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Showing papers on "Nucleation published in 2000"


Book
01 Jan 2000
TL;DR: In this article, the authors present an approach to cluster formation based on the first-order phase transition of nucleation in the first order phase and the second-order transition in the second order phase.
Abstract: Thermodynamics of Nucleation: First-Order Phase Transitions Driving Force for Nucleation Work for Cluster Formation Nucleus Size and Nucleation Work Nucleation Theorem Properties of Clusters Equilibrium Cluster Size Distribution Density-Functional Approach. Kinetics of Nucleation: Master Equation Transition Frequencies Nucleation Rate Equilibrium Stationary Nucleation First Application of the Nucleation Theorem Nonstationary Nucleation Second Application of the Nucleation Theorem Nucleation at Variable Supersaturation. Factors affecting Nucleation: Seed size Line Energy Strain Energy Electric Field Carrier-Gas Pressure Solution Pressure Preexisting Clusters Active Centres. Applications: Overall Crystallization Crystal Growth Third Application of the Nucleation Theorem Induction Time Fourth Application of the Nucleation Theorem Metastabiltiy Limit Maximum Number of Supernuclei Size Distribution of Supernuclei Growth of Thin Films Lifetime of Amphiphile Bilayers. Appendices References Author index Subject Index.

1,128 citations


Journal ArticleDOI
10 Aug 2000-Nature
TL;DR: This work shows from experimental data that the homogeneous nucleation of ice from supercooled aqueous solutions is independent of the nature of the solute, but depends only on the water activity of the solution, and presents a thermodynamic theory for homogeneous ice nucleation, which expresses the nucleation rate coefficient as a function of water activity and pressure.
Abstract: The unique properties of water in the supercooled (metastable) state are not fully understood. In particular, the effects of solutes and mechanical pressure on the kinetics of the liquid-to-solid phase transition of supercooled water and aqueous solutions to ice have remained unresolved. Here we show from experimental data that the homogeneous nucleation of ice from supercooled aqueous solutions is independent of the nature of the solute, but depends only on the water activity of the solution--that is, the ratio between the water vapour pressures of the solution and of pure water under the same conditions. In addition, we show that the presence of solutes and the application of pressure have a very similar effect on ice nucleation. We present a thermodynamic theory for homogeneous ice nucleation, which expresses the nucleation rate coefficient as a function of water activity and pressure. Recent observations from clouds containing ice are in good agreement with our theory and our results should help to overcome one of the main weaknesses of numerical models of the atmosphere, the formulation of cloud processes.

1,093 citations


Journal ArticleDOI
TL;DR: In this article, general trends in structural evolution in polycrystalline films, as a function of processing conditions and materials class, are discussed in terms of these fundamental kinetic processes.
Abstract: ▪ Abstract Polycrystalline films have wide variety of applications in which their grain structures affect their performance and reliability. Thin film growth techniques and growth conditions affect grain shapes, the distribution of grain sizes, and the distribution of the crystallographic orientations of grains. Variations in these structural properties are affected by the conditions under which grain nucleation, growth, coarsening, coalescence, and thickening occur. General trends in structural evolution in polycystalline films, as a function of processing conditions and materials class, are discussed in terms of these fundamental kinetic processes.

774 citations


Journal ArticleDOI
TL;DR: In this paper, the structure of ultrathin ZrO2 layers on Si(001) using medium energy ion scattering and cross-sectional transmission electron microscopy was examined.
Abstract: We have examined the structure of ultrathin ZrO2 layers on Si(001) using medium energy ion scattering and cross-sectional transmission electron microscopy. Films can be deposited on SiO2 layers with highly abrupt interfaces by atomic layer deposition. On HF stripped Si(001), nucleation was inhibited, resulting in poorer film morphology. ZrO2 showed remarkable stability against silicate formation, with no intermixing even after high temperature oxidation. The oxide is vulnerable to high temperature vacuum annealing, with silicidation occurring at temperatures above 900 °C.

696 citations


Journal ArticleDOI
TL;DR: In this paper, a Mg-Y-Nd-based alloy (WE54) was characterised using transmission electron microscopy and the formation of three separate metastable phases, α platelets of an as yet unidentified phase, and the phases designated β′ and β1, preceding formation of the equilibrium phase β.

