Nucleation in solids: The induction and steady state effects

Dislocation phenomena described with free volume concept and Eyring's rate process theory

Dislocation phenomena in solids under simple shear stress are theoretically addressed with the free volume concept and Eyring's rate process theory for obtaining a generic and unified description. The obtained equations do not have any restrictions to specific materials and are compared with various theories and empirical equations like the Hall-Petch and its inverse forms. Moreover, our equations are used to fit experimental data of mechanical properties and dislocation density against grain sizes available in the literature. A good agreement with observations is achieved, indicating that our theoretical framework is sound. Our findings provide a theoretical foundation for the very common dislocation phenomena observed among many solid materials including pure metals, metallic alloys, ceramics, and even geological scale entities, potentially clearing out many inconsistencies and puzzles in the literature.

Nucleation kinetics model for primary crystallization in Al-Y-Fe metallic glass

The high density of aluminum nanocrystals (>10²¹ m^-3) that develop during the primary crystallization in Al-based metallic glasses indicates a high nucleation rate (∼10¹⁸ m^-3 s^-1). Several studies have been advanced to account for the primary crystallization behavior, but none have been developed to completely describe the reaction kinetics. Recently, structural analysis by fluctuation electron microscopy has demonstrated the presence of the Al-like medium range order (MRO) regions as a spatial heterogeneity in as-spun Al₈₈Y₇Fe₅ metallic glass that is representative for the class of Al-based amorphous alloys that develop Al nanocrystals during primary crystallization. From the structural characterization, an MRO seeded nucleation configuration is established, whereby the Al nanocrystals are catalyzed by the MRO core to decrease the nucleation barrier. The MRO seeded nucleation model and the kinetic data from the delay time (τ) measurement provide a full accounting of the evolution of the Al nanocrystal density (N_v) during the primary crystallization under isothermal annealing treatments. Moreover, the calculated values of the steady state nucleation rates (J_ss) predicted by the nucleation model agree with the experimental results. Moreover, the model satisfies constraints on the structural, thermodynamic, and kinetic parameters, such as the critical nucleus size, the interface energy, and the volume-free energy driving force that are essential for a fully self-consistent nucleation kinetics analysis. The nucleation kinetics model can be applied more broadly to materials that are characterized by the presence of spatial heterogeneities.

State Parameter-Based Yield Strength Model for Integration in Finite Element User-Material Routines

A new state parameter-based user-subroutine for finite-element software packages, which can be used to simulate microstructure-dependent stress–strain relations, is presented. Well-established precipitation kinetics, strain hardening and strengthening models are brought into a condensed form to optimise computational efficiency, without losing their predictive capabilities. The framework includes main strengthening mechanisms, such as, precipitation strengthening, solid solution strengthening, the cross-core diffusion effect and work hardening. With the novel user-subroutine, the microstructure evolution of various thermo-mechanical treatments on the full integration point grid of the finite element (FE) mesh can be calculated. The validation of the simulations is carried out by mechanical testing as well as microstructure characterisation of an Al-6082 alloy, including transmission electron microscopy (TEM) investigations after various annealing times at 180 °C.

Copper-Based Alloys with Optimized Hardness and High Conductivity: Research on Precipitation Hardening of Low-Alloyed Binary CuSc Alloys

Copper alloys, combining optimized strength with high electrical and thermal conductivity, are analyzed in-depth, in order to meet the increasing requirements of today’s and tomorrow’s applications in the electrical and automotive industries. The conducted research analyzes alloys with up to 0.3 wt.% scandium, as an alloying element with limited solubility in copper. For the simultaneous enhancement of mechanical strength and conductivity, precipitation hardening is the conducted process method, accompanied by experimental and simulation-based investigations. Therefore, the influence of aging temperatures, in the range of 350 °C to 500 °C, is analyzed in combination with 25%, 50%, and 75% prior cold deformation. CuSc starts precipitating at 375 °C, without prior cold working, whereas mechanical deformation refines the growing intermetallic precipitates. Higher temperatures improve the formation of precipitates but carry the risk of overaging. The first key achievement is to use a thoroughly examined thermomechanical treatment, investigating the growth of precipitates to reach significantly higher hardness than the benchmark alloy, CuZr0.15. Furthermore, the analyzed CuSc alloys show advantages in the investigated recrystallization behavior, making them, especially, applicable for higher operating temperatures. Future research will assess ternary alloying combinations, to further scoop the latent potential of CuSc alloys.

