Induction time for crystal growth

An expression is derived for the induction time for crystal growth. It is shown that this induction time is not uniquely determined, and is dependent on experimental conditions. Induction time for crystal growth, unlike the induction time for nucleation, becomes unbounded if defined rigorously.     

Induction time in crystallization of gas hydrates

The kinetics of the initial stage of crystallization of one-component gas hydrates in aqueous solutions are analyzed. The temporal evolution of the volume of hydrate crystallized and the moles of gas consumed are determined. Expressions are derived for the supersaturation dependence of the hydrate crystallite growth rate and the induction time in hydrate crystallization. These expressions are used for revealing how additives in the solution that act as kinetic inhibitors of hydrate crystallization can affect the induction time of the process. The results obtained are applied to crystallization of methane, ethane and cyclopropane hydrates.     

Kinetic of potash alum crystallisation

Metastable zone width of potash alum in aqueous solutions has been measured as function of the cooling rate in absence as well as in presence of seed crystals. From these data, the effective nucleation rate was calculated. Growth rate of potash alum crystals has been measured in a fluidized bed. Overall growth rate coefficient, k_G, was then used for determination of the mass transfer coefficient, k_D, and the rate constant of the intergration step k_r. The dependence of k_D on hydrodynamic conditions is discussed.     

Effects of LiPO3 glass crystallisation

The LiPO₃ glass crystallisation has been investigated with calorimetry, scanning electron microscopy, optical microscopy and X-ray powder diffraction. It was discovered that the crystallisation at a given temperature depends on the thermal prehistory of the sample. It is shown that the cooled samples can change over the course of several hours. From the microphotographs, it is clear that the surface crystallisation mechanism is predominant for this glass. The velocities of the crystallisation front expansion for 425, 440, 460 °C are 4.9, 18.6 and 34.5 μm/min, respectively.     

The induction time,interfacial energy and growth mechanism of maltitol in batch cooling crystallization

Maltitol is crystallized with seeds by cooling mode in industry, often with large amount of fine crystals and wide crystal size distribution. To eliminate the fine nucleation, it's necessary to understand the nucleation kinetics. In this work, the solubility of maltitol in water was measured by the gravimetric method, the nucleation kinetics of maltitol in batch cooling crystallization was investigated using focus beam reflectance measurement (FBRM), and a novel method was proposed to determine the induction time from the trend of the crystal median chord given by FBRM. Based on the relationship between the induction time and the supersaturation, the nucleation mechanism was obtained, including homogenous nucleation at high supersaturation and heterogenous nucleation at low supersaturation. Additionally, combining the classical nucleation theory (CNT) and Arrhenius’ principle, the crystal‐solution interfacial energy and the energy barrier of homogenous nucleation were calculated. From the scanning electron microscope (SEM) images, the growth mechanism of maltitol was identified as surface nucleation growth and the surface entropy factor calculated from the kinetic analyses of t_ind data corroborated this growth mechanism.     

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)     

Induction time of silver nanoparticles precipitation: Experiment and modeling

This paper describes the measurement of induction time in precipitation of silver nanoparticles at different temperatures and supersaturations, and models it with Smoluchowski's coagulation theory. Silver nanoparticles are synthesized by reaction of silver nitrate with hydrazine in the presence of sodium citrate as stabilizer. The rate of association between clusters is found to depend on temperature and their sizes. The activation energy for the association between two clusters and interfacial tension of silver nanoparticles were also estimated. The results also show that induction time decreases with increasing supersaturation and temperature. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Role of pore structure in salt crystallisation in unsaturated porous stone

Laboratory driven crystallisation of sodium sulphate and sodium chloride from concentrated solution in unsaturated porous stones has been performed. This contributes to a better understanding of the mechanisms by which salts crystallise and as a consequence limit the durability of porous materials which has an impact on buildings, civil constructions, and historical monuments. The identification of minerals in porous materials has been performed by scanning electron microscopy (SEM), Environmental Scanning Electron Microscopy (ESEM) and sequential profiles of X-ray diffraction (XRD) under temperature control of sample. The study of porous stones has been combined with experiments in capillary tubes. Data from SEM show that halite tends to precipitate on the surface of the stone with a similar distribution in all samples. However, the mirabilite–thenardite precipitation takes place preferably inside the stone and its depth from the surface and its relative concentration depends on the pore size distribution. In addition, mirabilite (Na₂SO₄·10H₂O) crystallises homogeneously, whereas thenardite (Na₂SO₄) and halite (NaCl) tend to nucleate heterogeneously. To explain the precipitation sequence from concentrated solutions in unsaturated porous materials, a detailed analysis of the thermodynamic equations has been carried out by establishing a simple model. The proposed model shows the influence of the pore structure both on the water activity and saturation degree of involved salts.     

Minerals successions crystallisation related to tunisian natural brines

Natural brines sampled from Sebkhats in southern part of Tunisia are considered to be seawater‐type solutions. The equilibrium solubility of this kind of solutions might be described by the fivefold seawatertype system Na⁺, K⁺, Mg²⁺, Cl^‐, SO₄^2‐ // H₂O. The crystallisation sequences of salts, observed under solar evaporation, of two different Tunisians brines is discussed. Very important differences between the foreseeable results, based on the Equilibrium Solubility Diagram at 25 °C, and the experimental ones are settled. An attempt to explain the differences, based on the so‐called “solar sequences” as well as the “solar diagram” of evaporation, is made. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interactions in protein solutions near crystallisation: a colloid physics approach