663 citations


Journal ArticleDOI
02 Mar 2000-Nature
TL;DR: Results from an aerosol dynamics model with a ternary nucleation scheme indicate that nucleation in the troposphere should be ubiquitous, and yield a reservoir of thermodynamically stable clusters 1–3 nm in size.
Abstract: The formation of new atmospheric particles with diameters of 3–10 nm has been observed at a variety of altitudes and locations. Such aerosol particles have the potential to grow into cloud condensation nuclei, thus affecting cloud formation as well as the global radiation budget. In some cases, the observed formation rates of new particles have been adequately explained by binary nucleation, involving water and sulphuric acid1, but in certain locations—particularly those within the marine boundary layer1,2 and at continental sites1,3—observed ambient nucleation rates exceed those predicted by the binary scheme. In these locations, ambient sulphuric acid (H2SO4) levels are typically lower than required for binary nucleation1, but are sufficient for ternary nucleation4 (sulphuric acid–ammonia–water). Here we present results from an aerosol dynamics model with a ternary nucleation scheme which indicate that nucleation in the troposphere should be ubiquitous, and yield a reservoir of thermodynamically stable clusters 1–3 nm in size. We suggest that the growth of these clusters to a detectable size (> 3 nm particle diameter) is restricted by the availability of condensable vapour. Observations of atmospheric particle formation and growth from a continental and a coastal site support this hypothesis, indicating that a growth process including ternary nucleation is likely to be responsible for the formation of cloud condensation nuclei.

635 citations


Journal ArticleDOI
TL;DR: The nucleation and growth of aligned multiwall carbon nanotubes by microwave plasma-enhanced chemical vapor deposition have been studied in this article, where the authors proposed a detailed model to explain these experimental observations.
Abstract: The nucleation and growth of aligned multiwall carbon nanotubes by microwave plasma-enhanced chemical vapor deposition have been studied. The nanotubes nucleate and grow from catalytic cobalt islands on a silicon substrate surface, with both their diameter and length dependent on the size of the cobalt islands. Electron microscopy reveals that the nanotubes grow via a ‘‘base growth’’ mechanism. The nanotubes grow initially at a very rapid and constant rate ~;100 nm/s! that decreases sharply after the catalyst Co particles become fully encapsulated by the nanotubes. We propose a detailed model to explain these experimental observations on nucleation and growth of nanotubes. © 2000 American Institute of Physics.@S0003-6951~00!00443-5# Carbon nanotubes with different structure and morphology can now be fabricated with several techniques. Experiments performed, mostly on individual nanotubes, show that they have extraordinary electrical and mechanical properties. 1 To investigate their macroscopic properties and potential technological applications it is essential to have nanotube materials with controlled diameter, length, orientation, location, and microstructure. Although the laser ablation method 2 can produce high quality single-walled carbon nanotubes with some control in diameter and electronic properties, 3 the process is not compatible with conditions

506 citations


Journal ArticleDOI
TL;DR: In this paper, small-angle X-ray scattering (SAXS) was used to follow orientation-induced crystallization of isotactic polypropylene (i-PP) in the subcooled melt at 140 °C after step shear under isothermal conditions.
Abstract: In-situ synchrotron small-angle X-ray scattering (SAXS) was used to follow orientation-induced crystallization of isotactic polypropylene (i-PP) in the subcooled melt at 140 °C after step shear under isothermal conditions. The melt was subjected to a shear strain of 1428% at three different shear rates (10, 57, and 102 s-1) using a modified Linkam shear stage. The SAXS patterns showed strong meridional reflections due to the rapid development of oriented polymer crystallites within the melt. On the basis of the SAXS data, a schematic representation of nucleation and growth in orientation-induced crystallization of i-PP is proposed. During flow, orientation causes alignment of chain segments of polymer molecules and results in the formation of primary nuclei in the flow direction. These nuclei facilitate the growth of oriented crystal lamellae that align perpendicular to the flow direction. The half-time of crystallization was calculated from the time evolution profiles of the total scattered intensity. Th...

459 citations


Journal ArticleDOI
TL;DR: A review of the present status of the problem of metal deposition and electrochemical phase formation and growth is made in this paper, with an overview of the major contributions of different electrochemical schools.

