Homogeneous Nucleation Theory Research Articles

On the theory of the nucleation of gas bubbles at grain boundaries and incoherent inclusions

On the base of the critical analysis of two-dimensional models of the nucleation of gas filled bubbles at grain boundaries of helium-implanted specimens under the action of tensile stresses, a new model is developed within the framework of the Reiss theory of homogeneous nucleation in binary systems. This approach considers that gas bubbles are formed as a result of agglomeration in a binary system of vacancies and gas atoms at grain boundaries, avoiding significant simplifications of previous models based on the classical nucleation theory for single-component (unary) systems. The new model is extended to consider the nucleation of Xe bubbles at grain boundaries in UO2 under irradiation conditions and can be used for numerical analysis of experimental observations after the foreseen implementation in a fuel performance code. A similar approach can be applied to the nucleation and growth of gas bubbles on incoherent inclusions, such as those observed in irradiated ODS steels.

In Situ Observation of Microstructure and Precipitate Phase Transformation during the Solidification of Mg‐Containing GH3625 Alloy at Different Cooling Rates

In practical applications, intermetallic compounds like Laves phase and metal carbides adversely affect the performance of nickel‐based superalloys. Using a high‐temperature confocal laser scanning microscope, the solidification process of as‐cast GH3625 alloy containing Mg at different cooling rates (−20, −35, and −50 °C min−1) is studied. Fitting curves of the volume fraction of the solid phase with solidification temperature before and after Mg treatment are obtained. Trends of solid phase transformation rates with solidification temperature are determined. Differential scanning calorimetry is employed to analyze and statistically evaluate the melting temperature range and enthalpy of each phase during the melting process. Experimental results demonstrate that Mg treatment significantly accelerates the alloy solidification at the cooling rates of −20 and −35 °C min−1, while reducing the area of residual liquid phase at the same solidification temperature, disrupting the Laves/NbC eutectic relationship, and regularizing NbC morphology, transitioning its distribution from aggregation to dispersion. After Mg treatment, the precipitation of the Laves phase is significantly reduced. As a result, the influence mechanism of Mg treatment on the phase transformation and microstructure of GH3625 is clarified based on homogeneous nucleation theory.

Bridging classical nucleation theory and molecular dynamics simulation for homogeneous ice nucleation.

Water freezing, initiated by ice nucleation, occurs widely in nature, ranging from cellular to global phenomena. Ice nucleation has been experimentally proven to require the formation of a critical ice nucleus, consistent with classical nucleation theory (CNT). However, the accuracy of CNT quantitative predictions of critical cluster sizes and nucleation rates has never been verified experimentally. In this study, we circumvent this difficulty by using molecular dynamics (MD) simulation. The physical properties of water/ice for CNT predictions, including density, chemical potential difference, and diffusion coefficient, are independently obtained using MD simulation, whereas the calculation of interfacial free energy is based on thermodynamic assumptions of CNT, including capillarity approximation among others. The CNT predictions are compared to the MD evaluations of brute-force simulations and forward flux sampling methods. We find that the CNT and MD predicted critical cluster sizes are consistent, and the CNT predicted nucleation rates are higher than the MD predicted values within three orders of magnitude. We also find that the ice crystallized from supercooled water is stacking-disordered ice with a stacking of cubic and hexagonal ices in four representative types of stacking. The prediction discrepancies in nucleation rate mainly arise from the stacking-disordered ice structure, the asphericity of ice cluster, the uncertainty of ice-water interfacial free energy, and the kinetic attachment rate. Our study establishes a relation between CNT and MD to predict homogeneous ice nucleation.

Bubble Dynamics in the Polyakov Quark-Meson Model

In the framework of the Polyakov quark-meson model with two flavors, the bubble dynamics of a first-order phase transition in the region of high density and low temperature are investigated by using the homogeneous thermal nucleation theory. In mean-field approximation, after obtaining the effective potential with the inclusion of the fermionic vacuum term, we build a geometric method to search two existing minima, which can be actually connected by a bounce interpolated between a local minimum to an adjacent global one. For both weak and strong first-order hadron quark phase transitions, as fixing the chemical potentials at μ=306MeV and μ=310MeV, the bubble profiles, the surface tension, the typical radius of the bounce, and the saddle-point action as a function of temperature are numerically calculated in the presence of a nucleation bubble. It is found that the surface tension remains at a very small value even when the density is high. It is also noticed that the deconfinement phase transition does not change the chiral phase transition dramatically for light quarks and phase boundaries for hadron and quark matter should be resized properly according to the saddle-point action evaluated on the bounce solution.