Cavity Nucleation and Growth in Nickel-Based Alloys during Creep

The number of fossil fueled power plants in electricity generation is still rising, making improvements to their efficiency essential. The development of new materials to withstand the higher service temperatures and pressures of newer, more efficient power plants is greatly aided by physics-based models, which can simulate the microstructural processes leading to their eventual failure. In this work, such a model is developed from classical nucleation theory and diffusion driven growth from vacancy condensation. This model predicts the shape and distribution of cavities which nucleate almost exclusively at grain boundaries during high temperature creep. Cavity radii, number density and phase fraction are validated quantitively against specimens of nickel-based alloys (617 and 625) tested at 700 °C and stresses between 160 and 185 MPa. The model’s results agree well with the experimental results. However, they fail to represent the complex interlinking of cavities which occurs in tertiary creep.

Thermodynamic, Kinetic and Strength Calculation of High Zinc Containing Al-Zn-Mg-Cu Alloys

High zinc containing Al-Zn-Mg-Cu is the research focus of ultra-high strength aluminum alloy. In the present paper, the Al-Zn-Mg-Cu multi-component system is studied when the content of Zn is 10.5 wt.%, 11 wt.% and 12 wt.%, respectively. The vertical sections of phase diagrams are calculated by the thermodynamic method. The precipitation parameters of the η’ phase, including the density of precipitate, precipitate radius and volume fraction, are obtained by using the methods of kinetic calculations. The yield strength of Al-Zn-Mg-Cu alloy with different content of Zn is calculated by an empirical model containing a chemical element and a microstructure parameter. The calculated results of yield strength are verified by experimental data and provide primary guidance to developing Al-Zn-Mg-Cu ultra-high strength aluminum alloys.

Influence of Cooling Scenarios on the Evolution of Microstructures in Nickel-Based Single Crystal Superalloys

The reprecipitation and evolution of γ’ precipitates during various cooling approaches from supersolvus temperature are studied experimentally and via phase field simulation in nickel-based single crystal superalloys. The focus of this paper is to explore the influence of cooling methods on the evolution of the morphology and the distribution of γ’ precipitates. It is demonstrated that small and uniform spherical shape γ’ particles formed with air cooling method. When the average cooling rate decreases, the particle number decreases while the average matrix and precipitate channel widths increase. The shape of γ’ precipitates which changed from spherical to cubic and irregular characteristics due to the elastic interaction and elements diffusion are observed with the decrease of the average cooling rate. The phase field simulation results are in good agreement with the experimental results in this paper. The research is a benefit for the study of the rejuvenation heat treatment in re-service nickel-based superalloys.

Nucleating a Different Coordination in a Crystal under Pressure: A Study of the B1-B2 Transition in NaCl by Metadynamics

Here we propose an NPT metadynamics simulation scheme for pressure-induced structural phase transitions, using coordination number and volume as collective variables, and apply it to the reconstructive structural transformation B1-B2 in NaCl. By studying systems with size up to 64 000 atoms we reach a regime beyond collective mechanism and observe transformations proceeding via nucleation and growth. We also reveal the crossover of the transition mechanism from Buerger-like for smaller systems to Watanabe-Tolédano for larger ones. The scheme is likely to be applicable to a broader class of pressure-induced structural transitions, allowing study of complex nucleation effects and bringing simulations closer to realistic conditions.