407 citations


Journal ArticleDOI
TL;DR: In this article, the influence of an electric current on the following solid state transformations in metals are considered: (1) intermetallic compound formation and growth in diffusion couples, (2) precipitation, (3) crystallization of amorphous alloys and (4) recrystallization and grain growth of cold worked metals.
Abstract: The influence of an electric current on the following solid state transformations in metals are considered: (1) intermetallic compound formation and growth in diffusion couples, (2) precipitation, (3) crystallization of amorphous alloys and (4) recrystallization and grain growth of cold worked metals. The formation and growth of intermetallic compounds were in qualitative accord with electromigration theory. Regarding precipitation, an electric current can either enhance or retard the precipitation rate, depending on the alloy, the current density and its frequency. Important factors appear to be the effect of current on the quenched-in vacancies and the presence of an internal stress. Both a continuous d.c. current and high current density electropulsing enhanced the crystallization rate of amorphous alloys. The effects are greater than can be explained by simple electromigration theory and suggest the cooperative motion of a larger number of atoms. Electropulsing enhanced the recrystallization rate of cold worked metals, but retarded subsequent grain growth. Enhancement of the recrystallization rate resulted mainly from an increase in the pre-exponential factor of the Arrhenius rate equation, which is considered to refer to the nucleation rate. Retardation of subsequent grain growth resulted from a lower residual dislocation density within the newly-formed grains.

371 citations


Journal ArticleDOI
TL;DR: In this paper, the role of background ionization in the generation and evolution of ultrafine atmospheric particles is developed through modeling and data analysis, and it is found that charged molecular clusters condensing around natural air ions can grow significantly faster than corresponding neutral clusters, and thus preferentially achieve stable, observable sizes.
Abstract: The role of background ionization in the generation and evolution of ultrafine atmospheric particles is developed through modeling and data analysis. It is found that charged molecular clusters condensing around natural air ions can grow significantly faster than corresponding neutral clusters, and thus preferentially achieve stable, observable sizes. Detailed microphysical simulations of this process seem to explain recent measurements of ultrafine particle behavior, as well as the diurnal variation seen in tropospheric mobility spectra. The proposed ion-mediated nucleation mechanism leads to the production of new particles under conditions that are unfavorable for binary homogeneous nucleation, and provides a consistent explanation for a variety of tropospheric observations.

Journal ArticleDOI
TL;DR: In this paper, the kinetics of phase transformation of nanocrystalline anatase samples were studied using x-ray diffraction at temperatures ranging from 600 to 1150 °C.
Abstract: The kinetics of phase transformation of nanocrystalline anatase samples was studied using x-ray diffraction at temperatures ranging from 600 to 1150 °C. Kinetic data were analyzed with an interface nucleation model and a newly proposed kinetic model for combined interface and surface nucleation. Results revealed that the activation energy of nucleation is size dependent. In anatase samples with denser particle packing, rutile nucleates primarily at interfaces between contacting anatase particles. In anatase samples with less dense particle packing, rutile nucleates at both interfaces and free surfaces of anatase particles. The predominant nucleation mode may change from interface nucleation at low temperatures to surface nucleation at intermediate temperatures and to bulk nucleation at very high temperatures. Alumina particles dispersed among the anatase particles can effectively reduce the probability of interface nucleation at all temperatures.

Journal ArticleDOI
TL;DR: Homogeneous nucleation within each sphere yields isothermal crystallizations which follow first-order kinetics, contrasting with the sigmoidal kinetics normally exhibited in the quiescent crystallization of bulk polymers.
Abstract: Crystallization within the discrete spheres of a block copolymer mesophase was studied by time-resolved x-ray scattering. The cubic packing of microdomains, established by self-assembly in the melt, is preserved throughout crystallization by strong interblock segregation even though the amorphous matrix block is well above its glass transition temperature. Homogeneous nucleation within each sphere yields isothermal crystallizations which follow first-order kinetics, contrasting with the sigmoidal kinetics normally exhibited in the quiescent crystallization of bulk polymers.

Journal ArticleDOI
TL;DR: In this paper, two simple microvoid nucleation models for modeling ductile fracture are discussed, and a method which applies multitension specimens including both smooth and notched cylindrical specimens for determining the micro void nucleation parameter is introduced.

