Classical Nucleation Model Research Articles

Molecular-Level Understanding of Continuous Growth from Iron-Oxo Clusters to Iron Oxide Nanoparticles.

The formation of inorganic nanoparticles has been understood based on the classical crystallization theory described by a burst of nucleation, where surface energy is known to play a critical role, and a diffusion-controlled growth process. However, this nucleation and growth model may not be universally applicable to the entire nanoparticle systems because different precursors and surface ligands are used during their synthesis. Their intrinsic chemical reactivity can lead to a formation pathway that deviates from a classical nucleation and growth model. The formation of metal oxide nanoparticles is one such case because of several distinct chemical aspects during their synthesis. Typical carboxylate surface ligands, which are often employed in the synthesis of oxide nanoparticles, tend to continuously remain on the surface of the nanoparticles throughout the growth process. They can also act as an oxygen source during the growth of metal oxide nanoparticles. Carboxylates are prone to chemical reactions with different chemical species in the synthesis such as alcohol or amine. Such reactions can frequently leave reactive hydroxyl groups on the surface. Herein, we track the entire growth process of iron oxide nanoparticles synthesized from conventional iron precursors, iron-oleate complexes, with strongly chelating carboxylate moieties. Mass spectrometry studies reveal that the iron-oleate precursor is a cluster comprising a tri-iron-oxo core and carboxylate ligands rather than a mononuclear complex. A combinatorial analysis shows that the entire growth, regulated by organic reactions of chelating ligands, is continuous without a discrete nucleation step.

Thermodynamic Overpotentials and Nucleation Rates for Electrodeposition on Metal Anodes.

Rechargeable batteries employing metal negative electrodes (i.e., anodes) are attractive next-generation energy storage devices because of their greater theoretical energy densities compared to intercalation-based anodes. An important consideration for a metal's viability as an anode is the efficiency with which it undergoes electrodeposition and electrodissolution. The present study assesses thermodynamic deposition/dissolution efficiencies and associated nucleation rates for seven metals (Li, Na, K, Mg, Ca, Al, and Zn) of relevance for battery applications. First-principles calculations were used to evaluate thermodynamic overpotentials at terraces and steps on several low-energy surfaces of these metals. In general, overpotentials are observed to be the smallest for plating/stripping at steps and largest at terrace sites. The difference in the coordination number for a surface atom from that in the bulk was found to correlate with the overpotential magnitude. Consequently, because of their low bulk coordination, the body-centered alkali metals (Li, Na, and K) are predicted to be among the most thermodynamically efficient for plating/stripping. In contrast, metals with larger bulk coordination such as Al, Zn, and the alkaline earths (Ca and Mg) generally exhibit higher thermodynamic overpotentials. The rate of steady-state nucleation during electrodeposition was estimated using a classical nucleation model informed by the present first-principles calculations. Nucleation rates are predicted to be several orders of magnitude larger on alkali metal surfaces than on the other metals. This multiscale model highlights the sensitivity of the nucleation behavior on the structure and composition of the electrode surface.

Amorphous-Phase-Mediated Crystallization of Ni Nanocrystals Revealed by High-Resolution Liquid-Phase Electron Microscopy.

Nonclassical features of crystallization in solution have been recently identified both experimentally and theoretically. In particular, an amorphous-phase-mediated pathway is found in various crystallization systems as an important route, different from the classical nucleation and growth model. Here, we utilize high-resolution in situ transmission electron microscopy with graphene liquid cells to study amorphous-phase-mediated formation of Ni nanocrystals. An amorphous phase is precipitated in the initial stage of the reaction. Within the amorphous particles, crystalline domains nucleate and eventually form nanocrystals. In addition, unique crystallization behaviors, such as formation of multiple domains and dislocation relaxation, are observed in amorphous-phase-mediated crystallization. Theoretical calculations confirm that surface interactions can induce amorphous precipitation of metal precursors, which is analogous to the surface-induced amorphous-to-crystalline transformation occurring in biomineralization. Our results imply that an unexplored nonclassical growth mechanism is important for the formation of nanocrystals.

