Classical Heterogeneous Nucleation Theory Research Articles

Direct numerical simulations of microlayer formation during heterogeneous bubble nucleation

In this article, we present direct numerical simulation results for the expansion of spherical cap bubbles attached to a rigid wall due to a sudden drop in the ambient pressure. The critical pressure drop beyond which the bubble growth becomes unstable is found to match well with the predictions from classical theory of heterogeneous nucleation imposing a quasi-static bubble evolution. When the pressure drop is significantly higher than the critical value, a liquid microlayer appears between the bubble and the wall. In this regime, the interface outside the microlayer grows at an asymptotic velocity that can be predicted from the Rayleigh–Plesset equation, while the contact line evolves with another asymptotic velocity that scales with a visco-capillary velocity that obeys the Cox–Voinov law. In general, three distinctive regions can be distinguished: the region very close to the contact line where dynamics is governed by visco-capillary effects, an intermediate region controlled by inertio-viscous effects away from the contact line yet inside the viscous boundary layer, and the region outside the boundary layer dominated by inertial effects. The microlayer forms in a regime where the capillary effects are confined in a region much smaller than the viscous boundary layer thickness. In this regime, the global capillary number takes values much larger then the critical capillary number for bubble nucleation, and the microlayer height is controlled by viscous effects and not surface tension.

A universal and accurate LPMI method for calculating mismatch in heterogeneous ice nucleation.

The interfacial correlation factor f(m,x), where m refers to the interaction among ice, water and the substrate and x refers to the ratio of the critical nucleation size to the surface topography characteristic size of the substrate, plays a crucial role in the classical theory of heterogeneous ice nucleation as it significantly impacts the energy of nucleation. Generally, a smaller value of f(m,x) indicates a higher propensity for ice nucleation. The degree of structural compatibility between ice and the substrate greatly influences f(m,x), particularly on specific substrates. Several approaches have been proposed to calculate the lattice matching based on this idea, which allows whether a surface is favorable for nucleation to be determined. However, none of these methods adequately correlates the mismatch index with ice growth phenomena. In this paper, we embarked on a new attempt to calculate the mismatch index by combining the lattice parameter and Miller index (LPMI). Droplet freezing experiments have been carried out on α-Al2O3 and silicon surfaces with different Miller indices to verify the rationality of the LPMI method. Furthermore, we validated the LPMI method extensively against other works and further demonstrated its readiness, accuracy and universality for freezing problems. The results consistently show that δd = 2|di - ds|/(di + ds) with interplanar spacing more accurately predicts heterogeneous ice nucleation rates across a wide range of substrates than δ1 = (ai - as)/ai with the lattice parameter of ice and the substrate and is more generally applicable than δ2D = (di - di)/di with the distances between two adjacent and congener atoms on the same plane. We believe that the proposed approach will aid in the selection of substrates for promoting or inhibiting heterogeneous nucleation on a specific substrate.

The smallest nanodrop describable via macroscopic interfacial concepts: Testing classical heterogeneous nucleation theory with perfect wetting down to 3 nm

HypothesisThe smallest nanodrop tractable with macroscopic notions such as the interfacial energy could be determined by comparing heterogeneous nucleation observations and capillary theory predictions at decreasing drop diameters dp. AnalysisThis is done here for the condensation of n-butanol vapors on polyethylene glycol nano-globules (3 nm ≤ dp ≤ 9 nm). We use published activation probability measurements P(w,dp), where w is the accurately controlled saturation ratio of n-butanol vapor in a gas stream exiting a saturator. The maximal saturation ratio achieved in the nucleation region by cooling this gas-vapor stream in the apparatus of Gallar et al. satisfies Smax = Cw. The key unknown constant C and the preexponential term K governing the nucleation rate are determined by assuming that classical theory applies to the largest particles used. This yields P(Smax,dp) data, directly comparable with capillary theory with perfect wetting. FindingsExcellent agreement is found above 5 nm for the critical dependence Smax(dp) resulting from the constraint P(Smax,dp) = 0.5. The entire P(Smax,dp) curves also agree closely between 5 and 7 nm. Smaller particles depart only slightly from theory, even at dp = 3 nm. Capillary theory hence describes accurately the heterogeneous nucleation process above 3–5 nm, provides a reliable method to determine Smax, and yields experimentally the nucleation rate constant K.

