Formation Of Critical Nucleus Research Articles

Silica polymerization and nanocolloid nucleation and growth kinetics in aqueous solutions

Amorphous silica precipitation from aqueous solutions at low temperatures (<100 °C) involves the initial nucleation and growth of silica polymers followed by aggregation, cementation and recrystallization to form opaline silica. In this study, silica polymerization was studied at temperature 23–80 °C, pH 2.48–9.65, and ionic strength 0.01–0.53 mol kg−1. Measured changes in the concentration of monomeric silica (SiO2(mono)) were fit assuming the polymerization reaction is fourth-order with respect to the difference between the concentration of silicic acid (Si(OH)4(aq)) and its concentration at equilibrium (Si(OH)4(aq)eq) with respect to amorphous silica:r=-k4AsmSi(OH)4(aq)-mSi(OH)4(aq)eq4where r is the overall rate of the reaction, As is the specific surface area of the formed polymers, calculated assuming particle-size-dependent solubility and a spherical polymer geometry, and k4 is the rate constant. The rate constant at zero ionic strength is given by:k0=Aexp-Ea/RTaOH-nwhere A is a pre-exponential constant (0.3822 mmol−3 cm−2 s−1), Ea is the activation energy (29.87 kJ mol−1), and n is equal to −0.80. The overall rate constant as a function of ionic strength (I) is given by:k4=k0Imwhere m is equal to 0.65. The rate constant increases by approximately six orders of magnitude from pH of 2 to 10 and one order of magnitude between temperature ∼20 and 80 °C. However, hydrolysis of silicic acid (Si(OH)4(aq)) at pH above ∼8 decreases the relative abundance of Si(OH)4(aq) while increasing the solubility of amorphous silica, thereby decreasing the rate of silica polymerization. The inferred reaction order is consistent with a reaction mechanism rate-limited by the formation of the cyclic tetramer across a wide range of pH. The time-dependence of the specific surface area during polymerization reflects the formation of critical nuclei towards the beginning of the polymerization process and Ostwald ripening of larger polymers towards the end of the polymerization process. The developed rate equation can predict rates of silica polymerization across a wide range of aqueous solution compositions.

Thermal stability of nanoscale ferroelectric domains by molecular dynamics modeling

Ultra-dense domain walls are increasingly important for many devices but their microscopic properties are so far not fully understood. In this study we combine atomistic and coarse-grained molecular dynamic simulations to study the domain wall stability in the prototypical ferroelectric BaTiO3. We transfer the discussion of the field-driven nucleation and motion of domain walls to thermally induced modifications of the wall without an external driving force. Our simulations show that domain wall dynamics and stability depend crucially on microscopic thermal fluctuations. Enhanced fluctuations at domain walls may result in the formation of critical nuclei for the permanent shift of the domain wall. If two domain walls are close - put in other words, when domains are small - thermal fluctuations can be sufficient to bring domain walls into contact and lead to the annihilation of small domains. This is even true well below the Curie temperature and when domain walls are initially as far apart as 6 unit cells. Such small domains are, thus, not stable and limit the maximum achievable domain wall density in nanoelectronic devices.

Reversible cross-linking facilitates the formation of critical nucleus in binary polymer blends.

Using self-consistent field theory, we study the effect of reversible cross-linking on the nucleation behavior of a binary polymer blend where only one of the components is able to form cross-links. To control the total number of cross-links and their distribution, we introduce a position-dependent cross-linking probability function that is characterized mainly by two parameters, the magnitude and the width. In the weakly cross-linked region, where the product of the magnitude and width, I, is small, the nucleation behavior is classical-like and the profile of the free energy excess is unimodal. In contrast, in the strongly cross-linked region, the profile of the free energy excess becomes bimodal, and the free energy minimum specifies a metastable nucleus. In a certain I, the free energy barrier for the metastable nucleus turns to be negative, which means it becomes more stable. In both cases, the free energy barrier of the critical nucleus is lower than that without cross-linking, indicating that cross-linking always facilitates nucleation although the dynamic behavior may be different when a metastable nucleus is involved during the nucleation process. The free energy analysis demonstrates that the interaction energy rather than the entropy is responsible for the properties of the critical nucleus. Our study provides an easy alternative way for the control of the nucleation behavior and may attract practical interest.

