Induction time in batch crystallisation

Three theoretical models of nucleation in batch crystallisation experiments are presented and compared. The first model, based on the assumption that the new particles are detected immediately after their birth, can be used for assessing the width of metastable zones for practical purposes of industrial crystallisation and crystalliser design. The second one is based on the conception that a certain period of time is needed for crystals, newly born in a solution, before they grow up to become visible; they cannot be detected during this period, though nucleation has already taken place. The third model assumes that all the subcrystals, present in the solution, must attain the visible size before the process of nucleation can be observed. The authors given preference to the second model for evaluating the effective parameters of nucleation.     

The annealing of alkaline-earth metal polymetaphosphate powders (I). Crystallisation and sintering processes

Amorphous barium, strontium, calcium and magnesium polymetaphosphate powders (MP₂O₆)_n, n = 20 were prepared by dehydration of the corresponding polymetaphosphate hydrate precipitates. These powders were annealed by different continuous and isothermal heat treatments over the temperature range 450° to 700 °C, the glass transition temperatures T_g to above (T_g + 120) °C. The morphologies at different degrees of crystallisation were studied by scanning electron microscopy. For the main crystallisation process (ten to sixty-seventy percent crystallisation), the powder particles retained their original pea-pod form; then after seventy percent crystallisation, these crystallised particles sintered laterally to lozenge-shaped twin-hexagonal crystals of lengths 0.5 to 3 μm. Differential thermal analysis confirmed that a markedly exothermic crystallisation process (overall enthalpy changes from about 30 to 45 kJ mol⁻¹) was occurring within the powder particles. Crystallisation rates varied from < 0.005 min⁻¹ at temperatures near T_g to > 0.5 min⁻¹ at higher temperatures; the activation energies for this process varied from 360 to 560 kJ mol⁻¹. The completely annealed crystals were studied by scanning electron microscopy, X-ray diffraction and further differential thermal analysis to 1000 °C. The X-ray diffraction d value patterns, the fusion temperatures and the enthalpies of fusion were all in close agreement with the literature values for the corresponding beta alkaline-earth metal polymetaphosphates prepared by melt crystallisation.     

Berechnung der Übersättigung bei der Kristallisation von InAs aus der Gasphase

It is proved that under experimental conditions for the growing of InAs crystals from the vapour phase the partial supersaturation of indium monoiodide corresponding to the difference of partial pressure of InJ_(g) in the source and in the crystallisation zones, can serve as a quantitative process parameter granting predictions on process development and results in a wide range of ruling conditions. Experiments confirmed the conclusions postulated on the base of quantitative analysis of the transport process. The analysis enables to controll the process parameters of crystal growth by chemical transport.     

Predicted nitrogen doping concentrations in silicon carbide epitaxial layers grown by hot-wall chemical vapor deposition

A simple quantitative model for the surface adsorption of nitrogen has been developed to simulate the doping incorporation in intentionally doped 4H–SiC samples during epitaxial growth. Different reaction schemes are necessary for the two faces of SiC. The differences are discussed, and implications to the necessary model adjustments are stressed. The simulations are validated by experimental values for a large number of different process parameters with good agreement.     

Effect of temperature programmes on protein crystallisation

Varying the temperature has been proven to be beneficial for improving the screening efficiency of protein crystallisation, and thus a crystallisation screening strategy based on this phenomenon can be developed. Such a temperature varying strategy can be applied in practical crystallisation screening, however, there are no guidelines for determining what temperature programme should be utilised. It is therefore necessary to investigate how the temperature programme affects the crystallisation process, so as to help people design a suitable temperature programme. For this purpose, we investigated the effect of temperature programmes on the protein crystallisation (lysozyme, proteinase K, and concanavalin A) that are characterised by different solubility behaviours with respect to temperature. Judging from the reproducibility studies of protein crystallisation with different temperature programmes, we recommend using linear temperature programmes for a moderate time period (24 to 48 h) and a large temperature range according to the properties of the proteins. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of introduction devices on crystallisation kinetic parameters in a supercritical antisolvent process

Supercritical CO₂ antisolvent processes developed in this work are based on two different introduction devices: the Concentric Tube Antisolvent Reactor (a capillary centred in a larger tube) and the Impinging Jet Technology (organic solution and supercritical CO₂ impinging face to face). Griseofulvin pharmaceutical compound is chosen to test those two processes. The different experimental results indicate the same trends as classical supercritical antisolvent process for the evolution of particle size and particle size distribution with process parameters (mainly concentrations and flow rates). The second and main part is dedicated to the use of these experimental results for deriving modelling evaluation. Concerning this part, it is first shown that, in a first approximation, these processes can be represented by a continuous, mixed suspension and mixed product removal crystallizer. This allows modelling the mass particle size distribution. It also allows giving some numerical data on kinetics parameters (nucleation and growth). Secondly, general kinetic laws are derived for each process. In particular in the case of the impinging jet technology, the energy dissipated in the medium by the flow rates must be included in the crystallisation kinetic law.     