"Anti-Condensation" Aluminum Superhydrophobic Surface by Smaller Nanostructures.

According to classical heterogeneous nucleation theory, the free energy barrier (ΔGc) of heterogeneous nucleation of vapor condensation ascends dramatically as the substrate nanostructure diameter (Rs) decreases. Based on this idea, we fabricated two types of superhydrophobic surfaces (SHSs) on an aluminum substrate by different roughening processes and the same fluorization treatment. Water vapor condensation trials by optical microscope and ESEM confirmed that on SHSs with submicron rectangle structures, a typical self-propelled motion of condensates or jumping condensation occurred. However, on SHS with coral-like micro/nano-structures, vapor nucleation occurred tardily, randomly, and sparsely, and the subsequent condensation preferentially occurred on the nuclei formed earlier, e.g., the condensation on such SHS typically followed the Matthew effect. Higher vapor-liquid nucleation energy barrier caused by smaller fluorinated nanostructures should be responsible for such a unique “anti-condensation” property. This study would be helpful in designing new SHSs and moving their application in anti-icing, anti-fogging, air humidity control, and so on.

Cluster activation studies with a diffusive condensation particle counter: Effect of chemical composition

We use KanomaxFMT's Fast Condensation Particle Counter (CPC) to study the growth (activation) of purified singly charged cluster ions of several salts by condensation of n-butanol vapor. Salts investigated include 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate (EMI-FAP), and four tetra-alkylammonium bromides (CpH2p+1)4N+-Br-, with p = 4, 6, 7, 12. The clusters studied contained up to 20 salt molecules, which were formed via a bipolar electrospray source, and were size-selected with a differential mobility analyzer. The CPC is operated at variable condenser and fixed saturator temperatures, Tc, Ts. It uses 75% sheath gas, such that most aerosol-containing fluid streamlines are near the channel center, and experience very similar maximal saturation ratios. This results in a steep initial dependence of the activation probability on Ts for selected particles. Therefore, a well-defined activation onset temperature Ts∗ is determined as a function of cluster composition, polarity (±), and mobility diameter (dp). Notwithstanding a modest material dependence found for the inferred Tc∗(dp) curves (±0.25 nm), the steepness of the activation curves measured permits determining particle size distributions for aerosols of known composition. There is some ambiguity in the precise temperature profile in the CPC channel. Nevertheless, using our best estimate, the onset condition for all but one of the seed particles studied agrees well with predictions from classical heterogeneous nucleation theory (Fletcher, 1962) when the pre-exponential term K in the nucleation rate is chosen appropriately. This enables the incorporation of materials properties into the sizing process in terms of only this single parameter K. This finding also provides a method to determine K experimentally, suggesting that the material dependence of the activation probability is due to the different interaction potentials between the clusters and the vapor. Tetraheptylammonium bromide is peculiar in that its cluster anions fit classical theory very much as all other materials studied, but its cluster cations do not.

Conformal and Stoichiometric Chemical Vapor Deposition of Silicon Carbide onto Ultradeep Heterogeneous Micropores by Controlling the Initial Nucleation Stage.

Conformal chemical vapor deposition (CVD) of silicon carbide (SiC) from methyltrichlorosilane (MTS) and hydrogen (H2) onto high-aspect-ratio (HAR; typically >100:1) three-dimensional features has been a challenge in the fabrication of ceramic matrix composites. In this study, the impact of heterogeneous underlayers on the initial nucleation of SiC-CVD was studied using HAR (1000:1) microchannels with a tailored wetting underlayer of Si(100) and dewetting underlayers of thermally formed amorphous silicon dioxide (a-SiO2) and turbostratic boron nitride (t-BN). Incubation periods were distributed in the microchannels on a-SiO2 and t-BN underlayers, with the longest period of 70 min found at the feature-bottom due to a decreased concentration (C) of film-forming species. The longer incubation periods with more dewetting underlayers arose due to demoted initial nucleation. Prolonged incubation at the feature bottom led to poor conformality because thick films had already formed at the inlet when film formation began at the feature bottom. The incubation periods were eliminated by increasing the supply of MTS/H2, in accordance with classical heterogeneous nucleation theory. In the meantime, carbon-rich SiC films formed in the vicinity of dewetting a-SiO2 and t-BN underlayers at the feature bottoms, with greater carbon segregation on more dewetting underlayers. This was probably due to the deposition of pyrocarbons (CH4, C2H2, and/or C2H4) generated from MTS/H2 in the gas phase. Decreasing the temperature (T) from 1000 to 900 °C prevented carbon-rich film formation, and the expected deposition rate of pyrocarbon decreased to 0.6% for the case of CH4. A higher C of MTS/H2 combined with a lower T enabled conformal and stoichiometric film formation on the heterogeneous HAR features.