Rational Solid-State Synthesis Routes for Inorganic Materials

The rational solid-state synthesis of inorganic compounds is formulated as catalytic nucleation on crystalline reactants, where contributions of reaction and interfacial energies to the nucleation barriers are approximated from high-throughput thermochemical data and structural and interfacial features of crystals, respectively. Favorable synthesis reactions are then identified by a Pareto analysis of relative nucleation barriers and phase selectivities of reactions leading to the target. We demonstrate the application of this approach in reaction planning for the solid-state synthesis of a range of compounds, including the widely studied oxides LiCoO₂, BaTiO₃, and YBa₂Cu₃O₇, as well as other metal oxide, oxyfluoride, phosphate, and nitride targets. Pathways for enabling the retrosynthesis of inorganics are also discussed.

Thermodynamic Modelling and Microstructural Study of Z-Phase Formation in a Ta-Alloyed Martensitic Steel

A thermokinetic computational framework for precipitate transformation simulations in Ta-containing martensitic Z-steels was developed, including Calphad thermodynamics, diffusion mobility data from the literature, and a kinetic parameter setup that considered precipitation sites, interfacial energies and dislocation density evolution. The thermodynamics of Ta-containing subsystems were assessed by atomic solubility data and enthalpies from the literature as well as from the experimental dissolution temperature of Ta-based Z-phase CrTaN obtained from differential scanning calorimetry. Accompanied by a comprehensive transmission electron microscopy analysis of the microstructure, thermokinetic precipitation simulations with a wide-ranging and well-documented set of input parameters were carried out in MatCalc for one sample alloy. A special focus was placed on modelling the transformation of MX into the Z-phase, which was driven by Cr diffusion. The simulation results showed excellent agreement with experimental data in regard to size, number density and chemical composition of the precipitates, showing the usability of the developed thermokinetic simulation framework.

A first step towards computational design of W-containing self-healing ferritic creep resistant steels

In this work, we combine a generic alloy-by-design model with a novel concept, the nucleation barrier for the formation of Laves phase to fill the creep cavities, in order to develop multi-component creep resistant steels with kinetically tuned self-healing behaviour. In the model the high-temperature long-term strength is estimated by integrating precipitation strengthening due to M23C6 carbides and solid solution strengthening, while the optimized compositional solutions are determined by employing the coupled thermodynamic and kinetic principles. W-containing Laves phase herein is selected as the self-healing agent to autonomously fill the grain boundary cavities, so as to prolong the creep lifetime. To achieve the effective healing reaction, the nucleation time for Laves precipitates are expected to coincide simultaneously with which creep cavities start to form or reach a healable size. Using experimental data from literature, an empirical relationship to estimate the incubation time for Laves phase formation has been constructed, from which the thermodynamic driving force for onset of precipitation as a function of temperature and intended precipitate nucleation time was derived. Three sample alloys have been selected among the desirable solutions, which are predicted to have the same strength but widely different Laves phase nucleation times. The calculations are also performed for different use temperatures to explore the compatibility between high temperature strength and timely cavity filling behaviour. In its current form the model is not expected to yield the truly optimal composition but to demonstrate how the kinetics of the healing reaction can affect the predicted optimal alloy compositions.

Integrated Physical-Constitutive Computational Framework for Plastic Deformation Modeling

An integrated framework for deformation modeling has been developed, which combines a physical state parameter-based formulation for microstructure evolution during plastic deformation processes with constitutive creep models of polycrystalline materials. The implementations of power law, Coble, Nabarro–Herring and Harper–Dorn creep and grain boundary sliding are described and their contributions to the entire stress response at a virtual applied strain rate are discussed. The present framework simultaneously allows calculating the plastic deformation under prescribed strain rate or constant stress, as well as stress relaxation after preceding stress or strain loading. The framework is successfully applied for the construction of deformation mechanism maps.