Effect of Carbon on Void Nucleation in Iron.

The study reports the significance of carbon presence in affecting void nucleation in Fe. Without carbon, void nucleation rates decrease gradually at high temperatures but remain significantly high and almost saturated at low temperatures. With carbon present, even at 1 atomic parts per million, void nucleation rates show a low-temperature cutoff. With higher carbon levels, the nucleation temperature window becomes narrower, the maximum nucleation rate becomes lower, and the temperature of maximum void nucleation shifts to a higher temperature. Fundamentally, this is caused by the change in effective vacancy diffusivity due to the formation of carbon-vacancy complexes. The high sensitivity of void nucleation to carbon comes from the high sensitivity of void nucleation to the vacancy arrival rate in a void. The void nucleation is calculated by first obtaining the effective vacancy diffusivity considering the carbon effect, then calculating the defect concentration and defect flux change considering both carbon effects and pre-existing dislocations, and finally calculating the void nucleation rate based on the recently corrected homogeneous void nucleation theory. The study is important not only in the fundamental understanding of impurity effects in ion/neutron irradiation but also in alloy engineering for judiciously introducing impurities to increase swelling resistance, as well as in the development of simulation and modeling methodologies applicable to other metals.

On the theory of nucleation of coherent inclusions in irradiated crystals

Based on a critical analysis of the existing model for the effect of excess vacancies and interstitials on the nucleation of coherent particles under irradiation, a new nucleation model is developed that uses the Brailsford-Bullough model for the steady state occupation probabilities of vacancies and interstitials at the particle interface, recently refined by the author. It is shown that, depending on the surface tension γ of a coherent particle, the nucleation mechanism can be qualitatively different. In the case of a relatively small γ, an instability can arise in the irradiated solid solution leading to the barrier-free nucleation of coherent precipitates. In the opposite case of a relatively large γ, the classical one-dimensional theory of homogeneous nucleation is applicable. In order to eliminate the uncertainty in the magnitude of surface tension (from the literature) and to better understand the underlying mechanisms of coherent particle nucleation in irradiation tests, additional atomistic studies are recommended.

Multiscale approach to the theory of nonisothermal homogeneous nucleation.

Molecular dynamics (MD) of the Lennard-Jones cluster in the environment of supersaturated vapor at fixed temperature and density is used for the investigation of nonisothermal nucleation. The results allow one to single out different processes occurring at different time scales, the Ornstein-Uhlenbeck fluctuations at the short time scale and a combination of slow diffusion and drift of the fluctuation packet that represents a cluster, at the long time scale. The multiscale approach is developed, in which a separate treatment of different time scales makes it possible to consider strongly correlated cluster size and temperature. This reduces the nonisothermal cluster evolution to a one-dimensional problem. The fluctuation packet drift velocity and diffusivity are calculated based on the cluster microscopic thermophysical parameters determined in this work from MD data for isothermal clusters. The proposed approach is consistent with the results of our MD simulation.

Application of binary homogeneous nucleation theory to the generation of liquid aerosols from water vapor with a highly dilute reactant

Application of binary homogeneous nucleation theory to the generation of liquid aerosols from water vapor with a highly dilute reactant

An entropic theory of homogeneous ice nucleation in non-ionic aqueous solutions.

The nucleation of ice from aqueous solutions is a process essential to myriad environmental and industrial processes, but the physical factors affecting the capacity of different solutes to depress the homogeneous nucleation temperature of ice are yet poorly understood. In this work, we demonstrate that for many binary aqueous solutions of non-ionic solutes, this depression is dominated by the entropy of the liquid phase. Employing the classic Turnbull interpretation of the interfacial free energy γ∼TSliquid-Ssolid and estimating solution entropies with a Flory-style modification of the ideal entropy of mixing that accounts for solute size effects, we demonstrate that mixing entropy alone predicts experimental homogeneous nucleation temperatures across a wide variety of non-ionic solutions. We anticipate that this physical insight will not only enhance a fundamental understanding of homogeneous nucleation processes across fields but also open new avenues to the rational design of aqueous solutions for desired nucleation behaviors.