Engineering Nucleation Kinetics of Graphite Nodules in Inoculated Cast Iron for Reducing Porosity

Inoculation of cast iron with spherical graphite (SGI) controls nucleation kinetics of graphite nodules and is used for improving casting performance and eliminating solidification micro-porosity. In this study, thermodynamic simulations were used to design inoculants. Thermal and chemical stability of different potential heterogeneous nuclei formed in the melt above the liquidus temperature and in the mushy zone during solidification was predicted. Several inoculation treatments of SGI were performed in laboratory heats. An automated SEM/EDX analysis was applied to examine the graphite nodule size distribution and the family of the non-metallic inclusions in the experimental castings. The data were used to reconstruct a relative graphite nodule nucleation rate in the castings. It was shown that the graphite nodule nucleation kinetics in the castings were significantly different from those predicted by classical nucleation models. In inoculated SGI, the observed bi-modal distribution of graphite nodules was related to a continuous nucleation that occurred towards the end of solidification. The origin of the continuous nucleation and the possibility of engineering graphite nodules nucleation kinetics to control SGI casting soundness by inoculation are discussed.

Modelling of differential scanning calorimetry heating curves for precipitation and dissolution in an Al-Mg-Si

A detailed understanding of precipitation is essential to alloy and process design in age hardened metals, but experimental observation of the underlying processes is challenging. To accelerate such investigations, we introduce a model to simulate Differential Scanning Calorimetry (DSC) curves. The precipitation behavior of an AA6016 aluminum alloy was simulated by a classical nucleation and growth model, coupled with a thermodynamic database containing Al, Mg, Si, Fe, Cu and Mn and their corresponding stable and metastable phases. The focus was laid on the evolution of the phases β″, β′, β (Mg2Si) and Si under isothermal and non-isothermal conditions. DSC tests with rates of 5 and 10 K/min were conducted in the temperature range of 100–500 °C. The simulations were compared to these experiments. Transmission Electron Microscopy (TEM) was used to verify the precipitate phases and their sizes. The simulation results agree well with the experimental DSC curves and particle sizes.

Parameters Determination of grain Microstructure Prediction for a Single Crystal Casting Simulation and Its Experimental Validation

Microstructure prediction is very important in single crystal casting simulation. In order to predict microstructure accurately, both grain nucleation and dendrite growth have to be modeled properly beside the correct setups on geometry, alloy chemistry, thermal/fluid, and processing conditions. For nucleation, the classic normal Gaussian distribution nucleation model was used. An extended KGT model was applied to predict the dendrite growth of multicomponent alloy castings. There are several parameters for both nucleation and growth models which are difficult to measure experimentally. The growth coefficients in the growth model are normally chemistry dependent. All parameters are critical to assure the reliability of the simulation. The current paper shows how to determine those parameters with the comprehensive knowledge of physics and its implementation behind the simulation model. It is intended to shed some light for the readers to better apply this model in their grain structure simulations, particularly on DC and single crystal castings, in the future by applying the presented methodology of the parameter determination in this paper. An even more important one is that a large amount of experiments have been performed. Excellent agreement has been reached statistically between experiment and simulation in terms of grain mis-orientation.

Crystal Nucleation and Growth in Undercooled Melts of Pure Zr, Binary Zr-Based and Ternary Zr-Ni-Cu Glass-Forming Alloys

Glass formation of a liquid undercooled below its melting temperature requires the complete avoidance of crystal nucleation and subsequent crystal growth. Even though they are not part of the glass formation process, a detailed knowledge of both processes involved in crystallization is mandatory to determine the glass-forming ability of metals and metallic alloys. In the present work, methods of containerless processing of drops by electrostatic and electromagnetic levitation are applied to undercool metallic melts prior to solidification. Heterogeneous nucleation on crucible walls is completely avoided giving access to large undercoolings. A freely suspended drop offers the additional benefit of showing the rapid crystallization process of an undercooled melt in situ by proper diagnostic means. As a reference, crystal nucleation and dendrite growth in the undercooled melt of pure Zr are experimentally investigated. Equivalently, binary Zr-Cu, Zr-Ni and Zr-Pd and ternary Zr-Ni-Cu alloys are studied, whose glass-forming abilities differ. The experimental results are analyzed within classical nucleation theory and models of dendrite growth. The findings give detailed knowledge about the nucleation-undercooling statistics and the growth kinetics over a large range of undercooling.