Study of the activation barrier of metastable liquid crystallization by metadynamics

The crystallization of Lennard-Jones fluid under weak supercooling was studied in molecular dynamics simulation with the metadynamics method. The Steinhardt parameter Q6 for a group of particles around a random atom and the system's potential energy were chosen to describe phase transition. The change in collective variables was observed in the process of overcoming the activation barrier of crystallization. The critical nucleus formation data were obtained. Keywords: metadynamics, Lennard-Jones fluid, metastability, activation barrier.

Unveiling relaxation and crystal nucleation interplay in supercooled germanium liquid

A well-designed study of the relationship between crystal nucleation and relaxation in supercooled liquids could clarify some critical issues in condensed matter science. In this article, we dwell on the kinetic spinodal temperature, TKS – where the times of first critical nucleus formation and structural relaxation curves cross over – and the Kauzmann temperature, TK – where the entropy of the supercooled liquid and crystal equalize. Germanium liquid was used as a model system, for which a reliable Stillinger-Weber potential and crystal nucleation kinetics are available. Using molecular dynamics (MD) simulations, we obtained the self-diffusion coefficient, D(T), and the shear viscosity, η(T), down to T=0.7·Tm, where Tm is the equilibrium melting temperature. In this way, three relaxation times were determined in the supercooled liquid: (i) via the shear viscosity, τη; (ii) the incoherent intermediate scattering function, τα; and (iii) the self-diffusion coefficient, τD. We found that τα(T)≈τD(T) and τη(T)<τα(T), corroborating the findings of recent experimental and computational studies conducted with other four substances. Hence, the viscosity only gives a lower bound to the intrinsic structural relaxation times,τα(T). We also compared the MD values of the atomic transport coefficient across the supercooled liquid/critical nucleus interface, D*, with those obtained by the classical nucleation theory (CNT) and found that the activation energies of D(T), η(T), and D*(T) are similar. The birth times of the first critical crystal nucleus at steady-state conditions, τ1(T), obtained in our previous study for the same material, were extrapolated to lower temperatures using the CNT for different sample sizes. We found that τ1(T) is much longer than the nucleation time-lags, confirming the establishment of the steady-state nucleation regime. A relevant finding is that the τα(T) and τ1(T) curves indeed cross over, confirming the existence of a kinetic spinodal for this liquid. Finally, we demonstrate that if the Kauzmann temperature existed for germanium, it would be located well below the TKS; hence, crystallization would intervene in the cooling path before the supercooled germanium liquid could reach TK, thus averting the entropy paradox, posed by Kauzmann in 1948. These findings shed light on several fundamental questions related to supercooled liquids.

The effect of transient nucleation behavior on thermal stability of Fe48Co32P14B6 metallic glass

The experimental isothermal kinetic curves for Fe48Co32P14B6 glass measured in the temperature range 683–714 K have been analyzed with using the analytical equation derived as a combination of the integral form of Kolmogorov’s equation of mass crystallization kinetics and the Kashchiev’s transient nucleation model. The transient nucleation rates show the trend to the steady-state values with increasing of annealing temperature. From a combination of the kinetic data and the values of crystal growth velocity, U, determined from the structural data, the steady-state nucleation rate values have been estimated. These data are analyzed within the classical nucleation theory and the work of the critical nucleus formation and the specific interfacial free energy values have been calculated. It has been established that transient behavior of nucleation rate in Fe48Co32P14B6 glass results in an increase of the onset crystallization time by 6.4 to about 3 times at 683 and 714 K, respectively. The temperature dependence of the transient time in the glass investigated is compared with that of the effective diffusivity as well with the similar data found for Fe40Ni40P14B6 and Fe40Co40P14B6 glasses and the possible reason of the observed changes in the degree of non-stationarity of nucleation rate has been discussed.

