Terms Of Classical Nucleation Theory Research Articles

Theory of crystal nucleation of glass‐forming liquids: Some new developments

AbstractExperiments on crystal nucleation are predominantly interpreted theoretically in terms of classical nucleation theory (CNT). This theory relies on thermodynamic concepts developed by Gibbs. Their application implies that the bulk properties of critical clusters governing nucleation are widely identical to those of the newly evolving macroscopic phases. Size effects are incorporated into CNT exclusively by a curvature dependence of the surface tension. This method works well but only down to temperatures near to the maximum of the steady‐state nucleation rate. This maximum (at) is correlated with the glass transition temperature,, that is,. For lower temperatures, significant deviations between theoretical predictions and experimental data are observed. We describe here different methods how a curvature dependence of the surface tension can be introduced to describe crystal nucleation correctly in the range. Problems occurring at, denoted sometimes as “breakdown of CNT,” are shown to be caused by the glass transition of the liquid. Modifications of CNT are advanced resolving them and giving also the possibility of interpretation of a variety of further experimental data in crystal nucleation (including hysteresis effects in cooling and heating, nucleation flashes in heating) in terms of CNT.

Salt-concentration-dependent nucleation rates in low-metastability colloidal charged sphere melts containing small amounts of doublets

We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concentration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while postsolidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The full data set, however, shows an unexpected scaling of the nucleation rate densities with metastability times the number density of particles. Parameterization of our results in terms of classical nucleation theory reveals unusually low interfacial free energies of the nucleus surfaces and nucleation barriers well below the thermal energy. We tentatively attribute our observations to the presence of doublets introduced by the employed conditioning technique. We discuss the conditions under which such small seeds may induce nucleation.

Crystal Nucleation and Growth in Cross-Linked Poly(ε-caprolactone) (PCL).

The crystal nucleation and overall crystallization kinetics of cross-linked poly(ε-caprolactone) was studied experimentally by fast scanning calorimetry in a wide temperature range. With an increasing degree of cross-linking, both the nucleation and crystallization half-times increase. Concurrently, the glass transition range shifts to higher temperatures. In contrast, the temperatures of the maximum nucleation and the overall crystallization rates remain the same, independent of the degree of cross-linking. The cold crystallization peak temperature generally increases as a function of heating rate, reaching an asymptotic value near the temperature of the maximum growth rate. A theoretical interpretation of these results is given in terms of classical nucleation theory. In addition, it is shown that the average distance between the nearest cross-links is smaller than the estimated lamellae thickness, which indicates the inclusion of cross-links in the crystalline phase of the polymer.

Effects of Microstructure and Sample's Surface to Volume Ratio on Pressure-Induced Nucleation and Transformation to Crystalline and Apparently Amorphous Solids.

Heterogeneous nucleation in a polycrystalline solid occurs (i) at the surface of its container, (ii) at its microstructural sites, namely, grain boundaries, grain junctions, and intergrain-strain regions, and (iii) at the defect sites, namely, dislocations, vacancies, and stacking faults (planar defects) in its single crystal grains. We analyze their thermodynamic and kinetic effects in terms of classical nucleation theory by taking into account (a) the increase in Gibbs free energy, G, due to the lattice misfit of the nuclei forming in the parent phase and (b) the decrease in G due to the angle subtended by the nucleus on the external surface, grain boundaries, and grain junctions. Hence we deduce that several combinations of nucleation sites in different materials and also in different polycrystalline samples of the same material may produce the same energy barrier against nucleation and overall growth. The overall nucleation and growth rates are dependent upon the surface to volume ratio, χ, of a sample in a vessel and the vessel's material. Pressurizing a crystalline solid is known to produce either its polymorphic crystal form or a solid that shows no Bragg peaks and appears amorphous. We argue that when self-diffusion rate becomes slower than the pressurizing rate, (dP/dt)T, a multiplicity of states nucleating at different sites become kinetically frozen on their path to crystal growth. In such a case, the transformed solid would appear amorphous. A solid of high χ would transform to a polymorph when (dP/dt)T is low and to a state that appears amorphous when (dP/dt)T is high. Known studies of 0.08-0.1 cm3 volume samples in diamond-anvil high pressure cells provide qualitative evidence of formation of both crystal polymorphs and apparently amorphous solids. Methods are suggested for observing such an occurrence in large polycrystalline samples.