Analysis of the transient behavior of nucleation in the Fe40Ni40P14B6 glass

The experimental isothermal kinetic curves for the Fe40Ni40P14B6 glass measured in the temperature range from 617 to 662 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. Two free parameters of the model have been estimated: i) the crystallization time that is inversely proportional to the rates of nucleation and growth (τc) and ii) the transient nucleation time (τns). For both the times, an Arrhenius-type temperature dependence has been established, with activation energies of 38300 and 70650 K, respectively. Both the Avrami exponent, n, and the τns/τc ratio decrease as the annealing temperature rises (from 6.79 to 4.36 and from 1.47 to 0.025, respectively). This fact indicates approaching to the steady state nucleation rate. The steady state nucleation rate in the Fe40Ni40P14B6 glass estimated with using the values of growth rate available in the literature increases from 1.5 × 1016 to 1.7 × 1017 m−3s−1. The values of the crystal/liquid interfacial energy calculated within the classical model of homogeneous nucleation are 0.152–0.156 J/m2 in the temperature range investigated.

From Microparticles to Nanowires and Back: Radical Transformations in Plated Li Metal Morphology Revealed via in Situ Scanning Electron Microscopy

Li metal is the preferred anode material for all-solid-state Li batteries. However, a stable plating and stripping of Li metal at the anode-solid electrolyte interface remains a significant challenge particularly at practically feasible current densities. This problem usually relates to high and/or inhomogeneous Li-electrode-electrolyte interfacial impedance and formation and growth of high-aspect-ratio dendritic Li deposits at the electrode-electrolyte interface, which eventually shunt the battery. To better understand details of Li metal plating, we use operando electron microscopy and Auger spectroscopy to probe nucleation, growth, and stripping of Li metal during cycling of a model solid-state Li battery as a function of current density and oxygen pressure. We find a linear correlation between the nucleation density of Li clusters and the charging rate in an ultrahigh vacuum, which agrees with a classical nucleation and growth model. Moreover, the trace amount of oxidizing gas (≈10-6 Pa of O2) promotes the Li growth in a form of nanowires due to a fine balance between the ion current density and a growth rate of a thin lithium-oxide shell on the surface of the metallic Li. Interestingly, increasing the partial pressure of O2 to 10-5 Pa resumes Li plating in a form of 3D particles. Our results demonstrate the importance of trace amounts of preexisting or ambient oxidizing species on lithiation processes in solid-state batteries.

Experimental investigation and simulation of precipitation evolution in Mg-3Nd-0.2Zn alloy

In this research, precipitation evolution and strengthening behavior in Mg-3Nd-0.2Zn alloy during isothermal age treatment at 200°C are quantitatively studied by a combination of experimental investigation and computational simulation. Microstructure evolution, including volume fraction, number density, and size of precipitates are first measured by TEM and DSC techniques and then modeled using an integrated computational simulation method combining the CALPHAD (CALculation of PHAse Diagram) approach and classical nucleation model. The focus of the analysis is set on the evolution of key strengthening precipitate β’. Critical kinetic parameters such as particle interfacial energy and nucleation site number are obtained computationally by fitting the model to the experimental data. Mechanical properties of a series of Mg-Nd-Zn alloys are predicted using the simulated microstructure evolution as inputs. Good agreement is found between simulated and measured results. Strategies for enhancing the precipitation hardening effect are presented and discussed based on the simulation results. The merit of this study is to use the obtained parameters to extrapolate microstructure evolution and mechanical properties when adjusting alloy composition and/or heat treatment conditions within a certain range, which will be very useful for further development and optimization of multi-component Mg alloys.

