A kinetic treatment of glass formation V: Surface and bulk heterogeneous nucleation

An analytical method is described for calculating the detailed distribution of crystallite sizes in a supercooled liquid, and the changes in this distribution as a function of temperature (time) while the liquid is cooled from above the melting point.This method, termed the analysis of crystallization statistics, is applied to the calculation of continuous cooling curves for anorthite and o-terphenyl as representative of inorganic and organic systems. In addition to homogeneous nucleation, bulk as well as surface heterogeneous nucleation are considered. The effects of distributions of heterogeneities with contact angles between 40 and 100° as well as overall concentrations of heterogeneities between 10³ and 10⁹ cm^?3 are considered. Heterogeneities with contact angles higher than about 100° are shown not to have an effect on the critical cooling rate for typical concentrations of heterogeneities.For liquids containing distributions of heterogeneities, the nucleation behavior is dominated by small concentrations of heterogeneities having small contact angles. Theoretical log (I_vη) versus (T_r³ΔT_r²)^?1 curves have been constructed for homogeneous nucleation + heterogeneous nucleation with a single type of heterogeneity and for homogeneous nucleation + heterogeneous nucleation with the heterogeneities distributed with regard to contact angle. In the former case, the curve is composed of two linear portions; and in the latter case, the curve shows pronounced curvature. The curvature reflects a continous change in the frequency of heterogeneous nucleation.Surface heterogeneous nucleation was assumed to originate at discrete surface heterogeneities and was shown to give rise to continuous cooling curves similar to those calculated for bulk heterogeneous nucleation.     

A Study of the Nucleation Kinetics,Linear Growth and the Overall Crystallization Kinetics of Meltspun Pd80Si20 Amorphous alloy

Nucleation kinetics, linear growth rate and overall isothermal crystallization kinetics of Pd Si amorphous alloy are studied by means of DSC and optical microscopy. It is found that both the histograms of the crystallite sizes and the DSC isotherms (resp. the time dependences of the degree of transformation α(t)) are best described by the model comprosing the simultaneous occurrence of two reactions of crystallization: heterogeneous as well as homogeneous non-stationary nucleation with subsequent three-dimensional growth in both cases. From the fit of the experimentally measured and the calculated according the model thus proposed distribution curves N_i(Φ) the stationary rates of heterogeneous and homogeneous nucleation, the number of quenched-in nucleation sites and the transient time lags of heterogeneous and homogeneous nucleation have been estimated. Using the values of these parameters kintic curves degree of transformation vs. time have been generated, which are closed to the exerimental x(t) curves obtained by means of DSC at isothermal conditions.     

Nucleation kinetics in deionized charged colloidal suspension

A systematic experimental study on the nucleation, crystallization and crystal-growth of one-component charged colloidal particles (122 nm diluted in pure water with densities between 0.5 μm⁻³ < n_p < 5 μm⁻³) is present by means of time resolved static light scattering spectroscopy revealing the heterogeneous and homogenous nature of the crystallization. The interactions between the charged colloidal particles are sufficiently strong to cause crystallization which described in terms of Debye-Hückel approximation. Crystallization starts always with the formation of compressed structurally heterogeneous precursor domains. The results show that the heterogeneous nucleation at the cell walls starts simultaneously with the homogeneous bulk nucleation and the rate density of the heterogeneous nucleation appears slightly higher. It has been also found that the overall crystallization consists of at least a two-step nucleation process involving formation of early stage nuclei or crystal precursor then followed by the main crystallization. The induction time, the number density of nuclei and the growth rate of crystals, is strongly dependent on particle concentration and on whether the nucleation are homogeneous in cell center or heterogeneous on cell walls.     

Nucleation velocity of NaPO3 melts

The time τ for visible crystallization of NaPO₃ melts is measured in the whole range of undercoolings from the melting temperature T_m to the temperature of vitrification T_g. It is shown that the time τ, needed for the appearance of a visible crystallization at high supersaturations is determined by the linear growth rate, whereas the rate of heterogeneous nucleation is the main factor, determining the experimentally measured time τ at low supersaturations. The specific surface energy σ at the melt-crystal interface is calculated from the data on nucleation velocity in the vicinity of T_m and the temperature dependences of both heterogeneous and homogeneous nucleation velocity for NaPO₃ melts are constructed. It is concluded that at normal cooling rates only nucleation, initiated by active crystallized cores could be observed for NaPO₃.     