Precipitation Versus Partitioning Kinetics during the Quenching of Low-Carbon Martensitic Steels

Low-carbon, low-alloy steels undergo auto-tempering and carbon partitioning to austenite during quenching to martensite. The microstructures of two such steels quenched at two cooling rates have been evaluated using electron microscopy to characterise lath and carbide precipitate morphologies, and the results have been compared with theoretical predictions based on the Thermo-Calc modules DICTRA and TC-Prisma. The modelling tools predicted the carbon depletion rates due to diffusion from the bcc martensite laths into austenite and the precipitation of cementite in the ferrite matrix. The predictions showed a satisfactory agreement with the metallographic results, indicating that the Thermo-Calc based software can aid in the design of new low-carbon martensitic steels.

Icephobic surfaces: Definition and figures of merit

Icephobic surfaces have a critical footprint on human daily lives ranging from aviation systems and infrastructures to energy systems, but creation of these surfaces for low-temperature applications remains elusive. Non-wetting, liquid-infused and hydrated surfaces have inspired routes for development of icephobic surfaces. However, high freezing temperature, high ice adhesion strength and subsequent ice accretion, low mechanical durability, and high production cost have restricted their practical applications. In this review, we provide a comprehensive definition for icephobicity through thermodynamics, heat transfer and mechanics of ice/water-material interface and elucidate physic-based routes through which nano-scale could help to achieve exceptional icephobic surfaces. Based on conservation laws, mathematical models are developed that accurately predict ice growth rate on various substrates and wind conditions. Through physics of fracture at ice-icephobic material interface, we cast a standard method for ice adhesion measurement that has the potential to eliminate discrepancies between reported ice adhesion from different laboratories. To assure long-time performance of icephobic surfaces, durability metrics need to be defined. We provide standard methods to examine mechanical, chemical, and environmental durability of icephobic surfaces. In the developed comprehensive framework on icephobicity in this review, performance of state-of-the-art icephobic surfaces are compared and main deficiencies in this field are highlighted.

Modeling of Microsegregation and Homogenization of 6xxx Al-Alloys Including Precipitation and Strengthening During Homogenization Cooling

Control of the homogenization process is important in obtaining high extrudability and desirable properties in 6xxx aluminum alloys. Three consecutive steps of the process chain were modeled. Microsegregation arising from solidification was described with the Scheil-Gulliver model. Dissolution of Mg₂Si, Si (diamond) and β-AlFeSi (β-Al₅FeSi) to α-AlFeSi (α-Al₁₂(FeMn)₃Si) transformation during homogenization have been described with a CALPHAD-based multicomponent diffusion Dual-Grain Model (DGM), accounting for grain size inhomogeneity. Mg₂Si precipitation and associated strengthening during homogenization cooling were modeled with the Kampmann-Wagner Numerical (KWN) precipitation framework. The DGM model indicated that the fractions of β-AlFeSi and α-AlFeSi exhibit an exact spatial and temporal correspondence during transformation. The predictions are in good agreement with experimental data. The KWN model indicated the development of a bimodal particle size distribution during homogenization cooling, arising from corresponding nucleation events. The associated strengthening, arising from solid solution and precipitation strengthening, was in good agreement with experimental results. The proposed modeling approach is a valuable tool for the prediction of microstructure evolution during the homogenization of 6xxx aluminum alloys, including the often-neglected part of homogenization cooling.

Micro-/Nanoscale Approach for Studying Scale Formation and Developing Scale-Resistant Surfaces