Utilizing in Situ Ec-S/TEM to Study Electrochemical Nucleation of Copper from a Bromide Electrolyte

Electrochemical nucleation of metals have long been investigated using chronoamperometry1, cyclic voltammetry2, and electrochemical impedance spectroscopy3 . The current/potential time transients from these methods are used as basis for models for various proposed nucleation mechanisms such as instantaneous and progressive nucleation4. Physical insight has been primarily inferred from the current/potential time transient models and ex situ analysis of the deposit thereafter. However, surface restructuring is known to occur ex situ. In situ methods, such as in situ STM5 and in situ AFM6, minimize ambiguous understanding due to surface restructuring; however, the time resolution of these methods are lacking7. Thus direct correlation between the nucleation processes and electrochemical measurements have not been studied in great detail due to the present lack of in situ characterization methods that permit the simultaneous acquisition of electrochemical measurements with high spatial resolution imaging and high time resolution processing within the electrolyte. Recent advances in liquid cell in situ electrochemical scanning/transmitting electron microscopy (ec-STEM), mitigates ambiguity due to surface restructuring following nucleation7, 8. In situ ec-STEM can acquire and analyze time-resolved images of the nucleation and growth process at the nanometer-scaled spatial resolution while quantitative electrochemical measurements are concurrently performed. Therefore, this technique can also provide clarity between nucleation growth and classical electrochemical nucleation models such as the Scharifker and Hills4 model and the Sluyter-Rehbach9 model. Recent advances in an all-copper flow battery has created a renewed interest in copper electrodeposition from a high halide electrolyte10. The high halide electrolyte is unique compared to traditional damascene plating in that the copper (I) oxidation state is stabilized. Here, we apply the in situ ec-STEM approach to investigate the electrochemical nucleation of copper in order to understand the negative electrode reaction in these all-copper batteries. This presentation compares the electrochemical nucleation of copper of high bromide ion electrolyte on a carbon versus copper electrode and discusses the nuances of in situ liquid cell ec-S/TEM. 1. Heerman, L.; Tarallo, A. Journal of Electroanalytical Chemistry 1999, 470, (1), 70-76. 2. Williams, D. E.; Wright, G. A. Electrochimica Acta 1976, 21, (11), 1009-1019. 3. Cachet, C.; Saïdani, B.; Wiart, R. Electrochimica Acta 1989, 34, (8), 1249-1250. 4. Scharifker, B.; Hills, G. Electrochimica Acta 1983, 28, (7), 879-889. 5. Itaya, K.; Tomita, E. Surface Science 1988, 201, (3), L507-L512. 6. Rynders, R. M.; Alkire, R. C. Journal of The Electrochemical Society 1994, 141, (5), 1166-1173. 7. Williamson, M. J.; Tromp, R. M.; Vereecken, P. M.; Hull, R.; Ross, F. M. Nat Mater 2003, 2, (8), 532-536. 8. Unocic, R. R.; Sacci, R. L.; Brown, G. M.; Veith, G. M.; Dudney, N. J.; More, K. L.; Walden, F. S., II; Gardiner, D. S.; Damiano, J.; Nackashi, D. P. Microscopy and Microanalysis 2014, 20, (02), 452-461. 9. Sluyters-Rehbach, M.; Wijenberg, J. H. O. J.; Bosco, E.; Sluyters, J. H. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 1987, 236, (1–2), 1-20. 10. Lloyd, D.; Magdalena, E.; Sanz, L.; Murtomäki, L.; Kontturi, K. Journal of Power Sources 2015, 292, (0), 87-94.

Reply to "Comment on 'Simple improvements to classical bubble nucleation models' ".