Transient nucleation effects in glass formation

We extend to the non-isothermal case a numerical technique that was developed to treat transient homogeneous nucleation in a one-component system by modeling directly the reaction by which clusters are produced. Calculations are presented for the nucleation frequency during the quench and for the number of nuclei produced and the volume fraction transformed at the end of quench for different rates of cooling from the melt. Three model systems are considered: an alkali silicate which is a relatively good glass former, and two metallic glasses. These show a wide range of critical cooling rates for glass formation. In some systems transient effects are predicted to be critical for glass formation. A simple technique is presented for determining when transient effects are important based on a calculation using steady state nucleation frequencies and macroscopic growth velocities.     

Induction periods and mechanism and kinetics of nucleation of barium tungstate crystal growth from sodium tungstate melts in platinum crucibles

Induction periods (t) and mechanism and kinetics of nucleation in barium tungstate crystallization from sodium tungstate melts in platinum crucibles were studied. A theoretical relation has been developed to express the dependence of t on the cooling rates (R_T) and the rate (R_c) of development of excess solute concentration. At any crystallization temperature the average rate-constant (k_n) for heterogeneous nucleation was related to R_c by (k_n/p)^1/(p+1) = 1/(tR_c^γ), where γ is a constant and p is the average number of particles in the critical nuclei. The critical temperature (T), critical supersaturation (S) and γ values were estimated.     

Determination of nucleation parameters and the solid liquid interfacial energy of the KCl‐ethanol‐water system

The kinetic parameters of homogeneous nucleation of KCl in different ethanol‐water solvent mixtures were determined at 25°C from the experimental measurements of the width of the metastable zone at different cooling rates. The ethanol mass ratio in the ethanol water solvent mixture was varied from 0‐0.9 and the metastable zone width for each solvent mixture was measured under the cooling rates of 10, 20 and 30 K/h. The influence of ethanol ratio on the activity coefficient was calculated. It was found that increasing the ethanol ratio in the solvent mixture leads to an increase in the mean molal activity coefficient. The experimental results obtained showed that the increase in the ethanol ratio in the solvent widens the metastable zone for the crystallization of KCl. Also it has inferred from the calculations based on the classical nucleation theory that increasing of the ethanol ratio in the solvent mixture resulted in an increase of the nucleation rate order, increase of the critical size of nuclei and increase of the solid liquid interfacial energy. It has been found that the solid liquid interfacial energy can be good correlated with inversely proportionality to the solubility. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of metastable zone width for combined anti-solvent/cooling crystallization

The metastable zone width (MSZW), induction time and primary nucleation kinetics have been measured and estimated for simultaneous anti-solvent and cooling crystallization of paracetamol in iso-propanol/water solution. ATR-FTIR spectroscopy and laser back-scattering are used to measure the solute concentration and primary nucleation event, respectively. Response surface analysis was applied to find the contribution of the crystallization mechanism on the MSZW and obtain a statistical model for quick estimation of the MSZW. Two theoretical approaches for the estimation of nucleation rate kinetic parameters from experimental data are presented. The methods are obtained by modifying the classical Nyvlt's correlation for simultaneous cooling/anti-solvent crystallizations. The nucleation order n for primary nucleation was deduced from the slope of a linear plot of log(MSZW) vs. log(cooling and anti-solvent rates). The induction time was also estimated by changing the classical methods for combined cooling and anti-solvent crystallization.     

Effect of Urea on Metastable Zone Width,Induction Time and Nucleation Parameters of Ammonium Dihydrogen Orthophosphate

Enhancement of the metastable zone width in ammonium dihydrogen ortho phosphate (ADP) was achieved by the addition of the organic compound Urea to ADP solution. The metastable zone width studies were carried out for various temperature cooling rates and the nucleation parameters are studied. The induction period was studied and the critical nucleation parameters calculated based on classical theory for homogeneous nucleation are discussed. The critical nucleation parameters increase with the increase in concentration of doping.     