Transient Nucleation in Ge–Sb–S Thin Films

The crystal nucleation behavior and kinetics in Ge1.8Sb36.8S61.4 thin films were studied using optical microscopy coupled with a computer-controlled heating stage. The single-stage in situ heat treatment method was chosen for the study of nucleation. In-situ experiments were performed in the temperature range of 236–295 °C. The time evolution of the number of nuclei at various temperatures revealed transient behavior at low nucleation times. The transient nucleation data were described using the Shneidman equation to get values of steady-state nucleation rate, induction period, and time-lag of nucleation for the studied temperatures. On the basis of nucleation experiments, the temperature dependence of crystal–liquid surface energy and decoupling of nucleation rate and viscosity was assessed. The nucleation rate data obtained from microscopy measurements were discussed in terms of classical nucleation theory. It was found that the nucleation curve with the maximum at 288 °C and previously published growth...

In Situ Interface Observation of 3C-SiC Nucleation on Basal Planes of 4H-SiC During Solution Growth of SiC from Molten Fe-Si Alloy

Solution growth is a promising process to obtain high-quality 4H-SiC crystal for application in high-voltage-power devices. Polytype transition from 4H-SiC into 6H-, 15R-, or 3C-SiC is one of the major issues to be solved to achieve rapid growth of large-diameter 4H-SiC crystals. In this study, the mechanism for the polytype transition to 3C-SiC during the solution growth process was determined from in situ interface observation of SiC growth on basal planes of 4H-SiC from Fe-36 mol.%Si alloy at 1680–1885 K. The nucleation behavior of 3C-SiC on 4H-SiC was discussed in terms of classical nucleation theory.

Quantifying the Effect of Stress on Sn Whisker Nucleation Kinetics

Although Sn whiskers have been studied extensively, there is still a need to understand the driving forces behind whisker nucleation and growth. Many studies point to the role of stress, but confirming this requires a quantitative comparison between controlled stress and the resulting whisker evolution. Recent experimental studies applied stress to a Sn layer via thermal cycling and simultaneously monitored the evolution of the temperature, stress and number of nuclei. In this work, we analyze these nucleation kinetics in terms of classical nucleation theory to relate the observed behavior to underlying mechanisms including a stress dependent activation energy and a temperature and stress-dependent whisker growth rate. Non-linear least squares fitting of the data taken at different temperatures and strain rates to the model shows that the results can be understood in terms of stress decreasing the barrier for whisker nucleation.

Phase transitions and kinetic properties of gold nanoparticles confined between two-layer graphene nanosheets

The thermodynamic and kinetic behaviors of gold nanoparticles confined between two-layer graphene nanosheets (two-layer-GNSs) are examined and investigated during heating and cooling processes via molecular dynamics (MD) simulation technique. An EAM potential is applied to represent the gold–gold interactions while a Lennard–Jones (L–J) potential is used to describe the gold–GNS interactions. The MD melting temperature of 1345K for bulk gold is close to the experimental value (1337K), confirming that the EAM potential used to describe gold–gold interactions is reliable. On the other hand, the melting temperatures of gold clusters supported on graphite bilayer are corrected to the corresponding experimental values by adjusting the εAu–C value. Therefore, the subsequent results from current work are reliable. The gold nanoparticles confined within two-layer GNSs exhibit face center cubic structures, which is similar to those of free gold clusters and bulk gold. The melting points, heats of fusion, and heat capacities of the confined gold nanoparticles are predicted based on the plots of total energies against temperature. The density distribution perpendicular to GNS suggests that the freezing of confined gold nanoparticles starts from outermost layers. The confined gold clusters exhibit layering phenomenon even in liquid state. The transition of order–disorder in each layer is an essential characteristic in structure for the freezing phase transition of the confined gold clusters. Additionally, some vital kinetic data are obtained in terms of classical nucleation theory.

Crystallization of Glass: What We Know, What We Need to Know

The relevance of the concepts of fragility and of the glass transition temperature for the understanding of crystal nucleation and growth in glass‐forming liquids is explored. It is shown that classical fragility can be relevant for the understanding of the crystallization behavior only if several severe conditions are fulfilled that are rarely met. By this reason, a new definition of liquid fragility is introduced shown to be able to reflect appropriately the maxima of crystal nucleation, growth, and overall crystallization rates. The origin of the previously reported correlations between glass transition temperatures and intensity of crystallization processes is specified. Further, interpreted in terms of classical nucleation theory, for a variety of oxide glass‐forming liquids, the thermodynamic barrier for homogeneous crystal nucleation exhibits at high undercooling an unusual increase with a decrease in temperature. Such behavior cannot be explained in terms of classical nucleation theory. Different directions of generalization of the classical theory are discussed, which may lead to a resolution of these problems. The realization of such generalization is considered to be a prerequisite for a generally deeper understanding of the complex phenomena occurring in melt crystallization with its rich field of applications.

Tensile Strength of Liquids: Equivalence of Temporal and Spatial Scales in Cavitation.