We reply to the Comment by Schmelzer and Baidakov [Phys. Rev. E 94, 026801 (2016)].10.1103/PhysRevE.94.026801 They suggest that a more modern approach than the classic description by Tolman is necessary to model the surface tension of curved interfaces. Therefore we now consider the higher-order Helfrich correction, rather than the simpler first-order Tolman correction. Using a recent parametrization of the Helfrich correction provided by Wilhelmsen et al. [J. Chem. Phys. 142, 064706 (2015)]JCPSA60021-960610.1063/1.4907588, we test this description against measurements from our simulations, and find an agreement stronger than what the pure Tolman description offers. Our analyses suggest a necessary correction of order higher than the second for small bubbles with radius ≲1 nm. In addition, we respond to other minor criticism about our results.

Comment on "Simple improvements to classical bubble nucleation models".

A critical analysis of several statements concerning experimental studies, molecular dynamics simulations, and the theoretical interpretation of bubble nucleation processes is performed. In particular, it is shown that the Tolman equation does not supply us, in general, with a satisfactory theoretically founded description of the curvature dependence of the surface tension and the dependence of the steady-state nucleation rate of bubbles and droplets on supersaturation in the framework of classical nucleation theory.

Isoconversional Kinetics of Nonisothermal Crystallization of Salts from Solutions.

In this study, differential scanning calorimetry (DSC) has been applied to measure the kinetics of nonisothermal crystallization of potassium nitrate and ammonium perchlorate from unsaturated and saturated aqueous solutions. DSC data have been analyzed by an advanced isoconversional method that demonstrates that the process is represented by negative values of the effective activation energy, which varies with the progress of crystallization. The classical nucleation model can be used to predict and understand the experimentally observed variation in the effective activation energy. The saturated and unsaturated solutions have demonstrated distinctly different crystallization kinetics. It is suggested that the unsaturated solutions undergo a change in crystallization mechanism from homogeneous to heterogeneous nucleation.

Precipitation evolution and hardening in Mg[sbnd]Sm[sbnd]Zn[sbnd]Zr alloys

Precipitation evolution and its correspondence to mechanical properties in Mg4SmxZn0.4Zr (x = 0, 0.3, 0.6, 1.3) (wt%) alloys are systematically investigated in this work. Precipitation sequences at 200 °C are identified using transmission electron microscopy (TEM), high-resolution TEM (HRTEM), and high angle annular dark field scanning transmission electron microscopy (HAADF-STEM). A new precipitate β′Z is found to present with the increase of Zn addition. With higher Zn content (>∼1 wt%), basal γ-series precipitates dominate. The transition in precipitation sequence agrees well with the change of mechanical properties. The microstructure and property evolution in the optimum Mg4Sm0.3Zn0.4Zr alloy is modeled based on obtained experimental data through a combination of classical nucleation and growth model and the CALPHAD (CALculation of PhAse Diagram) simulation. The obtained parameters are then used to predict the properties of other MgSmZnZr alloys under other heat treatment conditions. Good agreements are found between the calculated and measured data, which validate the accuracy of the current database and suggest a powerful tool for future optimization of this promising alloy system.

Ice-water interfacial energy between 235.35 and 237.15 K deduced from homogeneous nucleation rate

Stan's experimental data of ice nucleation are re-analyzed in this paper. The ice-water interfacial energy is calculated from available data by classical nucleation models. Linear regression is employed to model the relation between the nucleation rate and temperature. A linear equation is suggested to calculate the ice-water interfacial energy between 235.35 and 237.15 K. The equation indicates that the ice-water interfacial energy decreases with temperature quicker than what is suggested by recent studies. This implies that, according to Stan's experiment, the structure of water molecular cluster is more similar to that of ice nucleus. A hybrid ice-water model with the ratio of cubic ice to hexagonal ice being 2:1 is utilized. Linear average is performed on the hybrid ice-water interfacial energy by the ratio. The result fits well with the ice-water interfacial energy given by the suggested equation.