I present a review of current ideas from colloid physics which might be relevant in order to understand the onset of crystallisation and amorphous aggregation processes in protein solution. In particular, the inadequacy of DLVO theory to account for all phenomenological aspects of crystallisation, such as salt-specificity, and for the basic features of the phase diagram, such as the presence of a metastable fluid–fluid separation, is discussed. The fundamental role of additional short-range attractive forces, microscopically orginating from the salting-out effect, is conversely stressed. In order to establish a simple model of protein interparticle interactions near crystallisation, I discuss some recent results obtained by our group for the osmotic compressibility of the metastable fluid phase of hen egg-white lysozyme. Light scattering measurements were performed in an extended volume fraction range at pH=4.7 as a function of temperature, adding NaC1 to screen the electrostatic interactions. The experimental compressibility up to particle volume fractions Φ≈0.23 is very successfully compared to the theoretical expression for a model of adhesive (“sticky”) hard spheres. This surprising quantitative agreement, obtained using a very simple form for the effective interparticle force, suggests that the thermodynamics of the system in the fluid phase is mainly determined by the very short-range nature of the interactions, and is rather insensitive to the detailed form of the potential.     

The dissolution and crystallisation of amphoteric metal hydroxides from sodium hydroxide solutions: Ionic equilibria,crystalline phases and crystallisation mechanisms

The dissolution and recrystallisation of beryllium, zinc, cadmium and tin (II) hydroxides and chromium (III), iron(III), aluminium, scandium, yttrium, gallium and indium hydroxides, from sodium hydroxide solutions of concentrations C = 1 to 20 M at ambient temperatures, are surveyed. The different inic equilibria in metal hydroxide-sodium hydroxide systems are examined: the phases crystallising from different sodium hydroxide solutions are tabulated and crystallisation mechanisms are analysed.     

Influence of additives on periodic crystallisation in Gel(I). theory

A quantitative explanation is given for the influence of additives on periodic crystallisation in gel. The theory involves the diffusion of the outer, inner and the additive electrolytes. It is assumed that precipitation begins when the product of the concentrations of the reactants reaches a critical value. Expressions are found for the velocity constant and spacing coefficient incorporating the valency and concentration of the additive.     

The crystallisation of alkaline-earth metal tungstates from sodium tungstate melts

This paper presents studies on the crystallisation of alkaline-earth metal tungstates by slow cooling of saturated solutions in sodium tungstate melts at 700 to 1000 °C. Solubility-temperature diagrams were prepared for this temperature range. The effects of variation in the initial crystallisation temperature, cooling rate and metal salt structure on crystal number and size were investigated. Final crystal lengths increased with increase in the initial crystallisation temperature and decreased with increasing rate of cooling. Crystals grown from sodium tungstate melts at any temperature were generally smaller than those grown from lithium chloride melts (at the same temperature): they were similar in size to crystals grown from the metal chloride melts but crystallised at temperatures 150 ° to 250 °C lower.     

Oxynitride glasses, their properties and crystallisation - a review

Oxynitride glasses were first discovered as intergranular phases in silicon nitride based ceramics in which the composition and volume fraction of such oxynitride glass phases determine the properties of the material. In particular they have been shown to control high temperature mechanical properties. The desire to understand the nature of these grain boundary phases has resulted in a number of investigations on oxynitride glass formation and properties which have shown oxynitride glasses to possess refractory behavior and higher, elastic modulus, viscosity and hardness compared to the corresponding oxide glasses. This paper provides a review of the preparation and characterisation of oxynitride glasses and outlines the effect of composition, especially nitrogen content, on properties such as glass transition temperature, hardness, Young’s modulus and viscosity.     

Mechanisms controlling primary crystallisation of Ga20Te80 glasses

The kinetic study of the crystallisation process of Ga₂₀Te₈₀ glass from isothermal and continuous heating calorimetric data have been performed applying a recently developed procedure. The kinetic information was complemented with X-ray diffraction measurements. With this scope, three crystallisation patterns, with three-dimensional isotropic growth have been analysed: (i) site saturation and interface controlled growth. (ii) homogeneous nucleation with interface controlled growth and (iii) homogeneous nucleation with two simultaneous modes of crystal growth (interface- and diffusion-controlled). A complex model with two simultaneous modes of three-dimensional isotropic crystal growth with decreasing homogeneous nucleation and soft impingement has been applied for modelling primary crystallisation of the Ga₂₀Te₈₀ glass. The model goes beyond the isokinetic hypothesis when coupling isothermal and continuous heating kinetic data. The apparent activation energy E_a = (2.06 ± 0.03) eV/at obtained for the primary crystallisation of the phase Te is shown to correspond to an activation energy for nucleation E_I = (2.85 ± 0.03) eV/at and an interface controlled activation energy for growth E_u = (1.90 ± 0.03) eV/at at the crystallisation onset.     

Investigations on the crystallisation of potassium molybdenum bronzes from flux melts

Results are presented to identify the fields of primary crystallisation of red and blue potassium molybdenum oxide bronzes K_0.30MoO₃ and K_0.33MoO₃ in the ternary system K₂MoO₄–MoO₃–MoO₂. Starting from crystal growth experiments for the preparation of bronze crystals by electrolytic reduction the binary marginal systems K₂MoO₄–MoO₃ as well as MoO₃–MoO₂ and further pseudo‐binary sections have been investigated by differential thermo‐analysis, hot‐stage microscopy, and by quenching experiments under inert gas. We succeeded in determining phase transition temperatures in the binary section Mo₄O₁₁–K₂Mo₂O₇. Temperature and composition ranges have been found in this section to crystallise red and blue potassium molybdenum oxide bronzes. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Periodic crystallisation of magnesium hydroxide: effect of additives and gel

Effect of additives on the periodic crystallisation of magnesium hydroxide is investigated. The dependence of the concentration ageing and pH value of the gel on periodic crystallisation of magnesium hydroxide is also investigated. Velocity constant, spacing coefficient, and the flocculation value are reported. The experimental observations have been accounted.     

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.