Nucleation Curves Research Articles

Nucleation curves of methane–propane mixed gas hydrates in the presence of a stainless steel wall

Nucleation phenomena are important to many applications of gas hydrates and yet the nucleation curves of gas hydrate systems have rarely been measured, presumably due to the experimental difficulties involved. We measured the nucleation curves of Structure II (sII) forming methane–propane mixed gas hydrates in the presence of a stainless steel (SS) wall using the second generation High Pressure Automated Lag Time Apparatus (HP-ALTA MkII). The instrument can apply a large number of linear cooling ramps to a small volume of water under isobaric conditions and record maximum achievable subcooling distributions. The survival curves with respect to methane–propane mixed gas hydrate formation were constructed from the recorded data and then converted to nucleation curves using the novel protocol we had recently reported. The nucleation rates per unit length of the three-phase-line, where the guest gas, water and the stainless steel wall met, were derived as functions of system subcooling. We also extended the measurements of the nucleation curves of the same guest gas hydrate in the presence of a glass wall to lower cooling rates than previously studied, so that the nucleation curves of these two systems could be compared at the same cooling rates. Comparison of the nucleation curves of these two systems showed that the nucleation rates per unit length of the three-phase-line were broadly similar to each other. The same instrument and experimental protocols can be utilized for the derivation of nucleation curves of a guest gas of a different composition and/or in the presence of another solid wall.

Nucleation curves of model natural gas hydrates on a quasi‐free water droplet

Heterogeneous nucleation probability distributions of gas hydrates on a water droplet that was supported by inert and immiscible perfluorocarbon oil, perfluorodecalin is studied. The guest gas used was a mixture of 90 mol % methane and 10 mol % propane. The probability distribution was measured using a high pressure automated lag time apparatus under the guest gas pressure range of 6.7–12.5 MPa and the cooling rate range of 0.002–0.02 K/s. Nucleation curves were derived for unit area of water surface. The nucleation rate per unit area of water surface that was contained in a glass sample cell, which differed significantly from that on a quasi‐free water droplet, is also derived. It is concluded that the nucleation curves in the presence of a solid wall should be normalized to the unit length of the three‐phase line at which water, guest gas, and the solid wall meet. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2611–2617, 2015

Saccharose Inversion and Metastable Zone

AbstractIn the production of beverages, cookies, and candies, citric acid is often used as preservative or flavoring agent. Due to the sensitivity in stability of saccharose concerning pH and temperature, it is necessary to know how these two parameters affect the inversion of sugar and therefore the changes in the characteristics of saccharose crystallization. It can be shown that the inversion speed increases with increasing temperature. Also, the exposure time to the acid as well as the amount of acid lead to an increased inversion and therefore need to be controlled in industrial processes. With a temperature difference of 10 °C, inversion increases by the use of 2.13 % citric acid, e.g., by more than 250 %. The metastable zone shifts, but does not change in its width while inversion takes place and the solubility and nucleation curves are shifted to lower temperatures.

Growth and Characterization of Boric Acid Doped KDP Single Crystals Grow by Slow Evaporation Method

Boric acid (0.25, 0.5, 1.0 %wt) doped Potassium Dihydrogen Phosphate (KDP) bulk single crystals were grown from aqueous solutions by slow evaporation method. Solubility and nucleation curves were studied. The grown crystals were confirmed by powder X-ray diffraction analysis. Functional groups presented in the grown material have been identified using FTIR spectra. The temperature stability of the crystal has been confirmed by TGA. The mechanical strength was analyzed using Vickers hardness measurement.

Nucleation and growth in amorphous (GeS2)0.9(Sb2S3)0.1 thin films

The rates of isothermal nucleation and growth in chalcogenide glass thin films of (GeS2)0.9(Sb2S3)0.1 were studied using optical microscopy. Nucleation data was obtained from double stage heat treatment, followed by image analysis of polarized optical micrographs. The applicability of classical nucleation theory (CNT) to the nucleation data has been discussed. The growth data, corrected for viscosity suggest interface controlled 2D nucleated growth of β-GeS2 crystals. The isothermal curves of nucleation and growth determined by CNT and 2D nucleated growth model, respectively were found to be weakly intersecting. The nucleation curve had maxima at 350°C, which is below the glass transition temperature, while the growth curve had a peak at 439°C.