Kinetic modeling of multi‐component crystallization of industrial‐grade oils and fats

Transient crystallization kinetics is investigated for complex, industrial‐grade vegetable oils consisting of more than ten triacylglycerols (TAG). The classical nucleation model has been used to describe primary nucleation, while secondary nucleation has been described by a semi‐empirical approach. Growth is modeled using a modified Burton‐Cabrera‐Frank (BCF) model. Surface tensions and growth constants have been determined using focused‐beam‐reflectance measurements (FBRM). The required adjustable parameters in the model have been fitted to overall crystallization curves obtained by solid‐fat content (SFC) measurements for a given oil at different cooling rates and degrees of dilution. The developed model can accommodate more polymorphs simultaneously and performs well with respect to predicting crystallization onset, rate of crystallization and final SFC value. It can also qualitatively describe how higher cooling rates lead to formation of more meta‐stable crystals and smaller mean‐crystal sizes.Practical applications: The model provides a good starting point for developing more realistic, transient models for TAG crystallization with the ability to accommodate processing conditions and complex chemical compositions. Such a predictive model may provide a powerful tool to screen and optimize oil formulations in industrial processes and allow product developers to evaluate recrystallization events.An advanced transient, mathematical model describing the course of crystallization in natural, multi‐component, multi‐phase vegetable oils and fats has been developed. The model is based on well described nucleation and growth kinetics and accommodates the presence of more polymorphic crystal forms. The result is an industry‐relevant model aiding understanding and predictability of oil and fat crystallization with respect to processing conditions and chemical compositions.

Coil‐to‐Globule Transition of Poly(N‐isopropylacrylamide) in Aqueous Solution: Kinetics in Bulk and Nanopores

Differential scanning calorimetry (DSC) is used to study the kinetics of the coil‐to‐globule transition in aqueous solutions of poly(N‐isopropoylacrylamide) (PNIPAM) prepared in the bulk (3 and 10 wt%) and nanoconfined (10 wt% inside 30 nm silica pores) forms. It is demonstrated that the kinetics can be described in terms of the classical nucleation model. The proposed treatment affords estimating the free‐energy barrier and pre‐exponential factor of the transition. The application of the nucleation model to the DSC data collected for the three systems studied provides physical insights into the effect of increasing the transition temperature due to dilution and nanoconfinement. Dilution appears to raise the free‐energy barrier, whereas nanoconfinement causes a decrease in the pre‐exponential factor. image

Universal ferroelectric switching dynamics of vinylidene fluoride-trifluoroethylene copolymer films.

In this work, switching dynamics of poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] copolymer films are investigated over unprecedentedly wide ranges of temperature and electric field. Remarkably, domain switching of copolymer films obeys well the classical domain nucleation and growth model although the origin of ferroelectricity in organic ferroelectric materials inherently differs from the inorganic counterparts. A lower coercivity limit of 50 MV/m and 180° domain wall energy of 60 mJ/m2 are determined for P(VDF-TrFE) films. Furthermore, we discover in copolymer films an anomalous temperature-dependent crossover behavior between two power-law scaling regimes of frequency-dependent coercivity, which is attributed to the transition between flow and creep motions of domain walls. Our observations shed new light on the switching dynamics of semi-crystalline ferroelectric polymers, and such understandings are critical for realizing their reliable applications.

Amorphous to Crystal Conversion as a Mechanism Governing the Structure of Luminescent YVO4:Eu Nanoparticles

The development of functional materials by taking advantage of the physical properties of nanoparticles needs an optimal control over their size and crystal quality. In this context, the synthesis of crystalline oxide nanoparticles in water at room temperature is a versatile and industrially appealing process but lacks control especially for "large" nanoparticles (>30 nm), which commonly consist of agglomerates of smaller crystalline primary grains. Improvement of these syntheses is hampered by the lack of knowledge on possible intermediate, noncrystalline stages, although their critical importance has already been outlined in crystallization processes. Here, we show that during the synthesis of luminescent Eu-doped YVO4 nanoparticles a transient amorphous network forms with a two-level structuration. These two prestructuration scales constrain topologically the nucleation of the nanometer-sized crystalline primary grains and their aggregation in nanoparticles, respectively. This template effect not only clarifies why the crystal size is found independent of the nucleation rate, in contradiction with the classical nucleation models, but also supports the possibility to control the final nanostructure with the amorphous phase.