Blockage of pipelines due to accretion of salt particles is detrimental in desalination and water-harvesting industries as they compromise productivity, while increasing maintenance costs. We present a micro-/nanoscale approach to study fundamentals of scale formation, deposition, and adhesion to engineered surfaces with a wide range of surface energies fabricated using the initiated chemical vapor deposition method. Silicon wafers and steel substrates are coated with poly(1 H,1 H,2 H,2 H-perfluorodecylacrylate) or pPFDA, poly(tetravinyl-tetramethylcyclotetrasilohexane) or pV4D4, poly(divinylbenzene) or pDVB, poly(1,3,5,7-tetravinyl-1,3,5,7-tetramethylcyclotetrasilohexane) or pV3D3, and cross-linked copolymers of poly(2-hydroxyethylmethacrylate) and poly(ethylene glycol) diacrylate or p(PHEMA- co-EGDA). Particles of salt (CaSO₄·2H₂O) are formed and shaped with a focused ion beam and adhered to a tipless cantilever beam using a micromanipulator setup to study their adhesion strength with a molecular force probe (MFP). Adhesion forces were measured on the substrates in wet and dry conditions to evaluate the effects of interfacial fluid layers and capillary bridges on net adhesion strength. The adhesion between salt particles and the pPFDA coatings decreased by 5.1 ± 1.15 nN in wet states, indicating the influence of capillary bridging between the particle and the liquid layer. In addition, scale nucleation and growth on various surfaces is examined using a quartz crystal microbalance (QCM), where supersaturated solution of CaSO₄·2H₂O is passed over bare and polymer-coated quartz substrates while mass gain is measured in real time. The salt accretion decreased by 2 folds on pPFDA-coated substrates when compared to that on p(HEMA- co-EGDA) coatings. Both MFP and QCM studies are essential in studying the impact of surface energy and roughness on the extent of scale formation and adhesion strength. This study can pave way for the design of scale-resistant surfaces with potential applications in water treatment, energy harvesting, and purification industries.

Simulation of TTT Curves for Additively Manufactured Inconel 625

The ability to use common computational thermodynamic and kinetic tools to study the microstructure evolution in Inconel 625 (IN625) manufactured using the additive manufacturing (AM) technique of laser powder-bed fusion is evaluated. Solidification simulations indicate that laser melting and re-melting during printing produce highly segregated interdendritic regions. Precipitation simulations for different degrees of segregation show that the larger the segregation, i.e., the richer the interdendritic regions are in Nb and Mo, the faster the δ-phase (Ni3Nb) precipitation. This is in accordance with the accelerated d precipitation observed experimentally during post-build heat treatments of AM IN625 compared to wrought IN625. The δ-phase may be undesirable since it can lead to detrimental effects on the mechanical properties. The results are presented in the form of a TTT diagram and agreement between the simulated diagram and the experimental TTT diagram demonstrate how these computational tools can be used to guide and optimize post-build treatments of AM materials.

Nucleation and superstabilization in small systems

Phase transitions are known to present peculiarities in small systems that are related to depletion effects of the ambient phase. Mass conservation affects the conditions of thermodynamic equilibrium between a nucleus of the new phase and the matrix as compared with nucleation in infinite systems. This finite-size effect is known to delay the phase transition but can also impede nucleation in very small systems as it stabilizes the initial state, originally metastable in infinite systems. In this work, we investigate this superstabilization effect in the context of classical nucleation theory in multicomponent solutions and we derive an analytical expression for the system size below which nucleation becomes thermodynamically impossible. Comparing with the exact solution, our simple result is shown to accurately predict the superstabilization effect, and can therefore be used, for instance, as a guideline for the design of novel nanomaterials.

A Computational Framework for Material Design

A computational framework is proposed that enables the integration of experimental and computational data, a variety of user-selected models, and a computer algorithm to direct a design optimization. To demonstrate this framework, a sample design of a ternary Ni-Al-Cr alloy with a high work-to-necking ratio is presented. This design example illustrates how CALPHAD phase-based, composition and temperature-dependent phase equilibria calculations and precipitation models are coupled with models for elastic and plastic deformation to calculate the stress-strain curves. A genetic algorithm then directs the search within a specific set of composition and processing constraints for the ideal composition and processing profile to optimize the mechanical properties. The initial demonstration of the framework provides a potential solution to initiate the material design process in a large space of composition and processing conditions. This framework can also be used in similar material systems or adapted for other material classes.