Journal ArticleDOI
TL;DR: The rate of homogeneous nucleation of lysozyme crystals passes through a maximum in the vicinity of the liquid-liquid phase boundary hidden below the liquidus (solubility) line in the phase diagram of the protein solution, found that glycerol and polyethylene glycol shift this phase boundary and significantly suppress or enhance the crystal nucleation rates.
Abstract: The capability to enhance or suppress the nucleation of protein crystals opens opportunities in various fundamental and applied areas, including protein crystallography, production of protein crystalline pharmaceuticals, protein separation, and treatment of protein condensation diseases. Herein, we show that the rate of homogeneous nucleation of lysozyme crystals passes through a maximum in the vicinity of the liquid–liquid phase boundary hidden below the liquidus (solubility) line in the phase diagram of the protein solution. We found that glycerol and polyethylene glycol (which do not specifically bind to proteins) shift this phase boundary and significantly suppress or enhance the crystal nucleation rates, although no simple correlation exists between the action of polyethylene glycol on the phase diagram and the nucleation kinetics. The control mechanism does not require changes in the protein concentration, acidity, and ionicity of the solution. The effects of the two additives on the phase diagram strongly depend on their concentration, which provides opportunities for further tuning of nucleation rates.

Journal ArticleDOI
TL;DR: The effect of temperature on the overall crystallization and the crystal nucleation and growth rates of indomethacin polymorphs from the amorphous state were determined in this article.
Abstract: The effect of temperature on the overall crystallization, and the crystal nucleation and growth rates of indomethacin polymorphs from the amorphous state were determined Crystallization of amorphous indomethacin at temperatures close to or below its T g (42°C) favors the formation of the stable γ polymorphic form, while crystallization at higher temperatures favors the formation of the metastable α-crystal form Both the nucleation and growth rates for γ-indomethacin have maxima that coincide just above the T g of amorphous indomethacin The nucleation rate for α-indomethacin was found to have a maximum at 60°C, and the growth rate at 90°C Assuming a temperature dependent crystal–amorphous interface free energy, good agreement was observed between the experimental nucleation data and the predictions of the classical theory of nucleation The crystal–amorphous interface energy was higher for the γ than for the α-indomethacin Analysis of the crystal growth rates for both crystal forms showed that the mechanism of growth is by two-dimensional nucleation, but quantitative agreement with the theory was not found The interface energy for the α-crystal form, obtained from the growth data was in very good agreement with the value obtained from the nucleation data

Journal ArticleDOI
TL;DR: In this article, a series of decompression experiments using crystal-free, rhyolite melt were conducted to examine the development of large supersaturations due to delayed, homogenous (spontaneous) bubble nucleation.

Journal ArticleDOI
TL;DR: In this paper, a framework for modeling coupled nucleation, growth and coarsening in diluted alloys is presented, based on the method of finite differences, where the particle distribution is divided into a series of discrete size classes, each represented by a control volume.

Journal ArticleDOI
TL;DR: In this paper, the Bruggeman effective medium approximation (EMA) was used for the analysis of real-time spectroscopic ellipsometry (SE) data collected during the nucleation and growth of hydrogenated amorphous silicon (a-Si:H) thin films.
Abstract: Real-time spectroscopic ellipsometry (SE) data collected during the nucleation and growth of hydrogenated amorphous silicon (a-Si:H) thin films have been analyzed by applying one and two layer optical models incorporating different effective medium theories (EMT's). The purpose of the EMT's is to simulate the dielectric functions of the microscopically inhomogeneous nucleating and surface roughness layers used in the models. Five one-parameter EMT's have been considered in this study for the characterization of three classes of microscopically inhomogeneous layers, including (i) 5\char21{}20 \AA{}-thick nucleating layers consisting of isolated a-Si:H clusters on the underlying substrate, (ii) 10\char21{}15 \AA{}-thick nucleation-induced surface roughness layers on very thin (200 \AA{}) a-Si:H films, and (iii) 40\char21{}80 \AA{}-thick substrate-induced surface roughness layers on thicker (g2500 \AA{}) a-Si:H films. In all three applications, the Bruggeman effective medium approximation (EMA) provides the best overall fits to the time evolution of the SE data, and complexities beyond the simple one-parameter EMA cannot be justified in view of existing experimental limitations. Furthermore, many of the general features of nucleation, coalescence, and bulk layer growth deduced in the SE analysis and used in previous studies to understand and optimize materials and device fabrication, are found to be essentially independent of the EMT used in the analysis.