Исследование активационного барьера кристаллизации метастабильной жидкости методом метадинамики

The crystallization of Lennard-Jones fluid under weak supercooling was studied in molecular dynamics simulation with the metadynamics method. The Steinhardt parameter Q6 for a group of particles around a random atom and the system's potential energy were chosen to describe phase transition. The change in collective variables was observed in the process of overcoming the activation barrier of crystallization. The critical nucleus formation data were obtained.

In situ visualization of crystal nucleation and growth behaviors of linear and long chain branched polypropylene under shear and CO2 pressure

Crystallization and foaming behaviors of a semi-crystalline polymer in conditions comparable to those found in polymer processing, where the polymer melt experiences shear under elevated pressures, are key for modeling polymer processes and predicting the final structure and mechanical properties of polymer products. We investigate the crystallization behaviors of two different high-melt-strength polypropylene (PP) resins using a novel high-pressure visualization system that was developed to capture the crystallization process of a plastic specimen under high pressure and controlled shear. In situ visualization results under isothermal conditions demonstrate that both linear and long chain branched (LCB) PP exhibit crystal growth rates and nucleation densities that increase with higher applied shear stress but reach an optimum value with increasing CO2 pressure. By selectively choosing processing conditions, we can enhance the formation of observable critical size nuclei and the exclusion of CO2 from the crystal growth front. Therefore, overall crystallization kinetics can be easily controlled through the effect of induced-shear stress and the presence of pressurized CO2.

Austenite to Ferrite Transformation in Fe – 9 %Cr Alloys. II. Determination of Growth Rates

The paper continues theoretical analysis of austenite to ferrite transformation in an Fe-9 %Cr alloy demonstrating a typical site-saturation behaviour under the condition of diffusionless growth of a phase. In the previous paper the K coefficient in the Avrami equations being the asymptotes of Calm’s solution of the site-saturation transformation kinetics was used that contained a constant activation energy indicating the small value of the work of critical nucleus formation. This approach permitted to determine activation energy of transformation that was found to be equal to about 300 kJ/mole. In the present paper a new method of finding Calm’s equation coefficients from bending point at isothermal curves plotted on double logarithmic scale is proposed. Actually this bending point is the intercept of the two above-mentioned asymptotes of the Cahn’s curve, and equating the formulae describing theses asymptotes allows to find the coefficients in question. Given the average austenite grain size, it permits to find numerical values of growth rates. The activation energy thus acquires the exact physical meaning of the energy barrier at the interphase interface; its value was found to be 286 kJ/mole, which is close to previous results. The growth rates were thus determined as a function of temperature and the TTT diagram for the alloy is calculated that shows close correspondence with experiment.

Heterogeneous nucleation of YBCO via fluorine based MOD process: thermodynamic and kinetic approach

The nucleation of YBa2Cu3O7−δ (YBCO) film deposited via metal organic decomposition (MOD) approach is a complex process that has a key role in YBCO film crystalline orientation and, consequently, superconducting properties. Up to now, several studies have been carried out to clarify this step in the fluorine based MOD route which employs only or partially metals trifluoroacetate for the precursor solution preparation. However, these previous works provided only qualitative indications, whereas a quantitative theoretical investigation seems to be still lacking.In this paper, the free energy for critical nucleus formation of fluorine based MOD YBCO has been determined according to the classical nucleation theory. The volume contribution to the free energy is computed using thermodynamic data on (Y, Ba, Cu, O) systems available from the literature. The free energy barrier for nucleation depends upon nucleus orientation, via the work of adhesion and surface energies of vacuum/nucleus interfaces. The model is applied to describe heterogeneous nucleation of YBCO on (001) SrTiO3 single crystal and provides quantitative information on nucleation barriers as a function of temperature and both precursor and gas phase compositions. Through a kinetic approach, the energy barriers are further employed to estimate the fraction of c-oriented nuclei as a function of temperature and water partial pressure.Comparison with experimental data from literature lends support to the proposed computations. Therefore, the results shown in this work may be useful in designing the YBCO deposition process in order to obtain films with superior superconducting properties avoiding expensive and time-consuming experimental optimizations.