Development of a Detailed Nucleation and Growth Model for CANTERA Implemented in Li-Air Batteries

Heterogenous nucleation and growth (HNG) is the process by which dissolved species precipitate and adsorb on solid surfaces. HNG occurs as a prominent method mechanism in several systems, such as water filtration and metal-air batteries. Though it has been included in some model studies, wider adoption has been inhibited by a lack of standardized tools. The development of an open source CANTERA model for HNG provides a standardized framework for researchers to incorporate HNG while developing their models to an examine the impact of different chemistries on their systems.This presentation will demonstrate the HNG model with electrochemical impacts by applying it to an Li-Air battery model. Li-Air batteries are an important area of research in the energy storage field, as their high energy density could increase the range of electric vehicles to be comparable with current ICE vehicles. Despite the increase in interest, most models of Li-air batteries have relied on simplifying assumptions to represent deposition of Li₂O₂ [1], [2]. Preliminary 1D Li-O₂ model results using standard surface reaction rate forms are shown in Figure 1, demonstrating surface-limited reactions with increasing discharge rate. These will be compared to novel simulations with rate capabilities calculated using HNG kinetics. Additional results will examine the impact of precipitate morphology and catalyst loading. Model results will be presented alongside and experimental validation data. Figure 1: Preliminary 1D model results showing Li-O2 battery discharge at varying currents. Results show surface-area-limited discharge with increasing current density. These standard model results will be compared and contrasted to those using novel simulations with rates predicted by classical heterogeneous nucleation and growth theory.

Effects of Ti-bearing inclusions on intragranular ferrite nucleation

Abstract The effect of Ti-bearing inclusion characteristics, such as size and marginal composition, on intragranular ferrite (IGF) nucleation has been explored in single sample through SEM and EDS. It can be seen that Ti-bearing inclusions can induce IGF nucleation, and this nucleation ability was scaled by the number of its induced lathes. Statistical analysis suggested that this ability may be correlated with inclusion size, and independent of Ti2O3 content in inclusion. The former can be attributed to the classical theory of heterogeneous nucleation. The latter can be explained by the relationship between the diffusion quantity of Mn and its solubility in Ti2O3 based on the theory of an Mn-depletion zone. Moreover, a probabilistic feature was observed in the nucleation phenomenon which may be due to a small difference in formation energy between the ferrite side plate and the IGF. These results may be helpful to clarify the nature of oxide metallurgy of a Ti-bearing inclusion.

A New Approach in Numerical Modeling of Inoculation of Primary Silicon in a Hypereutectic Al-Si Alloy

The applicability of classical heterogeneous nucleation theory for an inoculated Al-18.6Si (wt pct) alloy was investigated. Nucleation model proposed by Perepezko was used to study heterogenous nucleation of primary silicon in phosphorus-inoculated alloys. For this system, the nucleation temperature was found to be the most crucial variable in the model. If a spherical cap model is assumed for heterogenous nucleation, then the contact angle changes only by the interfacial energy. However, the data applied to Perepezko’s model showed it changed by undercooling. Therefore, it is suggested that the Perepezko’s nucleation model is not applicable for analyzing data in inoculated hypereutectic Al-Si alloy. Instead, for the first time, the free growth model developed by Greer to study the inoculation of Aluminum by Al-Ti-B was used for the Al-18.6Si (wt pct) alloy inoculated with Al-Fe-P. The results of modeling compared with the experimental data showed that the free growth model gives a closer approximation when predicting the size of the primary silicon in the investigated alloy. Mechanical properties of the as-cast hypereutectic alloys are influenced by size and shape of the primary silicon and eutectic silicon, type, size, and frequency of entrainment defects and residual stresses. Finer silicon particles lead to higher tensile strength in the cast components. Being able to predict the size of primary silicon particles will facilitate control of the inoculation process, to enhance mechanical properties such as tensile strength. Developed model here provides a basis to predict the size of primary silicon in hypereutectic Al-Si alloys treated with phosphorous-containing inoculants.