Journal ArticleDOI
TL;DR: In this paper, the aligned carbon nanotubes are believed to be the result of a competition growth process along the normal direction of the substrate and the surface diffusion of carbon atoms on the large iron particle leads to the formation of the observed bamboo-like structure.

Journal ArticleDOI
TL;DR: In this paper, the authors reviewed some pertinent research aimed at understanding surface nucleation from both qualitative and quantitative points of view, including surface quality, tips, cracks and scratches, foreign particles and surrounding atmosphere.
Abstract: In this paper we review some pertinent research aimed at understanding surface nucleation from both qualitative and quantitative points of view. The majority of quantitative studies discuss the crystal nucleation kinetics of soda-lime-silica glasses and alkali-free silicate (cordierite, anorthite and diopside) glasses. We emphasize the kinetics of surface nucleation and consider the effects of surface quality, tips, cracks and scratches, foreign particles and surrounding atmosphere on crystallization. Related nucleation mechanisms are discussed.

Journal ArticleDOI
TL;DR: In this article, the formation of dispersoids containing Mn and/or Cr in Al-Mg-Si alloys was studied metallographically and by means of electrical resistivity measurements.
Abstract: The formation of dispersoids containing Mn and/or Cr in Al–Mg–Si alloys was studied metallographically and by means of electrical resistivity measurements. Special emphasis was placed on the nucleation mechanisms. For alloys containing Mn and/or Cr it was shown that during the heating of the as-cast alloys to 580°C (which is a typical homogenization temperature) and at a heating rate of 3 K min −1 , an intermediate phase, referred to as the ‘u-phase’ nucleated on the β′-Mg 2 Si needles. The phase has a hexagonal unit cell with a =0.670 nm, c =0.808 nm. The precipitates were rod-shaped and were lined up in the [100] directions in the Al lattice. The phase was found to be rich in Mn and/or Cr. With continued annealing, dispersoids containing Mn and Mn+Cr nucleated heterogeneously on the ‘u-phase’ precipitates before these precipitates dissolved. The nucleation sites for the dispersoids with Cr were not conclusively identified.

Journal ArticleDOI
TL;DR: The γTuRC therefore acts as a minus-end-capping protein, as confirmed by electron-microscopic examination of gold-labelled εTuRCs, and these data support a nucleation model for γ TuRC function that involves capping of microtubules.
Abstract: Microtubule nucleation from centrosomes involves a lockwasher-shaped protein complex containing gamma-tubulin, named the gamma-tubulin ring complex (gammaTuRC). Here we investigate the mechanism by which the gammaTuRC nucleates microtubules, using a direct labelling method to visualize the behaviour of individual gammaTuRCs. A fluorescently-labelled version of the gammaTuRC binds to the minus ends of microtubules nucleated in vitro. Both gammaTuRC-mediated nucleation and binding of the gammaTuRC to preformed microtubules block further minus-end growth and prevent microtubule depolymerization. The gammaTuRC therefore acts as a minus-end-capping protein, as confirmed by electron-microscopic examination of gold-labelled gammaTuRCs. These data support a nucleation model for gammaTuRC function that involves capping of microtubules.

Journal ArticleDOI
TL;DR: In this article, the generic heterogeneous effect of foreign particles on three dimensional nucleation was examined both theoretically and experimentally, and it was shown that the nucleation observed under normal conditions includes a sequence of progressive heterogeneous processes, characterized by different interfacial correlation function f(m,x)s.
Abstract: The generic heterogeneous effect of foreign particles on three dimensional nucleation was examined both theoretically and experimentally. It shows that the nucleation observed under normal conditions includes a sequence of progressive heterogeneous processes, characterized by different interfacial correlation function f(m,x)s. At low supersaturations, nucleation will be controlled by the process with a small interfacial correlation function f(m,x), which results from a strong interaction and good structural match between the foreign bodies and the crystallizing phase. At high supersaturations, nucleation on foreign particles having a weak interaction and poor structural match with the crystallizing phase (f(m,x)→1) will govern the kinetics. This frequently leads to the false identification of homogeneous nucleation. Genuine homogeneous nucleation, which is the up-limit of heterogeneous nucleation, may not be easily achievable under gravity. In order to check these results, the prediction is confronted wit...