Development of the Reiss theory for binary homogeneous nucleation of aerosols

Development of the Reiss theory for binary homogeneous nucleation of aerosols

Enhanced nucleation of bimodal molecular weight distribution polymers: A molecular dynamics study

We perform coarse-grained molecular dynamics (CGMD) simulations to study the homogeneous nucleation of bimodal and unimodal molecular weight distribution polymers with equivalent average molecular weight. First, a statistical method is proposed to determine the critical nuclei and thus calculate the free energy barrier of nucleation. From the temperature dependence of diffusion coefficient, we also determine the activation energy of diffusion. Then we calculate the nucleation rate and find that it is consistent with the classical nucleation theory for homogeneous nucleation in semi-crystalline polymers. Compared with unimodal system, the bimodal system exhibits lower interfacial free energy and consequently lower free energy barrier for nucleation, while the two systems have similar activation energy for diffusion. This suggests that the promoted nucleation rate of bimodal molecular weight distribution polymer is a result of the reduction of interfacial free energy, which is eventually a consequence of chain-folding nucleation of long chain component.

Focused Nanosecond Pulsed Laser‐Induced Homogeneous Nucleation in Undercooled Oxide Melts

Induced homogeneous nucleation of undercooling melt is a fundamental challenge with exciting implications for composite ceramic and metal alloy materials. Nucleation can be induced externally, but physical mechanical properties reduce due to the introduction of impurities. Herein, a novel focused nanosecond pulsed laser‐induced nucleation approach is demonstrated for oxide ceramic melts at undercooled state. Using a self‐made aerodynamic levitation setup, the pulsed laser‐induced nucleation is controlled by optimizing the pulse energy density at different undercooled temperatures. Exploiting this approach, nucleation and growth are observed from surface of undercooled alumina (Al2O3) and neodymium yttrium aluminum garnet (Nd:YAG) melts with high‐speed camera. The undercooling sample experiences a nucleate–solidify–recalescence–remelting–recalescence–solidify process. The correlation between nucleation time and undercooling temperature confirms that the undercooled melt is nucleated homogeneously by the pulsed laser. The special microstructural of samples agrees well with the prediction of two‐step nucleation theory. Therefore, an assumption for the nucleation mechanism with the high‐speed images and the microstructure analysis is proposed. This proposed method may provide a different perspective for the classical nucleation theory of homogeneous nucleation.

Primary Growth Behavior of Sulfur Particles through the Throttle Valve in the Transmission System of High Sulfur Content Natural Gas

The deposition of sulfur particles in gathering and transportation pipeline system can cause serious safety problems and economic losses. When the high sulfur content natural gas (HSCNG) flows through the throttle valve of the gathering and transportation system, it will cause the supersaturation of elemental sulfur in the gas phase, and then the sulfur crystal nuclei and sulfur particles will appear in the pipeline system. Studying the initial growth behavior of sulfur crystal nuclei and sulfur particles can lay a necessary prerequisite for the accurate prediction of sulfur particle deposition in high sulfur content natural gas gathering and transportation (HSCNGGT) pipelines. Based on the homogeneous nucleation theory in crystallization kinetics, a mathematical model of elemental sulfur nucleation was established. Taking the throttling condition in the process of HSCNGGT as an example, the effects of temperature, pressure and H2S concentration in HSCNG on the critical nucleation radius and nucleation rate of elemental sulfur were explored. The results show that: (1) after the supersaturation of elemental sulfur, sulfur crystal nuclei with nanoscale radius will be precipitated. The temperature and pressure after throttling have great influence on the nucleation radius, and the influence of H2S concentration on the nucleation radius is more complex. (2) The temperature, pressure and H2S concentration after throttling also have great influence on the nucleation rate. By solving the growth kinetics model of sulfur particles based on Brownian condensation, it is found that the nano-sized sulfur crystal nuclei can grow into micron-sized sulfur particles in a very short time.

