Re-examination of effects of nucleation temperature and time on glass crystallization

The effects of nucleation temperature and time on the kinetics of non-isothermal glass crystallization have been re-examined to demonstrate the limitations of some approximate solutions used to extract kinetic parameters from differential thermal analysis (DTA) experiments. Those features were analyzed by numerical solutions of equations describing the dependence of fraction crystallized on the rates of nucleation and growth, and the corresponding transient time, reported for lithium disilicate. It was shown that the temperature of maximum nucleation rate varies on changing the nucleation time. Some guidelines were established to assist the selection of suitable conditions to perform crystallization studies by DTA, and to extract the values of activation energy and dimensionality of growth from the dependences of crystallization peak temperature on heating rate, and nucleation time. The main limitations of these methods were identified and discussed.     

A kinetic treatment of glass formation VII: Transient nucleation in non-isothermal crystallization during cooling

The analysis of crystallization statistics has been modified to allow for time-dependent (transient) nucleation. To establish its accuracy, the numerical analysis has been applied to isothermal crystallization kinetics and shown to yield crystallization versus time curves which compare very closely with curves calculated analytically with or without the inclusion of transient nucleation.The numerical analysis including transient has been used to calculate the critical cooling rates for glass formation in anorthite and o-terphenyl considering (1) only homogeneous nucleation and (2) homogeneous nucleation + heterogeneous nucleation for 10⁷ heterogeneities cm^?3 with contact angles between 40° and 100°. It has been shown that inclusion of time-dependent nucleation in the calculations does not change the critical cooling rates for glass formation calculated assuming steady-state homogeneous nucleation in both materials. The critical cooling rate in anorthite calculated including steady-state heterogeneous nucleation was found to be decreased only slightly by the inclusion of time-dependent nucleation; while the critical cooling rates calculated for o-terphenyl were not change at all by the inclusion of time-dependent nncleation.The lack of an effect of time-dependent nucleation on the critical cooling rates calculated assuming only homogeneous nucleation is explained by the relatively small transient times on the high temperature side of the nucleation peak (a temperature range which has an overwhelming effect on the overall crystallization process because of the relatively high crystal growth rates in this range).Although the critical cooling rates associated with heterogeneous nucleation are large, the nucleation here takes place at relatively small undercooling where the transient times are relatively small. Thus, transient nucleation causes only a temporary delay in the over all crystallization, and its effect on the critical cooling rate is small.     

DTA peak shift studies of primary crystallization in glasses

Following the recognition during the last decade that knowledge of the shift in the exothermic crystallization DTA peak as a function of pre-DTA isothermal heat-treatment times and temperatures, can provide quantitative information about the crystallization kinetics, there has been renewed interest in DTA investigations of crystallization of glasses. Most studies to date, however, have focussed on the kinetics of polymorphic crystallization (where the compositions of the crystal and the parent glass are the same). These studies have established that the DTA peak shifts to lower temperatures with increased pre-DTA heat-treatment times and JMAK-based formalisms have been developed to extract the steady state nucleation rate from the DTA peak shift data. In this paper, we report new results on the DTA peak shift in systems undergoing primary crystallization (where the compositions of the crystal and glass are different). The DTA results show that the exothermic peak temperature decreases initially but increases later on, becoming significantly larger than the initial value, with increase in the pre-DTA heat-treatment time at a fixed temperature. This increase at long times has not been reported previously and is qualitatively different than the monotonic decrease reported for polymorphic crystallization. To rationalize these new results, a model of primary crystallization has been developed which includes homogeneous nucleation, diffusion-controlled growth, Gibbs-Thomson effect, and a mean field soft-impingement correction during growth. Based on this model and experimental results, it is concluded that the initial shift to lower temperatures is due to an increase in the number of nuclei (as concluded previously by others for the case of polymorphic crystallization) and the later shift towards high temperatures in our experiments is due to diffusion-controlled growth during the pre-DTA heat treatment.     