Water Freezes at Near-Zero Temperatures Using Carbon Nanotube-Based Electrodes under Static Electric Fields.

Although static electric fields have been effective in controlling ice nucleation, the highest freezing temperature (Tf) of water that can be achieved in an electric field (E) is still uncertain. We performed a systematic study of the effect of an electric field on water freezing by varying the thickness of a dielectric layer and the voltage across it in an electrowetting system. Results show that Tf first increases sharply with E and then reaches saturation at -3.5 °C after a critical value E of 6 × 106 V/m. Using classical heterogeneous nucleation theory, it is revealed that this behavior is due to saturation in the contact angle of the ice embryo with the underlying substrate. Finally, we show that it is possible to overcome this freezing saturation by controlling the uniformity of the electric field using carbon nanotubes. We achieve a Tf of -0.6 °C using carbon nanotube-based electrodes with an E of 3 × 107 V/m. This work sheds new light on the control of ice nucleation and has the potential to impact many applications ranging from food freezing to ice production.

Molecular dynamics studies of bubble nucleation on a grooved substrate

The classical heterogeneous nucleation theory explains that the groove in the substrate is a desirable place to breed a bubble nucleus. However, the existing research method cannot reproduce the nucleation process. Therefore, in the present study, the molecular dynamics simulation method is conducted to investigate the bubble nucleation on grooved substrates with different wettability. The simple L-J liquid argon is heated by the platinum grooved substrate, whose temperature is controlled by Langevin thermostat. Results show that the groove has significant impacts on bubble nucleation from two aspects: improve thermal energy transfer efficiency and support an initial bubble nucleus. For the substrate with a hydrophilic groove, a visible bubble nucleus generates on the groove region from nothing because of liquid in there obtaining more thermal energy than that on the smooth region within the same time. Moreover, the nucleation rate is improved with the increase of groove hydrophilicity. On the other hand, for the substrate with a hydrophobic groove, some residual gases form an initial bubble nucleus at the initial moment of the nonequilibrium simulation stage, and it takes some time to grow up. Furthermore, a method based on the competition between atomic potential energy and atomic kinetic energy is used to explain the formation of the bubble nucleus on the different wetting substrates. The present simulation study of bubble nucleation on the grooved substrate is another support for the classical heterogeneous nucleation theory.

Repeated nucleation behaviors of pure bismuth under a high magnetic field

The influence of a high magnetic field (HMF) on the repeated nucleation behaviors of pure bismuth has been investigated by differential thermal analysis (DTA). The HMF reduces the maximum and mean values of undercooling. Moreover, the HMF helps to stabilize the undercooling because the HMF suppresses the thermal convection. Furthermore, the nucleation rates are calculated by the statistical analysis of random nucleation events. The decrease in undercooling under the HMF is mainly attributed to the reduction of the contact angle, calculated by fitting the nucleation rates on the basis of the classical heterogeneous nucleation theory for spherical cap nuclei.

Bacteria as Cloud Condensation Nuclei (CCN) in the Atmosphere

Bacteria activation and cloud condensation nuclei (CCN) formation have been studied in the atmosphere using the classical theory of heterogeneous nucleation. Simulations were performed for the binary system of sulfuric acid/water using laboratory-determined contact angles. Realistic model simulations were performed at different atmospheric heights for a set of 140 different bacteria. Model simulations showed that bacteria activation is a potentially favorable process in the atmosphere which may be enhanced at lower temperatures. CCN formation from bacteria nuclei is dependent on ambient atmospheric conditions (temperature, relative humidity), bacteria size, and sulfuric acid concentration. Furthermore, a critical parameter for the determination of bacteria activation is the value of the intermolecular potential between the bacteria’s surface and the critical cluster formed at their surface. In the classical nucleation theory, this is parameterized with the contact angle between substrate and critical cluster. Therefore, the dataset of laboratory values for the contact angle of water on different bacteria substrates needs to be enriched for realistic simulations of bacteria activation in the atmosphere.