Antiscaling Magnetic Slippery Surfaces

Scale formation is a common problem in a wide range of industries such as oil and gas, water desalination, and food processing. Conventional solutions for this problem including mechanical removal and chemical dissolution are inefficient, costly, and sometimes environmentally hazardous. Surface modification approaches have shown promises to address this challenge. However, these approaches suffer from intrinsic existence of solid-liquid interfaces leading to high rate of scale nucleation and high adhesion strength of the formed scale. Here, we report a new surface called magnetic slippery surface in two forms of Newtonian fluid (MAGSS) and gel structure (Gel-MAGSS). These surfaces provide a liquid-liquid interface to elevate the energy barrier for scale nucleation and minimize the adhesion strength of the formed scale on the surface. Performance of these new surfaces in both static and dynamic (under fluid flow) configurations is examined. These surfaces show superior antiscaling properties with an order of magnitude lower scale accretion compared to the solid surfaces and offer longevity and stability under high shear flow conditions. We envision that these surfaces open a new path to address the scale problem in the relevant technologies.

Kinetics and Mechanisms of γ' Reprecipitation in a Ni-based Superalloy

The reprecipitation mechanisms and kinetics of γ′ particles during cooling from supersolvus and subsolvus temperatures were studied in AD730^TM Ni-based superalloy using Differential Thermal Analysis (DTA). The evolution in the morphology and distribution of reprecipitated γ′ particles was investigated using Field Emission Gun Scanning Electron Microscopy (FEG-SEM). Depending on the cooling rate, γ′ particles showed multi or monomodal distribution. The irregularity growth characteristics observed at lower cooling rates were analyzed in the context of Mullins and Sekerka theory, and allowed the determination of a critical size of γ′ particles above which morphological instability appears. Precipitation kinetics parameters were determined using a non-isothermal JMA model and DTA data. The Avrami exponent was determined to be in the 1.5–2.3 range, suggesting spherical or irregular growth. A methodology was developed to take into account the temperature dependence of the rate coefficient k(T) in the non-isothermal JMA equation. In that regard, a function for k(T) was developed. Based on the results obtained, reprecipitation kinetics models for low and high cooling rates are proposed to quantify and predict the volume fraction of reprecipitated γ′ particles during the cooling process.

Kinetic theory of diffusion-limited nucleation

We examine binary nucleation in the size and composition space {R,c} using the formalism of the multivariable theory [N. V. Alekseechkin, J. Chem. Phys. 124, 124512 (2006)]. We show that the variable c drops out of consideration for very large curvature of the new phase Gibbs energy with composition. Consequently nuclei around the critical size have the critical composition, which is derived from the condition of criticality for the canonical variables and is found not to depend on surface tension. In this case, nucleation kinetics can be investigated in the size space only. Using macroscopic kinetics, we determine the general expression for the condensation rate when growth is limited by bulk diffusion, which accounts for both diffusion and capillarity and exhibits a different dependence with the critical size, as compared with the interface-limited regime. This new expression of the condensation rate for bulk diffusion-limited nucleation is the counterpart of the classical interface-limited result. We then extend our analysis to multicomponent solutions.

Data analysis and other considerations concerning the study of precipitation in Al-Mg-Si alloys by Atom Probe Tomography

Atom Probe Tomography (APT) analysis and hardness measurements were used to characterize the early stages of precipitation in an Al–0.51 at%Mg–0.94 at%Si alloy as reported in the accompanying Acta Materialia paper [1]. The changes in microstructure were investigated after single-stage or multi-stage heat treatments including natural ageing at 298 K (NA), pre-ageing at 353 K (PA), and automotive paint-bake ageing conditions at 453 K (PB). This article provides Supporting information and a detailed report on the experimental conditions and the data analysis methods used for this investigation. Careful design of experimental conditions and analysis methods was carried out to obtain consistent and reliable results. Detailed data on clustering for prolonged NA and PA treatments have been reported.