Observation of nucleation effect on crystallization in lithium aluminosilicate glass by viscosity measurement

The crystal nucleation effect in lithium aluminosilicate glasses was investigated by the viscosity measurement with aid of the fiber elongation method. The abrupt increase of viscosity due to the crystallization of glass was observed in viscosity-temperature curve but the minimum viscosity temperature (T_η) related with crystallization showed a strong dependence on the nucleation state such as nucleation temperature, nucleation time and heating rate. The results by viscosity agreed well with those of DTA. The nucleation effect on the microstructure of glass-ceramics was also discussed. Finally, the nucleation effect on the crystallization kinetics was approached quantitatively by calculating the crystal volume from viscosity value.     

Protein crystallization in low gravity by step gradient diffusion method.

Two-step crystallization experiments were conducted in low gravity employing a liquid-liquid diffusion method in an effort to eliminate problems associated with protein crystal growth under the supersaturating conditions required for nucleation. Experiments were performed in diffusion cells formed by the sliding of blocks on orbit. Step gradient diffusion experiments consisted of first exposing protein solutions in diffusion half-wells for brief periods to initiating buffer solutions of high precipitant concentrations to induce nucleation followed by expoure of the same protein solutions to solutions of lower precepitant concentration to promote growth of induced nuclei into crystals. To avoid convective disturbances that occur when solutions of discrepant densities are interfaced at normal gravity, crystallization of hen egg-white lysozyme and rabbit skeletal muscle aldolase by step gradient diffusion was investigated in low gravity on four NASA space shuttle flights. In general, the largest ctystals of both proteins formed at the highest initiating precipitant concentration used, which is consistent with nuclei formation upon brief exposure to high precipitant concentration, and that these nuclei are competent for sustained growth at lower precipitant concentration. The two-step approach dissociates nucleation events from crystal growth allowing parameters affecting nucleation kinetics such as time, precipitant concentration and temperature of nucleation to be varied separately from conditions used for post-nucleation growth.     

Nucleation Catalysis in Metastable Liquids: Inborn Active Sites

A simple formalism is developed in order to analyze the nucleation activity of inborn “week” or “strong” active sites in metastable liquids which can play in nucleation kinetics a role, similar to this of heterogeneous nucleation cores. As examples are examined the influence of Bernal holes and fluctuatively formed Frenkel voids on bubble nucleation, of athermal supercritical nuclei and heterophase fluctuations, frozen‐in in the thermal prehistory of the system on any process of phase formation, and of structural defects, due to change of composition or created in redox processes on crystallization. The analysis is performed in analogy with the known treatment of the influence of heterogeneous foreign cores on nucleation kinetics. Different changes of the metastable liquid are investigated, considering both isobaric thermal quenches and change of pressure at isothermal conditions. The effect of inborn active sites on both steady nucleation rate Iss and on nucleation time lag τ^# is investigated. In this way the whole kinetics of nucleation is constructed using the known approximative solutions of the more general, transient theory of nucleation.     

Viscosity of metglas 2826 near the glass transition using rapid heating

An attempt was made to measure the temperature dependence of viscosity of Metglas 2826 near the glass temperature using rapid heating. This temperature region is normally inaccessible to viscous flow measurements due to crystallization. The melt viscosity, heat of fusion at the melting temperature, and the melting temperature itself were also measured. These parameters are used to calculate the critical cooling rate needed to avoid crystallization via standard nucleation/crystal growth/transformation theory.     

Crystallization mechanisms of acicular crystals

In this contribution, we present an experimental investigation of the growth of four different organic molecules produced at industrial scale with a view to understand the crystallization mechanism of acicular or needle-like crystals. For all organic crystals studied in this article, layer-by-layer growth of the lateral faces is very slow and clear, as soon as the supersaturation is high enough, there is competition between growth and surface-activated secondary nucleation. This gives rise to pseudo-twinned crystals composed of several needle individuals aligned along a crystallographic axis; this is explained by regular over- and inter-growths as in the case of twinning. And when supersaturation is even higher, nucleation is fast and random.In an industrial continuous crystallization, the rapid growth of needle-like crystals is to be avoided as it leads to fragile crystals or needles, which can be partly broken or totally detached from the parent crystals especially along structural anisotropic axis corresponding to weaker chemical bonds, thus leading to slower growing faces. When an activated mechanism is involved such as a secondary surface nucleation, it is no longer possible to obtain a steady state. Therefore, the crystal number, size and habit vary significantly with time, leading to troubles in the downstream processing operations and to modifications of the final solid-specific properties.These results provide valuable information on the unique crystallization mechanisms of acicular crystals, and show that it is important to know these threshold and critical values when running a crystallizer in order to obtain easy-to-handle crystals.     

