agreement with experiments. This new nucleation model is confirmed to represent the time-dependent collision behavior. The parameters of model are strongly related to the physical properties of crystal and fluidization conditions.

Experimental probes of silver metal nanoparticle formation kinetics: Comparing indirect versus more direct methods

AbstractThe kinetics of noble metal nanoparticle formation in bottom‐up syntheses are important for controlling and optimizing these methods. Hence, experimental probes that are easily accessible to most laboratories are also of interest. We collected kinetic curves for the formation of silver nanoparticles in a modified Turkevich method with citrate acting as the reducing and stabilizing agent by (i) measuring the change in silver nanoparticle surface plasmon resonance by UV‐visible spectroscopy, a somewhat indirect method, and then also by (ii) measuring the change in silver ion concentration by ion‐selective electrode potentiometry and/or atomic absorption spectroscopy, two more direct methods. The resulting sigmoidal kinetic curves were curvefitted with the Finke‐Watzky two‐step kinetic model of slow, continuous nucleation and fast autocatalytic growth to extract average rate constants. We found that the kinetic curves obtained by following the change in silver ion concentration were apparent mirror images of those constructed by following the change in nanoparticle surface plasmon resonance, and that their respective curvefits displayed the same sigmoidal characteristics. The resultant values of the rate constants for nucleation and growth overlapped within experimental error between the methods and showed similar trends over the range of citrate concentrations studied. The use of multiple probes in this work to follow the kinetics of nanoparticle formation helps fill a need for the comparison and evaluation of different methods available to scientists, particularly those considered easily accessible.

Kinetics of Gaseous Species Formation During Steam Gasification of Municipal Solid Waste in a Fixed Bed Reactor

Surrogate municipal solid waste (MSW) has been prepared to represent high plastic content waste with low fixed carbon in order to be utilized for feedstock for the gasification and pyrolysis. The major components are plastic (PE and PP), food and kitchen waste, and paper, whereas the minor components are textile, rubber, and biomass. Reactions were conducted in small drop tube fixed bed reactor with isothermal reaction temperature at 700, 800, and 900 °C. Steam was supplied as the gasifying agent for the main purpose of producing hydrogen-rich gas. Pyrolysis was also conducted at the same condition to observe the characteristic differences. Producer gas, including H2, CH4, and CO, of both the reactions was a function of the temperature, whereas CO2 showed a reversed trend when the reaction temperature was increased. Simple kinetic models of those gaseous formations were studied for describing the related parameters. It is challenging to determine the kinetics of the individual gas generation while most kinetic studies have focused on mass deterioration. The commonly used kinetic model of nucleation of Avrami–Erofe'ev (A2) could well predict the mechanism of the gas formation of gasification. In parallel, the pyrolysis conformed to the A3 model due to the slower rate of char and tar decomposition when the gasifying agent was absent. The activation energy of each gaseous species and the fitting of experimental data with the selected models are examined in this study.

Isothermal crystallization of glycine in semi-continuous mode by anti-solvent addition

This article focuses on the isothermal semi-continuous crystallization of glycine aqueous solution by adding an anti-solvent, ethanol. The effect of the ethanol concentration on solubility and the impact of the ethanol flow rate on the metastable zone width and on the size distribution of the crystals were investigated. The study showed that increasing the ethanol concentration in the medium decreases solubility for the studied temperatures and that increasing the ethanol flow rate causes a widening of the metastable zone without inducing any noticeable effect on the crystals’ size distribution. In addition, nucleation kinetic models were determined for two temperatures (30 and 56 °C).

Insight into Fast Nucleation and Growth of Zeolitic Imidazolate Framework-71 by In Situ Static Light Scattering at Variable Temperature and Kinetic Modeling

Zeolitic imidazolate frameworks (ZIFs) represent an important subclass of porous metal organic frameworks (MOFs). The present work continues a previous study on ZIF-71 nanocrystal formation at room temperature (Cryst. Growth Des. 2016, 16, 2002–2010), which proposed a four-step formation process. It introduces a kinetic nucleation and growth model, which satisfactorily reproduces in situ time-resolved static light scattering data measured at room temperature in the previous work and at variable temperatures in the present work. Successful fitting can only be achieved with a precursor reaction being put before particle nucleation. The kinetic analysis provides rate constants for the precursor reaction, for particle nucleation, and for particle growth via monomer addition, and the equilibrium concentration of nonconsumed matter at the end of reaction. The rate constants of the precursor reaction and the nucleation process increase with temperature, which is counterintuitive if compared to classical nucleati...

Kinetic Model for Two-Step Nucleation of Peptide Assembly.

Intermediate dynamic assemblies are increasingly seen as necessary for the initial desolvation and organization of biomaterials to achieve their final crystalline order. Here we present a general peptide assembly model for two-step nucleation. The model predicts the phase transitions and equilibria between different phases by employing a combination of the Flory-Huggins parameter, the particle growth constant, and the binding energy to assemblies. Monte Carlo simulations are used to demonstrate how the system evolves from pure solution phases to the final thermodynamic assembly phase via an intermediate metastable particle phase. The final state of the system is determined by the solubility of the particle and assembly phases, where the phase with the lower solubility accumulates. A rare three-phase equilibrium exists when the solubilities of the particles and assemblies are similar. Experimental support for this model is achieved with assembly of the amyloid peptide Ac-KLVFFAE-NH2 (Aβ(16-22)) in mixed acetonitrile/water systems. Increasing the acetonitrile concentration decreases the number of particles, increases the particle size, and accelerates the assembly rate, all consistent with acetonitrile increasing the Aβ(16-22) peptide's solubility of particles but with little influence on the stability of the assemblies. Taken together, our model captures the transition from the metastable particle phase to the higher order peptide assembly through two-step nucleation.