Journal ArticleDOI
TL;DR: In this article, the authors demonstrate the use of 2D combinatorial libraries to investigate thin-film dewetting, using a set of thin films of polystyrene on silicon substrates containing orthogonal, continuous variations of thickness (h), and temperature (T), representing about 1200 practical state points per library.
Abstract: Combinatorial methods involving data collection in multiparameter space allow a rapid identification of measured property trends as a function of system parameters. The technique has been applied with success to pharmaceutical, inorganic and organic materials synthesis, but not significantly to measurements of polymeric films and coatings. We demonstrate the use of 2-D combinatorial libraries to investigate thin-film dewetting. We have prepared libraries of thin films of polystyrene on silicon substrates containing orthogonal, continuous variations of thickness (h), and temperature (T) that represent about 1200 practical state points per library. The libraries were screened for dewetting behavior using automated optical microscopy. Dewetting trends were visibly apparent on the libraries, and a comprehensive map of the T, h, and time (t) dependence was generated in a few hours. The combinatorial libraries, spanning a large T, h, and t range, not only reproduced known dewetting structures and phenomena but also enabled a novel T, h superposition of the heterogeneous nucleated hole dewetting kinetics. We observed three hole nucleation regimes as a function of thickness: heterogeneously nucleated holes (h > 55 nm), a crossover regime where both heterogeneous and capillary instability nucleation compete (33 nm < h < 55 nm), and a regime of holes nucleated by capillary instability (16 nm < h < 33 nm).

Journal ArticleDOI
TL;DR: In this paper, the authors studied the nucleation of crystals of a model protein from aqueous solutions using a novel technique that allows direct determinations of homogeneous nucleation rates.
Abstract: We have studied the nucleation of crystals of a model protein from aqueous solutions using a novel technique that allows direct determinations of homogeneous nucleation rates. At a constant temperature of 12.6 °C we varied the thermodynamic supersaturation by changing the concentrations of protein and precipitant. We found a broken dependence of the homogeneous nucleation rate on supersaturation that is beyond the predictions of the classical nucleation theory. The nucleation theorem allows us to relate this to discrete changes of the size of the crystal nuclei with increasing supersaturation as (10 or 11) → (4 or 5) → (1 or 2). Furthermore, we observe that the existence of a second liquid phase at high protein concentrations strongly affects crystal nucleation kinetics: (i) Crystal nucleation rates are lower than expected in the phase region of liquid−liquid demixing. (ii) In the immediate proximity of this region, nucleation rates vary by factors of up to 2 in identical experiments. Since for this regi...

Journal ArticleDOI
TL;DR: In this paper, it was demonstrated that reactive mechanical Alloying for short time (2 h) is an effective way to strongly improve the hydrogen storage properties of both magnesium and (Mg + 10 wt % M ) mixtures.

Journal ArticleDOI
TL;DR: In this article, the hydrogen desorption kinetics of mechanically milled MgH2+5at.%V nanocomposite were determined under various desorptions pressures and temperatures.

Journal ArticleDOI
TL;DR: In this article, the authors measured the times to nucleate CO2 hydrates from CO2 dissolved water under pressure and 8.6 K supercooling using different methods to prepare the water.
Abstract: We measured the times to nucleate CO2 hydrates from CO2 dissolved water under pressure and 8.6 K supercooling using different methods to prepare the water. These times ranged from 50 min to more than 7200 min, depending on the preparation method. The nucleation rates were calculated by fitting the observed nucleation probability distributions to a nucleation rate equation. The nucleation rates significantly increased when the water had previously frozen as ice and melted (freezing-memory effect), except when the meltwater was heated to 298 K before nucleation. The nucleation rates also increased with O2-saturated meltwater, but decreased with degassed water.

Journal ArticleDOI
TL;DR: In this paper, variable-temperature atomic force microscopy in the temperature range 200-800 K was used to study the nucleation and growth of Pd on cleaved MgO(001) surfaces.
Abstract: Nucleation and growth of Pd on cleaved MgO(001) surfaces were studied by variable-temperature atomic force microscopy in the temperature range 200-800 K Constant island densities (similar to 3x10(12)cm(-2)) were observed over a wide temperature range, indicating nucleation kinetics governed by point defects with a high trapping energy These results are compared to a rate equation model that describes the principal atomistic nucleation and growth processes, including nucleation at attractive point defects Energies for defect trapping, adsorption, surface diffusion, and pair binding are deduced, and compared with recent nb initio calculations