Spontaneous crystallization of potassium chloride from aqueous and aqueous‐ethanol solutions; Part 3: Model of the crystallization process

A model of spontaneous crystallization process was proposed. The model describes kinetics of the crystallization process after the end of the induction period. To test the model the published earlier data on crystallization and aggregation kinetics of potassium chloride at its spontaneous crystallization from supersaturated aqueous and aqueous‐ethanol solutions were used. It was found excellent coincidence of the experimental and theoretical data on concentration of the salt and the total number of crystals in solution at crystallization. Somewhat change for the worse was at the theoretical calculations of crystal size distribution at the end of the crystallization process. It indicated that the ways of calculation of size of crystals and their weight fraction in deposit were very approximate. The model allows predicting with satisfactory accuracy kinetics of crystallization using such general parameters of potassium chloride as the specific surface energy and the height of the nucleus‐bridges between crystals at coalescence. It needs further test of the model for other salts. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth and melting of metallic nanoclusters in glass: A review of recent investigations

The mechanisms of nucleation and growth and the solid-to-liquid transition of metallic nanoclusters embedded in sodium borate glass were recently studied in situ via small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS). SAXS results indicate that, under isothermal annealing conditions, the formation and growth of Bi or Ag nanoclusters embedded in sodium borate glass occurs through two successive stages after a short incubation period. The first stage is characterized by the nucleation and growth of spherical metal clusters promoted by the diffusion of Bi or Ag atoms through the initially supersaturated glass phase. The second stage is named the coarsening stage and occurs when the (Bi-or Ag-) doping level of the vitreous matrix is close to the equilibrium value. The experimental results demonstrated that, at advanced stages of the growth process, the time dependence of the average radius and density number of the clusters is in agreement with the classical Lifshitz-Slyozov-Wagner (LSW) theory. However, the radius distribution function is better described by a lognormal function than by the function derived from the theoretical LSW model. From the results of SAXS measurements at different temperatures, the activation energies for the diffusion of Ag and Bi through sodium borate glass were determined. In addition, via combination of the results of simultaneous WAXS and SAXS measurements at different temperatures, the crystallographic structure and the dependence of melting temperature T _m on crystal radius R of Bi nanocrystals were established. The experimental results indicate that T _m is a linear and decreasing function of nanocrystal reciprocal radius 1/R, in agreement with the Couchman and Jesser theoretical model. Finally, a weak contraction in the lattice parameters of Bi nanocrystals with respect to bulk crystals was established. The text was submitted by the authors in English.     

Spontaneous crystallization of sodium chloride from aqueous‐ethanol solutions; Part 3: Examination of a model of the crystallization process

In the present work the examination of the proposed earlier model of spontaneous crystallization process was done. The model describes kinetics of the crystallization process after the end of the induction period. To test the model the published data on crystallization and aggregation kinetics of sodium chloride at its spontaneous crystallization from supersaturated aqueous‐ethanol solutions were used. It was found an excellent coincidence of the experimental and theoretical data on concentration of the salt and the total number of crystals in solution at crystallization. The model allows predicting with satisfactory accuracy kinetics of crystallization using such general parameters of sodium chloride as the specific surface energy and the height of the nucleus‐bridges between crystals at coalescence. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sintering process of glasses in the system Na2O-B2O3-SiO2

In this work, the sintering process of different glasses in the system Na₂O-B₂O₃-SiO₂ has been studied. The studied compositions are suitable for sealing the gas manifolds of molten carbonate fuel cells. Sealing glasses are usually applied on the surfaces to be sealed using powder glass mixed with an organic medium. The agglomerant elimination and the sintering of the glass powder take place during the thermal treatment. Three different particle sizes of glass powder and different sintering temperatures and times have been used to reveal the influence of the specific surface area and viscosity on sintering. The control of these parameters allows optimization of the sealing conditions of the glasses. Dense materials have been characterized as well as the sintering mechanism. Two processes take place during the thermal treatment: the sintering process and the quartz crystallisation. Both processes act in opposite directions on the glass densification. Crystallisation is the dominant process at long times and high temperatures. The viscous flow Scherer model has been adequately applied to the experimental data.     

A diffusion-controlled kinetic model for growth of Au-catalyzed ZnO nanorods: Theory and experiment

A kinetic model for growth of ZnO nanorods via vapor–liquid–solid (VLS) mechanism based on the bulk diffusion of Zn atoms through the Au–Zn droplet is presented. The dependences of the growth rate on size are given quantitatively. A general expression for the growth rate of nanorods during VLS process is derived. The derived formula shows the dependences of growth rate on lateral size of nanorods, concentration and supersaturation of Zn atoms in the liquid droplet. Based on the presented kinetic model the smaller nanorods have faster growth rate. Au-catalyzed ZnO nanorods are grown by chemical vapor transport and condensation (CVTC) process experimentally. Theoretical and experimental rate/radius curves are compared to each other. Theoretical predictions are in good agreement with the experimental results.     