Adsorption isotherms and nucleation of methane and ethane on an analog of Titan’s photochemical aerosols

In planetary atmospheres, adsorption of volatile molecules occurs on aerosols prior to nucleation and condensation. Therefore, the way adsorption occurs affects the subsequent steps of cloud formation. In the classical theory of heterogeneous nucleation, several physical quantities are needed for gas condensing on a substrate like aerosols, such as the desorption energies of the condensing gases on the substrate and the wetting parameters of the condensed phases on the substrate. For most planetary atmospheres, the values of such quantities are poorly known. In cloud models, these values are often approximately defined from more or less similar cases or simply fixed to reproduce macroscopic observable quantities such as cloud opacities. In this work, we used the results of a laboratory experiment in which methane and ethane adsorption isotherms on tholin, an analog of photochemical aerosols, are determined. This experiment also permits determination of the critical saturation ratio of nucleation. With this information we then retrieved the desorption energies of methane and ethane, which are the quantitative functions describing the adsorption isotherms and wetting parameters of these two condensates on tholin. We find that adsorption of methane on tholin is well explained by a Langmuir isotherm and a desorption energy ΔFo = 1.519 ± 0.0715 × 10−20 J. Adsorption of ethane tholin can be represented by a Brunauer-Emmett-Teller isotherm of type III. The desorption energy of ethane on tholin that we retrieved is ΔFo = 2.35 ± 0.03 × 10−20 J. We also determine that the wetting coefficients of methane and ethane on tholin are m = 0.994 ± 0.001 and m = 0.966 ± 0.007, respectively. Although these results are obtained from experiments representative of the Titan case, they are also of general value in cases of photochemical aerosols in other planetary atmospheres.

Nucleation of Poly(lactide) on the Surface of Different Fibers

The nucleation process of poly(lactide) (PLA) on a series of fibers was studied by means of in situ polarized optical microscope during crystallization. Several synthetic and natural fibers (polyethylene terephthalate, carbon, Kevlar, glass, hemp, linen, and cellulose) were employed and compared to custom-spun fiber of stereocomplex (SC) enantiomeric PLA blend. Meaningful differences in the nucleating ability toward PLA could be found for all of the considered fibers. SC PLA fibers display extremely high nucleating efficiency, with the development of a continuous transcrystalline morphology on their surface, up to high crystallization temperatures. Quantitative measurement of the nucleation rate allowed a comparison of the different fiber substrates in the light of classical heterogeneous nucleation theory, by considering the interfacial free-energy difference parameter, Δσ, directly related to the nucleation barrier. The topography of the fibers surface was investigated by atomic force microscopy and ten...

Numerical investigation of PM2.5 size enlargement by heterogeneous condensation for particulate abatement

Vapor heterogeneous condensation with PM2.5 as nuclei is a promising approach to enlarge the particle sizes and thus facilitate subsequent particulate abatement by the existing inertial separators. However, the investigation on PM2.5 size enlargement by vapor heterogeneous condensation, which is important to optimize the particulate abatement process, has been largely lacking. In this study, the evolution of particle size distribution due to vapor heterogeneous condensation on the surfaces of polydisperse insoluble PM2.5 was modelled based on the classical heterogeneous nucleation theory and the condensation droplet growth theory. Using this model, the effects of operational parameters on the particle size distribution after heterogeneous condensation were numerically investigated. The results show that the polydisperse fine particles shift to monodisperse coarse particles at a small contact angle, whereas bimodal particle size distribution after heterogeneous condensation is generated at a large contact angle. Higher vapor saturation ratio, higher gas temperature, longer residence time, and greater geometric mean particle size are beneficial to PM2.5 size enlargement and subsequent particulate abatement. Moreover, the geometric standard deviation of particle sizes has little effect on the PM2.5 size enlargement. The model predictions of the particle size distribution after vapor heterogeneous condensation match well with the experimental data.