SIMULATION OF AMMONIA SPRAY UNDER BOTH NORMAL EVAPORATING AND SUPERHEATED CONDITIONS

A predictive three-dimensional Eulerian-Lagrangian framework for ammonia spray is suggested, and its evolution characteristics under both normal evaporating and superheated conditions are unraveled. First, a simplified boundary model considering the effects of superheated fluid behaviors within the nozzle on the injection velocity and angle was proposed. The real vapor-liquid equilibrium theory is applied in the evaporation model to improve the prediction accuracy of the phase change. An explosion model with the homogenous nucleation theory was used to simulate the burst process. Then, the spray experiment for the liquid ammonia under varied conditions was conducted, and the high-speed diffused back illumination and schlieren approaches were adopted to measure the spray evolutions. Following that, the simulation results were verified against the experimental data under both normal evaporating and superheated conditions, and good agreements indicated that the suggested framework was feasible to accurately and efficiently simulate the evolutions and morphology of ammonia spray. Finally, the transient evolution characteristics of ammonia spray under various conditions were discussed. The heavy cooling effect of ammonia evaporation makes the initial fuel temperature have a notable effect on its spray penetration and expansion.

Kinetics of Nucleation in Superheated Liquid Oxygen-Nitrogen Solutions. 1. Experiment and Classical Homogeneous Nucleation Theory.

The method of lifetime measurement has been used to investigate the kinetics of spontaneous boiling-up of superheated liquid oxygen-nitrogen solutions. Experiments have been conducted at pressures of 0.5 and 1.0 MPa in the range of nucleation rates 104-108 m-3 s-1 in the whole concentration range. The temperature and concentration dependences of the nucleation rate have been determined. The sections corresponding to homogeneous nucleation have been singled out on experimental isobars. At fixed nucleation rates and pressures, the concentration dependence of the attainable-superheat temperature is close to a linear one. A comparison of experimental data with classical nucleation theory (CNT) has revealed systematic discrepancies, which are of qualitatively different character for pure liquids and solutions. In a pure liquid, the surface tension of critical bubbles is less, and in a solution, it is greater than at a flat interface.

Explosive Vaporization of Ethanol on Microheater during Pulse Heating

The article is devoted to the research of transient heat transfer, explosive vaporization and condensation in subcooled ethanol on microheater during pulsed heating. Experiments were performed using high-speed infrared thermography and visualization for various initial liquid temperatures 30–60 °C and heat fluxes in the range of 3.3–7.8 MW/m2. The evolution of temperature field of the microheater and liquid during transient heating and the nucleation temperatures for different heat fluxes and liquid subcooling were determined. It was shown that the nucleation temperature was almost independent on heating power and amounted to 194 °C, which is close to the calculations based on homogeneous nucleation theory. New experimental data were obtained on the times of convection and boiling onset, evolution of vapor bubbles, including the dependence of their maximum sizes on the heat flux and initial liquid temperature. It was shown that the maximum bubble size decreases with an increase in the heat flux and liquid subcooling, varying in the same range as for water. It was demonstrated that at low heat fluxes, during condensation, a liquid funnel was formed at the bubble top, which resembled the formation of a liquid jet during the collapse of cavitation bubbles.

Semiflexible oligomers crystallize via a cooperative phase transition.

Semicrystalline polymers are ubiquitous, yet despite their fundamental and industrial importance, the theory of homogeneous nucleation from a melt remains a subject of debate. A key component of the controversy is that polymer crystallization is a non-equilibrium process, making it difficult to distinguish between effects that are purely kinetic and those that arise from the underlying thermodynamics. Due to computational cost constraints, simulations of polymer crystallization typically employ non-equilibrium molecular dynamics techniques with large degrees of undercooling that further exacerbate the coupling between thermodynamics and kinetics. In a departure from this approach, in this study, we isolate the near-equilibrium nucleation behavior of a simple model of a melt of short, semiflexible oligomers. We employ several Monte Carlo methods and compute a phase diagram in the temperature-density plane along with two-dimensional free energy landscapes (FELs) that characterize the nucleation behavior. The phase diagram shows the existence of ordered nematic and crystalline phases in addition to the disordered melt phase. The minimum free energy path in the FEL for the melt-crystal transition shows a cooperative transition, where nematic order and monomer positional order move in tandem as the system crystallizes. This near-equilibrium phase transition mechanism broadly agrees with recent evidence that polymer stiffness plays an important role in crystallization but differs in the specifics of the mechanism from several recent theories. We conclude that the computation of multidimensional FELs for models that are larger and more fine-grained will be important for evaluating and refining theories of homogeneous nucleation for polymer crystallization.