It is well known that strain rate and size effects are both important in material failure, but the relationships between them are poorly understood. To establish this connection, we carry out molecular dynamics (MD) simulations of cavitation in Lennard-Jones and Cu liquids over a very broad range of size and strain rate. These studies confirm that temporal and spatial scales play equivalent roles in the tensile strengths of these two liquids. Predictions based on smallest-scale MD simulations of Cu for larger temporal and spatial scales are consistent with independent simulations, and comparable to experiments on liquid metals. We analyze these results in terms of classical nucleation theory and show that the equivalence arises from the role of both size and strain rate in the nucleation of a daughter phase. Such equivalence is expected to hold for a wide range of materials and processes and to be useful as a predictive bridging tool in multiscale studies.

Study of silver cluster formation from thin films on inert surface

We investigated the evolution of 6–130 nm silver thin films during vacuum annealing. The bimodal character of cluster size distribution was observed for 12–130 nm films. One average cluster size is 40–80 nm, other average size is 380–420 nm. At the same time it is shown that two simultaneous processes occur: coalescence and evaporation. The bimodality distribution character is associated with these two simultaneous processes. The initial 6 nm Ag film is found to be not continuous and to consist of aggregates of stuck clusters. The heating of this film up to 230 °C leads to the separation of clusters and unimodal character of cluster size distribution (average cluster size is up to 10 nm). The differences in behavior of 6–130 nm Ag thin films are discussed in terms of classical nucleation theory.

Supersaturation–Nucleation Behavior of Poorly Soluble Drugs and its Impact on the Oral Absorption of Drugs in Thermodynamically High-Energy Forms

In order to better understand the oral absorption behavior of poorly water-soluble drugs, their supersaturation-nucleation behavior was characterized in fasted state simulated intestinal fluid. The induction time (t(ind)) for nucleation was measured for four model drugs: itraconazole, erlotinib, troglitazone, and PLX4032. Supersaturated solutions were prepared by solvent shift method, and nucleation initiation was monitored by ultraviolet detection. The relationship between t(ind) and degree of supersaturation was analyzed in terms of classical nucleation theory. The defined supersaturation stability proved to be compound specific. Clinical data on oral absorption were investigated for drugs in thermodynamically high-energy forms such as amorphous forms and salts and was compared with in vitro supersaturation-nucleation characteristics. Solubility-limited maximum absorbable dose was proportionate to intestinal effective drug concentrations, which are related to supersaturation stability and thermodynamic solubility. Supersaturation stability was shown to be an important factor in determining the effect of high-energy forms. The characterization of supersaturation-nucleation behavior by the presented method is, therefore, valuable for assessing the potential absorbability of poorly water-soluble drugs.

Theory of pore formation in glass under tensile stress: Generalized Gibbs approach

A theoretical analysis is performed of the process of nucleation of a pore in small samples of an under-cooled diopside liquid, enclosed by a solid crystalline surface layer growing from the melt. Due to the density misfit of the crystal and liquid phases the growth of the crystalline layer leads to a uniform stretching of the encapsulated liquid. After reaching some critical values, the resulting tensile stress results in nucleation of a single pore. Nucleation of the pore is followed by its rapid growth, which decreases considerably the magnitude of elastic stresses and therefore eliminates the pre-condition for nucleation. This process has been analyzed earlier in terms of classical nucleation theory leading to a qualitatively correct interpretation. However, quantitatively, theoretical estimates performed in the framework of classical nucleation theory and experimental data differ. It is shown here that the generalized Gibbs approach results in a more adequate quantitatively correct description of the process of pore nucleation.

On the Melting and Freezing of Au−Pt Nanoparticles Confined in Single-Walled Carbon Nanotubes

A MD simulation method is used to simulate the melting and freezing of Au−Pt nanoparticles confined in armchair single-walled carbon tubes ((n,n)-SWNTs), applying the second-moment approximation of the tight-binding potentials for metal−metal interactions and Lennard-Jones potential for the metal−carbon interactions. The carbon atoms on the SWNTs are taken to be fixed. The structures, total energies, Lindemman indices, and radial and axial density distributions are used to examine the behaviors of melting and freezing for Au−Pt nanoparticles confined in (n,n)-SWNTs. The nucleation analysis is carried out in terms of classical nucleation theory. The simulation results demonstrate that the solid Au−Pt clusters confined within (n,n)-SWNTs have multishell structures, even in a melted cluster. In addition, for the confined Au−Pt nanoparticles, Pt atoms tend to stay at the position close to the SWNT wall, which is different from free Au−Pt nanoparticles. Simulation results reveal that SWNTs and compositions of nanoparticles have significant effects on the structures and physical properties of the confined Au−Pt nanoparticles. On the other hand, some important thermodynamic and dynamic parameters are estimated based on MD simulations and compared with available theoretical and experimental results.