On the possibility of devitrification of ancient glass

The question whether some crystallization will take place in old glass during long-time storage (up to 1000 years) at low temperatures well below T_g is considered theoretically. Evaluations for the systems Na₂O · SiO₂ and Li₂O · 2SiO₂ are carried out using the model of homogeneous and heterogeneous nucleation theory. For these systems a barely observable crystallized volume fraction will be reached at 300 K only after storage for astronomical periods (10⁶ ? 10¹³ years), depending on the number of heterogeneities and the contact angle of heterogeneity. If the observed strong influence of H₂O content in glass on crystallization is also taken into account, crystallization will not take place for at least 1000 years of storage at 300 K. This limiting value is close to archaeological periods and will therefore merit careful attention in further investigations.     

Protein crystal nucleation: Recent notions

The nucleation of protein crystals is reconsidered taking into account the specificity of the protein molecules. In contrast to the homogeneous surface properties of small molecules, the protein molecule surface is highly inhomogeneous. Over their surfaces proteins exhibit high anisotropic distribution of patches, which are able to form crystalline bonds, the crystallization patch representing only a small fraction of the total surface of the protein molecule. Therefore, an appropriate spatial orientation of the colliding protein molecules is required in order to create a crystalline cluster. This scenario decreases considerably the success ratio of the attempt frequency for crystal nucleation. On the other hand a heterogeneous nucleation of (protein) crystals may be accelerated due to the arrival on some support of under‐critical clusters that are formed in bulk solution; when arriving there they may acquire the property of critical nuclei. Thus, a plausible explanation of important peculiarities of protein crystal nucleation, as inferred from the experimental data, is suggested. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogeneous nucleation in cooling crystallization

Nielsen's equation has been applied for cooling crystallization of KCl from watery solutions. In the calculations activities are used instead of concentrations, the temperature and concentration dependence of both the activity and diffusion coefficients are considered. It is found that A) the interfacial tension between the crystal and its saturated solution is < 2.5 erg/cm², which is less by two orders of magnitude than that of between crystal and vacuum; B) homogeneous nucleation can take place even at very small supersaturations (ln S < < 0.01), which is unusual in precipitation.     

LPE growth rate calculations

The expressions for LPE growth rate calculations are developed on the basis of the steadystate growth model assuming the nucleation at the second interface and in the volume of the solution. The solution layer thickness can be calculated at which the LPE growth rate reaches maximum for any solution cooling rate. The interface and volume nucleation parameters, critical supersaturation and supercooling of the solution have been determined from experimental GaP LPE data within temperature range 800 – 1030°C. Calculated growth rates fit very closely with experimental rates of GaP LPE growth.     

Studies of homogeneous-nucleation-based crystal growth: significant role of phenyl ring in the structure formation

Low-temperature crystal growth was investigated in the fragile liquids of iso-propylbenzene, dimethylphthalate, diphenylphthalate, and 2-methyltetrahydrofuran by using an optical microscope. Homogeneous-nucleation-based (HNB) crystal growth was observed to proceed in the supercooled liquids of the former three substances around and below their glass-transition temperatures, as in the cases of o-terphenyl, toluene, and other fragile liquids, but not detected in 2-methyltetrahydrofuran. Thus far, the growth has been observed only for the substances possessing phenyl group(s) in the molecule. The maximum rates of the growth were found to decrease with increasing the size of substituents to the phenyl ring(s). It was concluded from this fact that the C-H?π(electron) intermolecular interaction between phenyl rings enhances to generate an ordered region required for the crystal nucleation and thereby the HNB crystal growth. Among all the observations of the HNB growth, a rough relation was found that the maximum growth rate increases with an increasing maximum-rate temperature normalized by the respective glass transition temperatures.     