Nanoclusters first: a hierarchical phase transformation in a novel Mg alloy

The Mg-Y-Zn ternary alloy system contains a series of novel structures known as long-period stacking ordered (LPSO) structures. The formation process and its key concept from a viewpoint of phase transition are not yet clear. The current study reveals that the phase transformation process is not a traditional spinodal decomposition or structural transformation but, rather a novel hierarchical phase transformation. In this transformation, clustering occurs first, and the spatial rearrangement of the clusters induce a secondary phase transformation that eventually lead to two-dimensional ordering of the clusters. The formation process was examined using in situ synchrotron radiation small-angle X-ray scattering (SAXS). Rapid quenching from liquid alloy into thin ribbons yielded strongly supersaturated amorphous samples. The samples were heated at a constant rate of 10 K/min. and the scattering patterns were acquired. The SAXS analysis indicated that small clusters grew to sizes of 0.2 nm after they crystallized. The clusters distributed randomly in space grew and eventually transformed into a microstructure with two well-defined cluster-cluster distances, one for the segregation periodicity of LPSO and the other for the in-plane ordering in segregated layer. This transformation into the LPSO structure concomitantly introduces the periodical stacking fault required for the 18R structures.

Atomistic and continuums modeling of cluster migration and coagulation in precipitation reactions

The influence of vacancy preference towards one of the constituents in a binary system on the formation of precipitates was investigated by atomistic and continuums modeling techniques. In case of vacancy preference towards the solute atoms, we find that the mobility of individual clusters as well as entire atom clusters is significantly altered compared to the case of vacancy preference towards the solvent atoms. The increased cluster mobility leads to pronounced cluster collisions, providing a precipitate growth and coarsening mechanism competitive to that of pure solute evaporation and adsorption considered in conventional diffusional growth and Ostwald ripening. A modification of a numerical Kampmann-Wagner type continuum model for precipitate growth is proposed, which incorporates the influence of both mechanisms. The prognoses of the modified model are validated against the growth laws obtained with lattice Monte Carlo simulations and a growth simulation considering solely the coalescence mechanism.

Homogeneous nucleation of epitaxial CoSi2 and NiSi in Si nanowires

Homogeneous nucleation is rare except in theory. We observed repeating events of homogeneous nucleation in epitaxial growth of CoSi(2) and NiSi silicides in nanowires of silicon by using high resolution TEM. The growth of every single atomic layer requires nucleation. Heterogeneous nucleation is prevented because of non-microreversibility between the oxide/Si and oxide/silicide interfaces. We determined the incubation time of homogeneous nucleation. The calculated and the measured nucleation rates are in good agreement. We used Zeldovich factor to estimate the number of molecules in the critical nucleus; it is about 10 and reasonable. A very high supersaturation is found for the homogeneous nucleation.

Effect of Temperature and Pressure on Surface Tension of Polystyrene in Supercritical Carbon Dioxide

The surface tension of polymers in a supercritical fluid is one of the most important physicochemical parameters in many engineering processes, such as microcellular foaming where the surface tension between a polymer melt and a fluid is a principal factor in determining cell nucleation and growth. This paper presents experimental results of the surface tension of polystyrene in supercritical carbon dioxide, together with theoretical calculations for a corresponding system. The surface tension is determined by Axisymmetric Drop Shape Analysis-Profile (ADSA-P), where a high pressure and temperature cell is designed and constructed to facilitate the formation of a pendent drop of polystyrene melt. Self-consistent field theory (SCFT) calculations are applied to simulate the surface tension of a corresponding system, and good qualitative agreement with experiment is obtained. The physical mechanisms for three main experimental trends are explained by using SCFT, and none of the explanations quantitatively depend on the configurational entropy of the polymer constituents. These calculations therefore rationalize the use of simple liquid models for the quantitative prediction of surface tensions of polymers. As pressure and temperature increase, the surface tension of polystyrene decreases. A linear relationship is found between surface tension and temperature, and between surface tension and pressure; the slope of surface tension change with temperature is dependent on pressure.