Nucleation in a Potts lattice gas model of crystallization from solution

Nucleation from solution is important in many pharmaceutical crystallization, biomineralization, material synthesis, and self-assembly processes. Simulation methodology has progressed rapidly for studies of nucleation in pure component and implicit solvent systems; however little progress has been made in the simulation of explicit solvent systems. The impasse stems from the inability of rare events simulation methodology to be combined with simulation techniques which maintain a constant chemical potential driving force (supersaturation) for nucleation. We present a Potts lattice gas (PLG) to aid in the development of new simulation strategies for nucleation from solution. The PLG captures common crystallization phase diagram features such as a eutectic point and solute/solvent melting points. Simulations of the PLG below the bulk solute melting temperature reveal a competition between amorphous and crystalline nuclei. As the temperature is increased toward the bulk melting temperature, the nucleation pathway changes from a one step crystalline nucleation pathway to a two step pathway, where an amorphous nucleus forms and then crystallizes. We explain these results in terms of classical nucleation theory with different size-dependant chemical potentials for the amorphous and crystalline nucleation pathways. The two step pathway may be particularly important when crystallization is favored only at postcritical sizes.

Grain refinement and coarsening in hypercooled solidification of eutectic alloy

Applying glass fluxing combined with thermal cycle, hypercooled solidification was achieved for Ni 78.6Si 21.4 and Fe 83B 17 eutectic alloys, thus giving grain refinement and coarsening, respectively, in the as-solidified morphologies. Based on the theoretical analysis in terms of classical nucleation theory (CNT), the above phenomenon can be ascribed to the effect of increased or decreased nucleation rate under hypercooled condition.

Hydrogen-induced modification of the medium-range structural order in amorphous silicon films

We use fluctuation electron microscopy to determine changes in the medium-range structural order of un-hydrogenated amorphous silicon thin films after they are exposed to atomic hydrogen at a substrate temperature of 230 °C. The films are deposited by magnetron sputtering at either 230 or 350 °C substrate temperature to obtain starting states with small or large initial medium-range order, respectively. The in-diffusion of atomic hydrogen causes the medium-range order to decrease for the small initial order but to increase for the large initial order. We suggest that this behavior can be understood in terms of classical nucleation theory: The ordered regions of small diameter are energetically unstable and can lower their energy by evolving towards a continuous random network, whereas the ordered regions of large diameter are energetically stable and can lower their energy by coarsening towards the nanocrystalline state.

Cavitation and the stability region of liquid lead at negative pressures: Molecular dynamics study

Cavitation kinetics has traditionally been described in terms of classical nucleation theory (CNT) based on the thermodynamic calculation of work on the formation of a nucleus of a new phase and the solution of the kinetic equation of the nucleus size distribution [1]. The application of CNT is often complicated by the uncertainty associated with the actual accuracy of the model approximations that underlie the theory, as well as by the absence of sufficiently reliable data on the surface tension at the interface and the equation of state of a metastable liquid.

Film thickness dependence of the NiSi-to-NiSi2 transition temperature in the Ni/Pt/Si(100) system

The effect of film thickness on the NiSi-to-NiSi2 transition temperature in the Ni/Pt/Si(100) system has been studied. Three sets of Ni/Pt/Si(100) bilayered samples with the same Ni:Pt ratios but with different film thicknesses were annealed by rapid thermal annealing at 750–900 °C. Both the x-ray diffraction analysis and the sheet resistance measurement show that the thermal stability of Ni(Pt)Si films improves with a decrease in film thickness. This property of Ni(Pt)Si films reveals the good potential for its applications in ultrashallow junctions. The experimental results are explained in terms of classical nucleation theory.

Particle formation and growth from ozonolysis of α‐pinene

Observations of particle nucleation and growth during ozonolysis of α‐pinene were carried out in Calspan's 600 m3 environmental chamber utilizing relatively low concentrations of α‐pinene (15 ppb) and ozone (100 ppb). Model simulations with a comprehensive sectional aerosol model which incorporated the relevant gas‐phase chemistry show that the observed evolution of the size distribution could be simulated within the accuracy of the experiment by assuming only one condensable product produced with a molar yield of 5% to 6% and a saturation vapor pressure (SVP) of about 0.01 ppb or less. While only one component was required to simulate the data, more than one product may have been involved, in which case the one component must be viewed as a surrogate having an effective SVP of 0.01 ppb or less. Adding trace amounts of SO2 greatly increased the nucleation rate while having negligible effect on the overall aerosol yield. We are unable to explain the observed nucleation in the α‐pinene/ozone system in terms of classical nucleation theory. The nucleation rate and, more importantly, the slope of the nucleation rate versus the vapor pressure of the nucleating species would suggest that the nucleation rate in the α‐pinene/ozone system may be limited by the initial nucleation steps (i.e., dimer, trimer, or adduct formation).