DETERMINATION OF THE METASTABLE ZONE WIDTH OF GLYCINE AQUEOUS SOLUTIONS FOR BATCH CRYSTALLIZATIONS

The aim of this study was to determine the metastable zone width of aqueous solutions of glycine for non-seeded batch crystallizations. The saturation curve was determined by studying the heating rate influence on the apparent saturation temperatures of several solutions. A linear regression was then applied to obtain the saturation temperatures. The spontaneous nucleation curve was obtained by measuring the crystallization temperatures of several solutions at different cooling rates. The results show that the apparent nucleation order of the glycine aqueous solutions was around 3.5 ± 0.5. Moreover, from the experimental data, a second-order polynomial model was established by using the experimental design method. This model enables the expression of crystallization temperature to be defined as a function of concentration and cooling rate. The results show that the model fits well (R2 > 0.99; Q2 > 0.98) and that the cooling rate is the most influential parameter.

Mechanism of Au Electrodeposition onto Indium Tin Oxide

Cyclic voltammetric and chronoamperometric methods were used to study the initial stage of Au electrodeposition on an indium tin oxide (ITO) surface.The nucleation process was controlled by the diffusion of [AuCl4].The cyclic voltammetry curves showed that the electrochemical reduction included two steps which were [AuCl4] → [AuCl2],and [AuCl2] → Au.Only one reduction peak was observed when the scan rate was comparatively slow and this peak separated into two peaks when the scan rate was increased.This phenomenon resulted from the disproportionation of [AuCl2] during the electrodeposition process.Chronoamperometry also proved the two step reaction mechanism and the diffusion coefficient of [AuCl4] was calculated to be 1.3×10-5 cm 2 · s-1.From the theoretical nucleation curves,an instantaneous three-dimensional nucleation mechanism was proposed for the nucleation of gold on ITO.Au electrodeposits were observed by field emission scanning electron microscopy (FE-SEM).SEM images of the electrodeposits showed that the morphology of the gold deposits was affected by the electrochemical deposition potential and time.

Analysis of the Nucleation Kinetics of Oxide Precipitates in Czochralski Silicon

Vacancy dependent nucleation curves were measured. They exhibit four maxima which all increase with increasing vacancy concentration. Even at 1000 {degree sign}C considerable nucleation takes place for high vacancy concentrations. The analysis of nucleation based on classical nucleation theory has shown that nucleation of oxide precipitates takes place at heterogeneous nucleation sites. These sites contain oxygen atoms and vacancies and it is assumed that these sites are VOn complexes with 2<n<6. They are stable between 450{degree sign}C and 700{degree sign}C. As-grown silicon wafers contain a certain concentration of nucleation sites. This concentration increases or decreases during prolonged annealing and, as a result, the nucleation rate increases or decreases with annealing time, respectively. The grown-in concentration of nucleation sites can be markedly increased by appropriate rapid thermal anneal (RTA) pre-treatments. Supersaturated vacancies are assumed to be stored during RTA cooling mainly by reactions of vacancies with oxygen monomers, dimers, and trimers.

Data evaluation of laminar flow diffusion chamber nucleation experiments with different computational methods

In order to evaluate the experimental data from laminar flow diffusion chamber (LFDC) experiments on homogeneous nucleation, an extensive postmeasurement computational analysis is required. The present work investigates the influence of the used computational methodology on the derived nucleation curves. To this end a reanalysis is made of previous LFDC experiments of 1-butanol nucleation in helium [D. Brus et al., J. Chem. Phys. 122, 214506 (2005)] using two different methods. The first method is based on single fluid heat and vapor transport in the carrier gas ignoring the aerosol processes, as commonly made in LFDC data evaluations. The second method is more comprehensive as is based on multidimensional computational fluid-particle dynamics. The calculations are made under the usual simplification of one-way coupling between fluid flow and particles, which is a valid approximation in most practical aerosols, while full aerosol dynamical effects are accommodated. Similar results were produced by the two methods. This finding corroborates the usual practice of omitting aerosol calculations in LFDC experimental data evaluation.