Influence of static magnetic field on the heterogeneous nucleation behavior of Al on single crystal Al2O3 substrate

This paper investigates the heterogeneous nucleation behavior of Al on single crystal Al2O3 substrate under the influence of static magnetic field (SMF). The nucleation temperature of the Al melt on the substrate was measured to decrease ~2.9°C under SMF, i.e. the undercooling was enhanced with the application of SMF. Using electric back-scatter diffraction (EBSD) and high-resolution transmission electric microscope (HRTEM), the interfacial crystal orientation matching of Al/Al2O3 was found to change dramatically, from {110}[011]Al~//{101¯0}[0001]Al2O3 without SMF to ~11.4o between {110}[1¯12]Al and {101¯0}[0001]Al2O3 under SMF, indicating that the SMF can increase the lattice misfit of Al/Al2O3 interface. The lattice matching deviation caused by SMF was supposed to lead to the increase of interfacial free energy of the nucleus/substrate interface, and thus the formation of critical nucleus and the undercooling were modified. The results demonstrate that SMF is capable of influencing the heterogeneous nucleation behavior of the melt.

Enhanced Degradation in Grain Refinement of Inoculated 2024 Al Alloy in Steady Magnetic field

The grain refinement of 2024 Al alloy inoculated with Al-5Ti-1B master alloy in a steady magnetic field (SMF) was investigated. It was shown that the degradation in grain refinement was enhanced and a cellular–dendritic transition of equiaxed primary α-Al grains occurred under the SMF. Employing a differential scanning calorimeter, the nucleation temperature of primary α-Al phase was found to decrease in the SMF, i.e., the undercooling was enhanced, and the kinetics of phase transformation was modified in the SMF. The enhanced degradation in grain refinement and increase in undercooling are attributed to the modified solid/liquid interfacial free energy and the delay of formation of critical nucleus due to the retarded migration rate of atoms in the liquid phase in the SMF. The cellular–dendritic transition of primary α-Al grains is ascribed to the modified constitutional undercooling at the solid/liquid interface, which results from the change in solute distribution by the damped convection and retarded diffusivity in the SMF. Additionally, the increase in growth dimension and the modified solid/liquid interfacial free energy under the SMF are also responsible for the enhanced constitutional undercooling and the cellular–dendritic transition.

Quantifying Nucleation Rates in Phase-Transforming Metal-Ion Intercalation Materials Based on Cyclic Voltammetry and Chronoamperometry Data

Phase-transforming cathode materials with a wide miscibility gap have been extensively studied for both Li-ion (LiFePO4, Li4Ti5O12) and Na-ion (Na3V2(PO4)3) batteries. In particular, LiFePO4 material has become a model system for the investigation of intercalation induced phase transformation mechanisms.1 Most of the state-of-the-art research on the phase-separating intercalation materials focuses on the elucidation of phase transformation mechanisms as well as on the theoretical assessment of the nucleation barrier heights based on the evidence from structural investigation and microscopic single particle-level experiments.2 In this work, we show that the new phase nucleation appears to be a characteristic rate-determining step for a wide range of intercalation materials (LiFePO4, V2O5, cation-rich Prussian blue analogues, Na3V2(PO4)3). We demonstrate that the nucleation rates (probabilities of critical nucleus formation) can be straightforwardly determined from the electrochemical experimental data. A simple experimental approach is proposed based on the classical nucleation theory toward interpreting electrochemical cyclic voltammetry and chronoamperometry data for phase-transforming electrodes.3 The new methodology provides for a facile assessment of the influence of various experimental factors (particle size, defect concentration, solvent nature, and surface coating) on the nucleation-controlled phase-transformation rates in intercalation materials.4 Experimental data analysis illustrates the validity of the applied approaches, which allows developing diagnostic criteria for distinguishing slow nucleation rate control from other possible rate-determining steps as well as obtaining quantitative estimates of the nucleation rate constants. R e f e r ence s 1. Malik, R.; Abdellahi, A.; Ceder, G. J. Electrochem. Soc. 2013, 160, A3179.2. Bai, P.; Bazant, M. Z. Nat. Commun. 2014, 5, 3585.3. Vassiliev, S.Yu.; Levin, E.E; Presnov, D.E; Nikitina, V.A. J. Electrochem. Soc. 2019, 166, A829.4. Iarchuk, A.R.; Nikitina, V.A.; Karpushkin, E.A.; Sergeyev, V.G.; Antipov, E.V.; Stevenson, K.J.; Abakumov, A.M. ChemElectroChem 2019, 6, 5090. Figure 1