Superhydrophobic polypropylene membrane with fabricated antifouling interface for vacuum membrane distillation treating high concentration sodium/magnesium saline water

Vacuum membrane distillation (VMD) is a promising technology for high salinity wastewater treatment. One of the key issues in VMD research is improving the antifouling performance of the hydrophobic porous membrane under proper interface modification theory and approach. In this work, the polypropylene (PP) composite membrane coated with SiO2 nanoparticles and fluorinated modification was fabricated to simultaneously enhance the interface roughness and superhydrophobicity. The fabricated superhydrophobic PP membrane was then applied to treat highly concentrated NaCl (15 wt%)/MgCl2 (from 3 to 9 wt %) saline solution in VMD process under various flow conditions. The model concerning the surface roughness and surface nucleation free energy was constructed to predict the influence of membrane surface structure on potential anti-fouling and anti-wetting properties. Classical heterogeneous nucleation theory was introduced to illuminate the improved performance of developed membrane with targeted surface morphology on inhibiting the initial interfacial nucleation process. The experimental results illustrated the fabricated superhydrophobic PP membrane exhibited unique anti-fouling and anti-wetting abilities, as well as extremely stable permeating flux even under low feed rate and highly concentrated salt solution system during the continuous operation. In addition, it was also indicated that sodium ion and magnesium ion with distinct features in the structure of water-ion solution system had the potential impact on the permeate flux decline and concentration polarization effect, which was helpful for further improving the stability and durability of this series modified membrane when treating the high concentrated multiple solution system.

A theoretical study on the activation of insoluble particles in atmospheric conditions

A theoretical analysis for the description of insoluble particles activation in the atmosphere has been performed using as framework the classical theory of heterogeneous nucleation. In the current work a model for heterogeneous nucleation for one-component and two-component gaseous systems was presented taking into account the process of surface diffusion during nucleating embryo formation. The theory predicts higher nucleation rates compared to the classical theory of heterogeneous nucleation and consequently higher probability of particle activation. The model including the effect of surface diffusion shows a qualitative agreement with experimental results of heterogeneous nucleation of water at different substrates. In addition, the process of heterogeneous nucleation of the sulphuric acid – water system on the surface of insoluble spherical aerosol particles in atmospheric conditions has been examined. Insoluble particle activation is depended on several factors such as the concentration of the participating vapours, the ambient temperature, the chemical composition and particle size. Our results show that activation of insoluble particles is an energetically favourable process under specific conditions in the atmosphere.

A Thermodynamic Study on the Effect of Solute on the Nucleation Driving Force, Solid–Liquid Interfacial Energy, and Grain Refinement of Al Alloys

Chemical composition is known to have significant effects on the grain refinement behavior of inoculated Al alloys during solidification. In this study, the influences of solute contents on the thermodynamic nucleation driving force and solid–liquid interfacial energy of binary Al alloys have been studied by CALPHAD method. The solute effect on the nucleation barrier and nucleation rate, thus on the grain refinement of Al alloys both with and without high potency nucleation particles, was analyzed based on the classical heterogeneous nucleation theory and free growth concept. Based on the classical heterogeneous nucleation theory, the calculation results reveal that Si has the effect of increasing the nucleation barrier of heterogeneous nucleation of grains and thus reduce the nucleation rate significantly. Alloying elements Cu and Mg have the effect of promoting heterogeneous nucleation and grain refinement. However, peritectic-forming elements, e.g., Ti, Zr, V, have only negligible effects on the nucleation barrier. For solidification of Al alloys inoculated with high potency nucleation particles, the effect of nucleation driving force caused by different solute elements on the grain size of inoculated aluminum alloys has been quantitatively studied by a grain size prediction model for isothermal melt solidification. It is revealed that the solute dependent Gibbs–Thompson coefficients of Al-Cu, Al-Mg, and Al-Si alloys have the influence of promoting the grain refinement by reducing the free growth undercooling.

Morphological and microstructural evolution of PbSe films grown on thermally oxidized Si (111) substrates by chemical bath deposition

Morphological and microstructural evolution of the PbSe films on the thermally oxidized Si (111) substrates during chemical bath deposition was studied by SEM, XRD and TEM. At the very early stage of deposition, sub-micron scale hemispherical particles are formed on the substrate and they grow with deposition time. The hemispherical particles consist of PbSe, PbSeO4, and PbO2 nanocrystals. Soon after appearance of hemispherical particles, small single crystalline PbSe cuboid particles begin to form mostly on the hemispherical particles and grow with deposition time. At the end of deposition, hemispherical particles are completely replaced by cuboid particles. The cluster mechanism seems to be working at the early stage of deposition, while the ion-by-ion mechanism dominates at the later stage of deposition. The classical heterogeneous nucleation theory is also needed to explain why hemispherical particles are nucleated in the initial stage, and cuboid particles are formed in the later stage of deposition.