Size-dependent nucleation and growth kinetics model for potassium chloride—Application in Qarhan salt lake

The nucleation process and crystallization kinetics of KCl were studied in order to investigate the problems in KCl production in Qarhan salt lake. The correlation between particle size and KCl crystal growth rate was studied in a continuous mixed-suspension mixed-product removal (MSMPR) crystallizer. Classical theory of primary nucleation was used to study the homogeneous and heterogeneous nucleation mechanism of KCl crystallization. Several size-independent growth models and size-dependent growth models, such as Bransom, C-R, MJ2, ASL, and MJ3, were examined by the population balance theory. Results showed that MJ3 model closely fitted the experimental data, the mean relative deviation was 0.94%, the crystal growth rate G=2068{1−exp[−1.081×10−5(L+961.882)]}.     

Evaluation of the guided random parameterization method for critical cooling rate calculations

We focus on a recently suggested approach to the calculation of critical cooling rates for glass formation. It is a “random parameterization” method that is guided by a limited number of isothermal scanning calorimetry experiments. However, several assumptions have been made in its derivation that may not mirror the actual crystallization behavior of most supercooled liquids, which may jeopardize the estimation of glass forming ability. We evaluate those assumptions and the applicability of the method is tested for lithium disilicate glass (which displays moderate internal nucleation rates) and dibarium titanium silicate glass (which displays very high internal nucleation rates, similar to those of metallic glasses). Both glasses nucleate homogeneously and exhibit polymorphic crystallization. Our calculations show that some overlooked variables, such as the sample geometry, nucleation induction-times, surface crystallization and the breakdown of the Stokes–Einstein/Eyring equation, have significant roles on the calculated time–temperature–transformation curves during heating experiments. We demonstrate that the proposed random parameterization method can only be used when a glass forming liquid that undergoes internal crystallization is cooled from above its liquidus to various test temperatures. If the sample undergoes predominant surface crystallization or if it is heated to the test temperature several corrections must be made.     

Grain size distribution in the Kolmogorov model for nucleation and growth: Heterogeneous versus homogeneous nucleation

A theory of grain size distribution in nucleation and growth reactions described by the KOLMOGOROV model is developed. The distribution of agglomerates of growing and impinging nuclei is explicitely calculated for the two cases of heterogeneous and homogeneous nucleation. The results are compared and discussed with respect to the investigation of the nucleation mechanism in crystallization processes.     

Properties and structure of AsTe glasses: (I). Glass-forming ability and related properties

AsTe glasses have been investigated for determining the molecular mechanisms of glass formation and of crystallization. Stable and homogeneous bulk glasses are prepared throughout the range of concentration from 20 to 65 at % As, by using an improved quenching method. GFA (glass-forming ability) is determined with respect to the rate of cooling. Density, microhardness, T_g and ΔC_p at T_g are measured in the whole range of glass formation. Finally a quantitative analysis of the kinetics of crystallization is carried out. It appears that most properties which involve molecular motions exhibit anomalies for As₄₀ Te₆₀ composition (As₂Te₃ is the unique definite compound of the system). So GFA shows a sharp depression for this critical composition; similarly enthalpy and kinetics of crystallization are drastically modified at As₄₀Te₆₀. For Te-rich glasses, crystallization occurs at low temperature by homogeneous nucleation with a small energy of activation. For As-rich glasses, crystallization occurs at much higher temperatures. Above 200°C it is controlled by growth with an high activation energy which indicates deep rearrangements of the relative positions of the atoms by chemical diffusion. A coherent analysis of all the data is developed which shows that important differences of local order exist between amorphous and crystalline states and also between the two well-distinct types of glasses we are dealing with. The aim of paper II is to determine these differences from diffraction data.     

Nucleation kinetics and critical cooling rate of glass-forming liquids

The critical cooling rate of a substance is the minimum linear rate at which its melt must be cooled to prevent crystallization entirely. In a number of systems this critical cooling rate has proved to be a useful quantitative experimental measure of the tendency to glass formation.The present paper describes a method of deriving theoretical values of the critical cooling rate from classical nucleation kinetics.In general, the calculated values show the correct tendency to glass formation.