Entire crystallization process of Lennard-Jones liquids: A large-scale molecular dynamics study.

By using a graphics processing unit-accelerated parallel algorithm on a compute unified device architecture platform, we perform large-scale molecular dynamics simulations in a Lennard-Jones system to observe the entire crystallization process, including metastable stage, critical nuclei formation, and the stage of crystal growth. Although the intermediated precursors that play a role in determining the polymorphs are predominantly bcc ordered, the polymorph selection is rather different at different stages. The precursors that have a relatively high orientational order will be on average in a denser region than uniform liquids, but microscopically the crystal nucleation happens without a density change. The average density of nuclei first increases significantly, and then almost keeps independent on the crystallite size after the growing post-critical nucleus becomes large enough. With such a large enough system, the crystal growth rate is able to be calculated directly by doing a linear fit to the temporal evolution of growing crystallite size. The obtained value of the growth rate indicates that the actual crystal growth in the Lennard-Jones system where the crystal-liquid interface has several kinds of structures is possibly driven by both collision-controlled and diffusion-controlled mechanisms.

Formation pathways for MgO·Al2O3 inclusions in iron melt

The crystallization of inclusions plays a decisive role in determining the structure, properties and size distribution of inclusions in steel. MgO·Al2O3 (MA) spinel is one of the most common inclusions having great influence on steel performance. Understanding the crystallization pathways of MA from molten steel is important to control their behaviors. Based on the thermodynamic properties of metastable phases of MA calculated by first principle prior to critical nucleus formation, the present work suggests that there are four possible pathways for MA inclusions nucleation from molten iron. According to the four nucleation pathways, the reaction among [Mg], [Al] and [O] could be the most probable pathway leading to MA inclusion formation, while Al2O3 reacting with MgO is almost impossible pathway for MA inclusion formation. The size of MA inclusions is dominated by the formation pathways, which have a close relationship with the adding ways of deoxidizer.

Studies on nucleation kinetics of pyridoxal 5-phosphate monohydrate in water

With the change of pH, the metastable zone of PLP in water was measured at various temperatures by applying laser monitoring method under normal pressure. The metastable zone became wider as the pH increased within the studied scope, but it became narrower as the temperature increased within the studied scope. With the change of supersaturation ratio, the induction period of PLP in water was also measured at various temperatures. According to the classical homogeneous nucleation theory, the crystal-solution interfacial tensions at various temperatures were calculated which were then used to calculated the primary nucleation parameters containing per unit volume free energy change (ΔGv), critical free energy change for the formation of critical crystal nucleus (ΔG*), radius of critical crystal nucleus (r*) and the molecular number in the critical crystal nucleus.

Structural Analysis and Growth Mechanism of Zn/ZnO Nanowires in AAO Template by Electrodeposition

To fully understand the mechanism of forming Zn and ZnO nanowires in electrodeposition, Anodic Alumina Oxide (AAO) membrane was used to electrodeposit Zn/ZnO nanowires by varying the potential. The structure of electrodeposited Zn/ZnO nanowires is studied by means of X-ray diffraction and scanning electron microscopy. Different deposition parameters were used to obtain different structure of electrodeposited nanowires. At -1.4 V with pH2.5, the pure Zn nanowires are electrodeposited. By lowering the potential to -1.0 V with same electrolytic concentration and pH, the formed nanowires are mixture of Zn and ZnO. Further decrease in potential to -0.6V, electrodeposited nanowires are of pure ZnO. The size of the critical cluster decreases with increasing the over potential. The formation of pure ZnO nanowires can be attributed to the formation of large size critical Zn nuclei, the larger size of nuclei favors the formation of pure zinc oxides nanowires.