A study of the primary crystallization of a mixed anion silicate glass

This paper presents the results of a study of the primary crystallization of a multicomponent mixed anion silicate glass. The primary phase, leucite, and the secondary phase, diopside, were formed by surface crystallization, while the secondary phase, phlogopite, was formed by volume crystallization. The influence of the particle size of glass powder samples in the range 0–1 mm on the temperature of the DTA crystallization peak, T p, the height of the peak, ( δT) p, and the parameter T p 2 /(Δ T) p was studied. The behaviors of the parameters ( δT) p and T p 2 /(Δ T) p depend only on the change in the surface-to-volume nuclei ratio, as is the case with polymorphic crystallization. However, the particle size ranges in which the surface, volume and mixed crystallization mechanism dominate are considerably narrower for this glass. The influence of the duration of a pre-DTA heat treatment on the parameters T p, ( δT) p, and Δ T p for fixed temperatures in the range T = 550–750 °C was investigated. The T p of the samples thermally treated for different times, at fixed temperatures, decreased up to t = 5 h and then increased to a value close to that of an as-quenched sample, after which the value remained constant. The curves of ( δT) p, and Δ T p as a function of time for fixed temperatures show a maximum. The influence of the temperature of the pre-DTA heat treatment on the parameters T p, ( δT) p, and Δ T p for fixed times of t = 1−5 h was also investigated. On increasing the pre-DTA heat treatment time, the curves changed significantly. The curves for 3 and 5 h in the temperature range 580–660 °C were similar to the nucleation curve, which indicated that the volume nucleation process proceeded in this temperature range. The behavior of these parameters, as a result of the simultaneous action of different nucleation mechanisms and crystal growth differ from those previously reported for the case of polymorphic crystallization.

Role of the particle size of graphite-like boron nitride in nucleation of cubic boron nitride

The influence of the reduced radius of grains of the graphite-like hexagonal boron nitride (h-BN) on the nucleation of the cubic boron nitride (c-BN) during synthesis from an initiator solution at a high pressure is analyzed. The colloidal mechanism of nucleation is confirmed experimentally. It is shown that there is a correlation between the nucleus sizes of the hexagonal boron nitride and the pressure of the onset of nucleation of the cubic boron nitride. The effect of these sizes of the hexagonal boron nitride on the concentration of crystal nuclei of the cubic boron nitride is studied. The kinetic nucleation curves are obtained. It is demonstrated that the concentration of crystallization centers depends on the thermodynamic and kinetic parameters, as well as on the particle size of the graphite-like hexagonal boron nitride.

Two Paths of Oxide Precipitate Nucleation in Silicon

The coherent agglomeration of interstitial oxygen into single-plane and double-plane plates can explain the two peaks in the M-shaped nucleation curves in Czochralski silicon. The density of nucleation sites for the double-plane plates corresponds to the VO2 concentration. Ab initio calculations have shown that the agglomeration of oxygen atoms in single-plane and doubleplane plates is energetically favorable. These plates are under compressive strain. VO2 agglomeration plays only a minor role for modeling the M-shaped nucleation curves because of prior homogenization treatments. It is of much higher impact if as-grown wafers are subjected to nucleation anneals because of the higher vacancy concentration which was frozen in during crystal cooling. This results in higher nucleation rates at higher temperatures. Because the oxygen diffusivity below 700 °C is important for the nucleation rate and many controversial results about the diffusivity in this temperature range were published, we have analyzed the data from literature. We have demonstrated that the effective diffusivity of oxygen at temperatures below 700 °C which corresponds to the quasi equilibrium dimer concentration is very similar to the extrapolation from oxygen diffusivity at high temperature. The high effective diffusivities from out-diffusion and precipitation experiments, and the somewhat lower effective diffusivities from dislocation locking experiments are the result of an ongoing formation of fast diffusing dimers because the equilibrium is disturbed as the result of the strongly increasing difference in the diffusion length between interstitial oxygen and the fast diffusing dimer with decreasing temperature.