Factorially designed crystallization trials of the full-length P0 myelin membrane glycoprotein. I. Precipitation diagram

P0 glycoprotein is the abundant membrane protein of myelin of the peripheral nervous system. We report now the statistical design of the crystallization experiments; based on our belief that important information regarding supersaturation of protein or its solubility nature, as well as metastable state, nucleation or precipitation, are hidden in the trials in which no crystals grow. It is possible to work out this information when the whole set of experiments is designed in such a way as to allow statistical analyses. We selected seven factors, which we believe to be important for crystallization: protein concentration, pH of buffer, nature of precipitant, concentration of precipitant, nature of detergent, additives and temperature. The experimental matrix and detailed work sheet to make 148 solutions having random but balanced combination of these levels were calculated using the program DESIGN. A visual evaluation of crystallization drops was performed using light microscopy. We were able to plot the precipitation boundary diagram. Based on this diagram we have eliminated factors (and levels) that were driving the protein into precipitation. It is known that the precipitation boundary is related to the solubility curves for protein crystals, in the neighborhood of which nucleation and further crystallization is most likely to occur. These conditions are currently being refined to identify important factors (or its levels) that can be crucial in obtaining large and well diffracting crystals. Full-length P0 protein has never been crystallized for structural determination.     

Non-equilibrium fluctuations as a plausible reason of the light scattered intensity peak in the glass transition region

The dependence of the scattered intensity on the time after a temperature jump in the glass transition region of oxide glasses was discussed. It was shown that this dependence had a maximum. It was found that the peak height and its location on the time scale depended on the prehistory of the glass. It was supposed that the reason for the enhancement of scattered intensity was the temperature gradient, which arose across the sample after the temperature jump. As the result of experimental studies it was shown that the peak height was proportional to the square of the temperature gradient. Taking into account these features it is assumed that the appearance of the maximum is associated with the non-equilibrium fluctuations produced by coupling between the hydrodynamic modes.     

Batch crystallization of soluble proteins: effect of precipitant, temperature and additive

Although techniques used for protein crystallization have been progressing greatly, successful crystallization is still largely empirical and operatordependent. The crystallization of biological macromolecules is a pretty complicated process involving numerous parameters, thus the detailed understanding of the effect of crystallization conditions on macromolecule crystallization is advantageous. In this study, we have investigated the effect of precipitant, temperature, and additive on the crystallization of lysozyme and chymotrypsinogen A. As the precipitant, sodium chloride is more effective to the crystallization of lysozyme, and ammonium sulfate is more suitable to the crystallization of chymotrypsinogen A. Temperature is found to have no effect on the crystal habit of chymotrypsinogen A, while lysozyme crystallization displays highly sensitive temperature dependence, gradually varied temperature can result in better crystal habit and quality of lysozyme crystals. Furthermore, non-electrolytic additives dimethyl sulfoxide (DMSO) and glycerol are found to not only to increase the protein's solubility, but also decrease the critical supersaturation S_c for explosive nucleation of highly supersaturated protein solution. It is suggested that these additives can affect the interactions between protein molecules, thermodynamic equilibrium, surface energy of the crystal, and nucleation process of protein crystallization.     