Development of a solvate as an active pharmaceutical ingredient: Developability,crystallisation and isolation challenges

The preclinical development of an active pharmaceutical ingredient (API) begins with the selection of a solid state form. A solvate may be selected for development if it is sufficiently stable and if the solvent quantity administered to the patient is lower than the tolerated potential daily exposure (PDE). The selection and process development of a solvate is presented here. The initial crystallisation process gave poor control over the particle size distribution (PSD) and inclusion of additional crystallisation solvent in the crystal lattice. These two API attributes were controlled using micronised seeds and optimising the crystallisation conditions. After filtration, slurry washing with a second solvent was used to replace the high boiling point crystallisation solvent to improve the drying efficiency. The slurry washing was modelled and studied in the laboratory to control the level of unbound crystallisation solvent in the API. The API desolvation during slurry washing was studied by considering thermodynamics, by construction of the ternary phase diagram, and kinetics aspects. This work provides useful approaches and considerations to assess the risks specific to the controlled production of a solvate that are rarely presented in the literature.     

The effect of the in-situ sublimation in the growth of HgI2 platelets from vapour

The Quality of HgI₂ platelets grown from the vapour phase has been studied, varying different growth parameters, i.e. starting material, addition of polyethylene, source/crystallisation temperature, in-situ sublimation. It has been found that the in-situ sublimation at high temperature is the essential factor for the production of HgI₂ platelets. This in-situ sublimation was made in the same growth ampoule at temperatures over 200 °C and prior to the growth process. All the other growth parameters studied in this work influenced the quality of the platelets although they did not affect their production. Finally, the grown platelets have been characterised by optical observation and by differential scanning calorimetry.     

Crystallisation kinetics,glass forming ability and thermal stability in glassy Se100 − xInx chalcogenide alloys

Differential scanning calorimetry (DSC) studies have been done under non-isothermal conditions at different heating rates for glassy Se_100 ? xIn_x (5 ≤ x ≤ 20) alloys. DSC traces with well-defined endothermic and exothermic troughs and peaks at glass transition (T_g), crystallisation (T_c) and melting (T_m) temperatures were observed. The crystallisation kinetics parameters, Avrami index (n), activation energy for crystallisation (E_c) and frequency factor (K_o), have been calculated on the basis of the classical Johnson–Mehl–Avrami (JMA) model and related methods derived by Kissinger, Augis–Bennett and Mahedevan. Activation energy for glass transformation (E_t) has been evaluated on the usual two different non-isothermal methods developed by Moynihan and Kissinger. An extension of the Augis–Bennett method well known for evaluating E_c to calculate E_t has been explored with satisfactory results. Results obtained from these methods are in close agreement with each other. Close correlation between E_t, E_c and heating rate (β) was observed. The glass forming ability (GFA) and thermal stability parameters have been calculated for each glass system. It was found that the proportion of indium additive changed significantly the values of glass/crystal transformation, GFA and thermal stability of the studied system.     

Verification of an analytical method for measuring crystal nucleation rates in glasses from DTA data

A recently proposed analytical (DTA) method for estimating the nucleation rates in glasses has been evaluated by comparing experimental data with numerically computed nucleation rates for a model lithium disilicate glass. The time and temperature dependent nucleation rates were predicted using the model and compared with those values extracted from an analysis of numerically calculated DTA curves. The validity of the numerical approach was demonstrated earlier by a comparison with experimental data. The excellent agreement between the nucleation rates from the model calculations and the computer generated DTA data demonstrates the validity of the proposed analytical DTA method.     

The relationship between statistical aspects of switching and the structure of chalcogenide glasses

Variation in the switching parameters, threshold voltage and delay time, has been observed for devices based on bulk chalcogenide glass. Experimental analysis revealed that the variation has two main components: (1) slow semi-reversible ageing taking place throughout the life of the device, (2) fast fluctuations occurring from operation to operation. It was further shown that the latter variation is not random but that correlation exists between sequential switching operations. A semi-quantitative theoretical model is presented to explain the observed phenomena in terms of microstructural changes in the glass during switching.     

An analytical model to represent crystallization kinetics in materials with metastable phase formation

The aim of this article is to propose a simple analytical model that can describe the isothermal crystallization process in materials when the formation of a stable crystalline phase is preceded by the formation of a metastable phase. This model explains deviations from the well-known Johnson-Mehl-Avrami-Kolmogorov kinetics theory and predicts the three slopes in Avrami’s plot. The model predictions were compared with experimental results obtained from X-ray measurements in the chalcogenide glasses with composition of Ge₂Sb₂Te₅ (thin films) and in aqueous solutions of methylhydrazine monohydrate during isothermal phase transformations. In order to validate the proposed model to represent experimental results, a computer program was developed. This program uses experimental data from measurements of the total volume fraction at different times during isothermal transformations and fits the model parameters that best represent the kinetic behavior of the system.     

A contribution to the kinetics of crystallisation of GaP by SSD process

The influence of some important factors which appear during the synthesis of GaP by the SSD-Process have been comprehended, and their mathematical relationships determined. The model for the growth of crystallisation is valid only for some definite and selected moments. For long-time experiments the computation of the speed of crystallisation should be carried out step-by-step.