Shortening Nucleation Time to Enable Ultrafast Phase Transition in Zn1Sb7Te12 Pseudo-Binary Alloy.

Zn1Sb7Te12 thin films have been deposited by magnetron co-sputtering of ZnTe and Sb2Te3 targets. The microstructure, phase-change speed, optical cycling stability, and crystallization kinetics have been investigated during thermal annealing and laser irradiation. The thermal-annealed and laser-irradiated films give a clear evidence of the coexistence of trigonal Sb2Te3 and cubic ZnTe phases, which are homogeneously distributed in a single alloy as confirmed by advanced scanning transmission electron microscopy. The formation of both phases increases the initial nucleation sites, leading to the rapid phase-change speed in the Zn1Sb7Te12 film. The film has a minimum crystallization time of ∼3 ns at 70 mW with almost no incubation period for the formation of critical nuclei compared to Ge2Sb2Te5 and other Zn-based films. Moreover, the complete crystallization of Zn1Sb7Te12 thin films is achieved within 10 ns. The ultrafast two-dimensional nucleation and crystal growth speed in Zn1Sb7Te12 obtained from the laser-irradiated system is almost 7 times faster compared to that in Ge2Sb2Te5 film. Controlling the crystallization process through doping ZnTe into Sb2Te3 is thus promising for the development of high-speed optical switching technology.

Ideal and Ultimate Tensile Strength of a Solid Body

The mechanical stability of an ideal elastic solid under infinitesimal and finitesimal changes in its state parameters is considered. The temperature and density dependences of the isothermic moduli of bulk compression K, simple shear, and tetragonal shear in a Lennard-Jones face-centered cubic (FCC) crystal have been determined by means of molecular dynamic experiments in the region of stable and metastable states. It has been shown that the crystalline phase remains stable under long-wave spatially nonuniform density fluctuations on the spinodal (K = 0) at pressures below the pressure of the endpoint of the melting line (p < pK < 0). Here, the critical nucleus formation work is also finitesimal. Hence, spinodal states in quasisteady- state processes at p < 0 not only are attainable, but the transition across the spinodal without destroying the homogeneity in the substance also proves to be feasible. In this case, the boundary of the ideal strength of a solid is set by the vanishing of the uniaxial compression modulus \(\tilde K\) for a certain specified deformation direction. The spinodal also is not the boundary of the ideal strength of a solid at positive and small negative pressures. A solid loses its ability for a restorative response to finitesimal spatially nonuniform density disturbances before the spinodal (\(\tilde K\) = 0) is attained.

Investigation of Deposits in Channels of Panels of a Heat-Transfer Agent

An analysis of the behavior of nanosized colloidal particles in a supersaturated solution made it possible to substantiate the possibility of increasing the heat-transfer efficiency in a heat exchanger during magnetic treatment of a heat-transfer agent. A model is proposed to weaken the scale during magnetic treatment of a water stream. A colloidal solution is shown to decrease its stability—the coagulation of colloidal particles begins—because of the deformation of the double electrical layer. As a result of increasing the effective radius of curvature of nanoparticles, the solution becomes strongly supersaturated with respect to forming aggregates, which accelerates the solidification of dissolved salts on them. The influence of the interfacial layer of nanoobjects decreases the energy of formation of critical nuclei (size effect) and their sizes. Since coagulation tends to decrease the concentration of critical nuclei in the solution, their loss should be compensated via the homogeneous generation of new nuclei. As a result, the concentration of suspended particles increases additionally and the antiscale effect is enhanced. The solidification flux of dissolved salts is shown to deposit mainly on suspended nanoparticles due to an increase in their total surface area and to the fact that the coefficient of mass transfer to suspension is higher than that to the wall by four orders of magnitude. The mathematical model constructed on the basis of the detected set of physical processes can be used to perform quantitative estimates of the antiscale effect in real power plants.