Modified classical homogeneous nucleation theory and a new minimum in free energy change: 2. Behavior of free energy change with a minimum calculated for various systems

In the previous study, modified classical homogeneous nucleation theory considering the free energy change in parent phase was developed, which revealed the presence of a minimum in nucleation curve (the curve of total free energy change versus nuclear radius) of binary solution. In the present study, using the modified theory, numerical calculations were performed for other various systems; liquid and solid solution systems with compound nuclei and mixed gas systems with liquid nuclei. The calculated results also proved the presence of a minimum in each nucleation curve of these various systems. The minimum in nucleation curves has been passed unnoticed by many researchers in various fields. Therefore, Kevin equation is misunderstood as it describes the maximum state. However, it should be the minimum state that Kelvin equation describes. The large difference between the critical radius size of water droplet calculated at the maximum point (17 Å at 200% humidity) and the observed micron order size of water droplet in cloud and fog can be explained through considering that the micron order droplet should be in the minimum state. The contradiction comes from the misunderstanding that a nucleation curve has only a maximum. Therefore, it is essential to review the various nucleation phenomena on the standpoint of the presence of a minimum. The influence of the change of initial content, initial pressure, interfacial tension, and number of nuclei in 1 mol system to the behavior of nucleation curve was discussed.

Modified classical homogeneous nucleation theory and a new minimum in free energy change: 1. A new minimum and Kelvin equation

The main concern of classical homogeneous nucleation theory has been a thermodynamic description of initial stage of nucleation from embryo to nucleus with a little larger size over the critical one, thus, the change of parent phase in the system has been assumed to be negligible because of the largeness in volume and mass comparing that of nuclei. As a result, the nucleation curve (free energy change versus nucleus size) passes through well-known single maximum point corresponding to the critical size of the nucleus. In the present study, thermodynamics of the classical homogeneous nucleation was re-visited and developed a modified equation for multi-component solution and gas system with multi-component nuclei by taking into account the change of the free energy of parent phase. Using this equation, the calculation of nucleation curve beyond the size of critical nucleus became possible. A calculation of A–B binary solution system revealed a new minimum point in the nucleation curve, in addition to the maximum point. This minimum point indicates the theoretical possibility to stabilize a large amount of nano-nuclei in equilibrium with the supersaturated parent phase. In addition, Kelvin equation was proved at the extremum on the nucleation curve. Many scientists have misunderstood that Kelvin equation corresponds to the maximum state because they have unnoticed the presence of the minimum and its stability. At the minimum state, the nuclei should be more stable than those at the maximum state. Thus, Kelvin equation should correspond to the minimum state rather than the maximum state.

Prediction of Dextrose Nucleation Kinetics by the Growth Rate of Crystallites

AbstractAn investigation on the dextrose nucleation carried out in the presence of seeds is reported. Induction time and nucleation point were measured in seeded solutions by eye and by using a nephelometer. The nucleation point was interpreted as the instant when crystallites, generated by seeds, grow up to crystals of detectable size. By applying the approach proposed by Kashchiev [1], the induction time values obtained were satisfactorily predicted when a birth and spread growth rate model was assumed. Moreover, by extending the same approach to the prediction of the nucleation point, obtained by linear cooling, a nucleation curve in good agreement with the experimental points was determined.

The PVT surface of water: critical phenomena near 0.195 GPa, 182 K

Abstract This paper uses data on the low temperature, high pressure properties of liquid water to identify the probable location of critical behavior on the PVT surface of the liquid. It points out the fact that five collections of information in the literature point to, or are consistent with, the region near 0.195 GPa, 182 K being a location for critical phenomena on the surface of liquid water. The point 0.195 GPa, 182 K is: the lowest temperature on the homogeneous nucleation curve; the intersection point of the fitted curves for temperature of maximum density and homogeneous nucleation; the extrapolated intersection of the hysteresis curves for the low density amorphous (LDA) and high density amorphous (HDA) water phase transition; and the lowest temperature on the calculated spinodle for water. The decompression induced melting behavior of ice IV tracks to the same point within experimental error. These observations are used along with reports of the density of water and ice as a function of pressure and temperature to construct a PVT surface for amorphous water in the range 0–0.35 GPa, 160–320 K. Extrapolation and structure-based criteria are used in areas where experimental data are lacking. Structure-based criteria refer to the chemical structure of the liquid, understood in terms of the packing density of water molecules. The volume expansion at low temperature, one atmosphere, for supercooled water is extrapolated by means of a fourth-order polynomial to the specific volume of ice Ih expanded by 2.3%. The specific volume difference between ice Ic and LDA at the same temperature and pressure is approximately 2.3%. The extrapolated temperature associated with this volume, 223 K, is shown as the limit of the homogeneous nucleation temperature, THL. The specific volume of amorphous water will decrease with decreasing temperature below THL. At this point the liquid volume will have expanded to its limit without the rupture of large numbers of hydrogen bonds. Because volume expansion, without major loss of stability, is no longer possible for the liquid it will behave like ice Ih and decrease in volume with decreasing temperature. The available data for the homogeneous nucleation temperature of water as a function of pressure have a low temperature limit in the PT plane near 0.195 GPa, 182 K. This value corresponds, within the error of the estimate, to the minimum in the conjectured stability limit of water. The corresponding point on the D2O PVT surface occurs at 0.211 GPa, 187 K. A tricritical point would be compatible with the topography of the H2O PVT surface near 0.195 GPa, 182 K. Features of the PVT surface of water are discussed in light of recent high pressure melting experiments, and other experimental data that point to critical phenomena in the low temperature PVT surface of water. The line of continuous transitions emanating from the high temperature side of a tricritical point would provide a reasonable basis for understanding the decompression induced melting behavior of H2O, and D2O, and the heat capacity of the supercooled liquid as a function of temperature.