Internal friction and structural relaxation of amorphous Fe---Mn---P alloys

Measurements of internal friction and dynamic modulus have been carried out on amorphous Fe_83−xMn_xP₁₇(x=9,12, or 15) alloys in the temperature range 300–800 K, as a function of applied frequency, by a forced oscillation method. The characteristic transition temperatures and activation energies for crystallization were measured by differential scanning calorimetry (DSC). The viscous flow of the sample was measured using a thermomechanical analyzer (TMA) under continuous heating conditions. Internal friction increases rapidly with temperature starting from 450 K for 0.1 Hz, 474 K for 0.5 Hz, 486 K for 1.0 Hz, 511 K for 5 Hz, and 525 K for 10 Hz for the Fe₇₄Mn₉P₁₇ specimen. It was found that the internal friction peak temperature was very closely the same as the steady state viscous flow temperature from the TMA curves for Fe₇₄Mn₉P₁₇ and Fe₆₈Mn₁₅P₁₇ but not for Fe₇₁Mn₁₂P₁₇. It is assumed that the internal friction peak does not correspond to the glass transition temperature or crystallization temperature for these alloy systems. Two maxima in the free-volume fraction and two minima in the viscosity were also found for the samples which exhibit a ‘mid-contraction’ in their TMA displacement curves. The internal friction peak occurred at the steady state viscous flow temperature. This occurrence means that the origin of the internal friction peak is related to the viscous flow behavior and free-volume fluctuation for this alloy system.     

Computer analysis of regularities of nucleation and crystal growth in a solid

An interplay between the homogeneous nucleation and growth processes during recrystallization and phase first-kind transformation was investigated. Computer simulation taking account of unsteadility of nucleation process and possibility of elimination of potential nucleation sites at a constant growth rate allowed to obtain the time dependence of nucleation rate of the new phase, Ṅ, in the total bulk of a sample. The various kinds of the dependence Ṅ including an increase, a constancy and a decrease are obtained.     

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.     

Crystal size distribution in precipitates

After a short introduction on the principles of nucleation and growth – here especially considering defect crystals – particle size distribution in precipitates is discussed. At first batch crystallization is referred to briefly. The situation in stirred continuous tank crystallizers is investigated in detail. Size distribution is considered in dependence on steady state flow rates of the reacting solutions, residence time of crystals in the tank, resulting in an exponential equation for the number of crystals per unit volume: \documentclass{article}\pagestyle{empty}\begin{document}$ n\left(r \right) = \frac{{\dot n_0 }}{{f\left(s \right)}}e^ - \frac{{vr}}{{V \cdot f\left(s \right)}} $\end{document}. With two and more tanks in series size distribution additionally becomes dependent on the difference of the supersaturations, of the occurrence of nucleation, and of the residence time of crystals in the various tanks. Equations for the size distribution are given for special conditions with two and more tanks in series.     

Study of lactose crystallization in water‐acetone solutions

This paper describes a study on the process of lactose crystallization using a water‐acetone solution. The selection of lactose was based on its significance for the pharmaceutical and food industries and on the fact that the crystallization of this organic compound has been little studied and is, unlike inorganic compounds, complex. The objective was to achieve lactose batch crystallization of solutions by analyzing the crystal growth under different operating conditions. To determine solubility curves, the experiments were carried out based on gravimetric methods. All the crystallization experiments were performed according to the methodology proposed by Nývlt in 1985, who uses the temperature at which the first crystals appear (nucleation) to establish the width of the metastable zone and the induction time. The results showed that crystals with different average diameters, shape factors, and recovered mass were obtained for different water‐acetone compositions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluation of nucleation rate by in‐situ focused beam reflectance measurement in an unseeded batch cooling crystallization

Nucleation kinetics in the cooling crystallization of hexahydro‐1,3,5‐trinitro‐1,3,5‐triazine (RDX) from γ‐butyrolactone was studied by converting total counts/s measured by in situ focused beam reflectance measurement (FBRM) into number of crystals. The classical nucleation rate model, which is derived exclusively from the thermodynamic state for the nucleation and molecular collision frequency, was found to be inadequate to describe the experimentally measured nucleation rates. However, the nucleation rates predicted by the modified classical nucleation rate model, inclusive of an additional temperature term, were found to be in good agreement with those measured in the present work. Furthermore, the metastable zone widths are also found to be more accurately predicted by the modified classical nucleation rate model than the classical approach, which assumes that the mass‐based nucleation rate is an exponential function of supersaturation and is equal to the supersaturation rate.     

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.