Choked liquid flow in nozzles: Crossover from heterogeneous to homogeneous cavitation and insensitivity to depressurization rate

The critical mass flow rate is the maximum flow rate that can pass through a constrained geometry such as a nozzle. For liquid CO2, it has been shown that homogeneous relaxation models systematically underpredict the critical mass flow rate. In this work, we demonstrate that a delay of the phase transition is necessary to reproduce experiments. To analyze this in further detail, two methodologies are presented: (1) the delayed homogeneous relaxation model (Delayed HRM), and (2) the metastable isentrope model (MIM). Delayed HRM is a relaxation model that can readily be incorporated into a spatially distributed description of the fluid flow, e.g. in ejectors. MIM assumes isentropic flow and instantaneous equilibrium up to the limit of metastability, and yields a geometry-independent critical mass flux as the solution of a set of algebraic equations. We compare the two methodologies to available experimental data on the critical mass flow rates of CO2 and H2O through nozzles, finding that they give nearly identical predictions. This suggests that the critical mass flow rate is mostly determined by the achievable degree of metastability before onset of phase change, and is rather insensitive to dynamic variables such as the depressurization rate or the rate of relaxation towards equilibrium. Using the limit of metastability predicted by homogeneous nucleation theory works well at high temperatures, rendering the methodologies completely predictive. They deviate on average 11% from experimental data on CO2, and thus outperform homogeneous relaxation models by a large margin, even when the latter employs several fitted parameters. Especially good agreement was found with experiments that employ a lubrication oil, which is hypothesized to suppress heterogeneous nucleation. The limit of superheat at lower temperatures must be described by heterogeneous nucleation theory. For water and CO2 we find a crossover between homogeneous and heterogeneous nucleation at T≈590 K and T≈285 K respectively. Moreover, the predicted limit of superheat falls on a single curve in the temperature–pressure space of water, and we present an empirical correlation of this curve. By combining this expression with the above methodologies, we obtained an average deviation of 3% with available experimental data on H2O mass flow rates.

On the Theory of Two-Dimensional Homogeneous Nucleation on Close-Packed Faces of Crystals Growing from Vapour

On the Theory of Two-Dimensional Homogeneous Nucleation on Close-Packed Faces of Crystals Growing from Vapour

Isothermal Crystallization and Time-Temperature Transformation of Amorphous Nifedipine: A Case of Polymorphism Formation and Conversion.

Crystallization of active pharmaceutical ingredients (APIs) from the supercooled liquid state is an important issue in determining the stability of amorphous pharmaceutical dispersions. In the present study, the isothermal crystallization from the supercooled liquid state of the pharmaceutical compound nifedipine was investigated by both rheological and differential scanning calorimetry (DSC) measurements, and the crystallization kinetics was fitted to the Johnson-Mehl-Avrami (JMA) equation. Both the crystallization induction time and completion time from the two methods were used to construct the time-temperature-transformation (TTT) diagram for nifedipine. A model based on a modification of classical homogeneous nucleation and crystal growth theory was employed to fit the induction and completion time curves. Both DSC and rheological methods give similar results for the crystallization kinetics of the nifedipine. From the crystallization kinetics modeling, the solid-liquid interfacial surface tension σSL of nifedipine was estimated and the value was found to be consistent with prior results obtained from melting point depression measurements as a function of crystal size. Evidence is shown that for temperatures below 110 °C, at the early stage of nucleation, NIF first nucleates into the metastable β'-form and later converts into the stable α-form during the isothermal crystallization. We are also able to report the heat of fusion of the γ'-NIF based on the calorimetric experiments.