Pressure induced nucleation in a Li 2O · 2SiO 2 glass

The concentration of nuclei ( N v) in a Li 2O · 2SiO 2 (LS 2) glass was measured using a newly developed differential thermal analysis technique, after densifying the glass at 1, 3, or 6 GPa pressure at 400 °C for 20 min. N v increased from 38×10 12 m −3 for an as-melted glass to 82×10 12 m −3 for a glass subjected to a pressure of 1 GPa, and remained nearly constant with further increase of pressure of up to 6 GPa. This increase in N v is equivalent to nucleating this LS 2 glass at the temperature (455 °C) of its maximum nucleation rate for 2 h. The average effective activation energy for crystallization for the densified glasses, 292±10 kJ/mol, was also the same as that of the (undensified) glass nucleated at 455 °C for 2 h, but was significantly smaller than that (358±10 kJ/mol) for an as-melted (undensified and unnucleated) glass. The present results show that applying an external pressure on this LS 2 glass shifts its nucleation curve to lower temperatures causing nuclei to form even at 400 °C. A decrease in viscosity at all temperatures with the application of pressure is suspected to be a reason for the enhanced nucleation observed for this LS 2 glass.

Liquid-to-crystal heterogeneous nucleation: bubble accelerated nucleation of pure supercooled water

Bubble formation in a single sample of pure water, held in the sample holder of our automated lag-time apparatus, is shown to lead to accelerated liquid-to-crystal heterogeneous nucleation. This phenomenon shifts the entire probability distribution for heterogeneous nucleation, together with the average lag-time 〈 τ〉, to significantly warmer temperatures. In the linear supercooling experiment analyzed here, this is equivalent to reducing the average time to nucleation. Using a single assumption tested in previous work, the entire ‘nucleation curve’ is extracted from a single experiment.

Nucleation kinetics of Cu6Sn5 by reaction of molten tin with a copper substrate

The nucleation kinetics of the η-phase (Cu6Sn5) intermetallic compound were investigated by hot dipping copper coupons in molten tin for 1 and 2 sec, at temperatures varying from 240°C to 300°C. In the scanning electron microscope (SEM), the Cu6Sn5 phase appears as small, rounded bumps of varying sizes, jutting out from the surface of the copper. The experimentally determined nucleation curves show the typical inverse C type behavior with a maximum nucleation rate occurring at an intermediate temperature. The role of surface finish on nucleation rate was also studied. Experimentally determined “effective nucleation rate” per unit area is presented and compared with theoretical predictions over the temperature range investigated. Relevant nucleation models and nucleation energetic parameters are also discussed.

An assessment of isothermal crystallization kinetics in glass by mathematical modeling

A mathematical model is presented to assess the devitrification kinetics of glasses under isothermal conditions. The model takes into account all the experimentally observable aspects of nucleation and growth behavior. A particle size distribution function is defined from the nucleation and growth parameters, and used to calculate the transformed volume fraction, the number of crystals and their mean and maximum radii according to the isothermal heat treatment time. The model was validated with a barium disilicate glass that crystallizes uniformly and rapidly into spherical particles; the nucleation and growth curves were therefore determined for BaSi 2O 5 crystals. The simulated and experimental results are compared and discussed. The model closely approximates the actual results, and can describe the devitrification kinetics of any glass matrix for which the nucleation and growth mechanisms have been defined.