Mathematical modelling of the SSD-process

In order to achieve a better agreement between the calculated and experimental results of crystal production by the SSD-process, it was essential to extend the application of the modell presented earlier (Weinert et al.). The thermal and geometrical conditions, which vary strongly during the course of the process and influence the GaP crystallisation, have never been taken into consideration. It has been attempted, in the present work, to consider these changes by dividing the total time of crystallisation into so small durations (Δt), that the evaluation model presented earlier for instant times can be successfully applied. The results of crystallisation for the total period can then be obtained through a mathematical analysis named as sequence correction of process parameters. It has been shown that an exact knowledge of the temperature distribution in the furnace will yield results which are in very good agreement with the experimental values. Moreover, the changes in the process parameters during the whole time of crystallisation have been represented graphically. — Application of this model to other systems, for example to GaAs, is also possible.     

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 crystallisation of alkaline-earth metal tungstates (molybdates,chromates, and sulphates) from metal chloride melts

This paper presents studies on the crystallisation of alkaline-earth metal tungstates, molybdates, chromates and sulphates by slow cooling of solutions in lithium chloride and alkaline-earth metal chloride melts at 600° to 1100°C. Solubility — temperature diagrams were prepared for this temperature range. The effects of solute — solvent interaction, crystallisation temperature range and rate of cooling on crystal form and size were investigated. Final crystal size increases with reduced rate of cooling and with increasing crystallisation temperature; barium sulphate crystallisation from lithium chloride melt is anomalous.     

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.     

Growth and Properties of Potassium Holmium Double Tungstate KHo(WO4)2

Potassium holmium tungstate KHo(WO₄)₂ crystal, as other tungstates, shows the high temperature irreversible structural phase transition. Owing to this, KHo(WO₄)₂ single crystals were grown due to spontaneous crystallisation with use of the High Temperature Solution Growth technique, which allows to lower the temperature of crystallisation below the temperature of the phase transition. K₂W₂O₇ was used as a solvent. It provides a very wide temperature range of crystallisation and does not introduce additional impurities into the melt. The starting flux contained 20 mol% of KHo(WO₄)₂ dissolved in K₂W₂O₇. It was found that potassium holmium double tungstate is pleochroic. The two different optical spectra: one spectrum for electrical vector of linearly polarised light parallel to optical Y axis (main spectrum) and second one for electrical vector perpendicular to Y axis were measured.     

Bulk crystallisation of (00l) oriented fresnoite Sr2TiSi2O8 in glass-ceramics of the Sr-Ti-Si-K-B-O system

This paper shows that glass-ceramics containing highly surface and bulk preferentially oriented fresnoite Sr₂TiSi₂O₈ crystals can be synthesised by a simple isothermal heat treatment of suitable glass compositions in the Sr-Ti-Si-K-B-O system. For all tested compositions, crystallisation starts from the free surfaces of the specimens and propagates to bulk with time. If most of these compositions lead to (00l) preferential orientation at the specimens' surfaces, bulk crystal texture is very composition dependent. The effects of variation in K₂O and B₂O₃ contents on the crystallisation have been studied. It is shown that low K₂O and high B₂O₃ contents are required to keep the (00l) orientation from the surface into the bulk. This result seems to be explained by the viscosities of the initial and residual glasses at the temperature of crystallisation: a low viscosity leads to a fine and homogeneous microstructure with small and strongly (00l) bulk oriented crystals.     

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.     

Supersaturation patterns in counter-diffusion crystallisation methods followed by Mach–Zehnder interferometry

We present experimental observation of the spatio-temporal pattern of supersaturation in counter-diffusion methods. These complex patterns were recorded by dynamical interferometric analysis using a Mach–Zehnder configuration. Tetragonal hen egg white lysozyme crystals were grown inside APCF (advanced protein crystallisation facility) reactors. Salt and protein diffusion profiles were obtained independently by performing duplicated experiments with and without protein in the protein chamber; salt gradients were observed directly while protein concentration profiles are computed from the differences in refractive index between the two experiments. As expected from computer simulations, the time evolution of supersaturation shows a maximum about 45 h after activation (although this value can change as a function of the starting conditions and the geometry of the reactor). Nucleation takes place before this maximum supersaturation is reached. This explains the trend of the growth rate versus time curves for experiments performed within APCF reactors (both on ground and in space) and in capillaries by the gel acupuncture technique. By using very low concentration agarose gel in the protein chamber, sedimentation and buoyancy effects are eliminated so that the effects of gravity on fluid dynamics and hence on the spatio-temporal evolution of supersaturation can be assessed. These results confirm experimentally the predicted behaviour of counter-diffusion systems and support their use in growing large high-quality protein single crystals.     

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.     

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.     

Preparation and some properties of synthetic proustite single crystals

Conditions for the preparation of proustite single crystals are reported. For selecting these conditions temperature gradients in the crystallisation zone and in the melt, the rate of moving of the crystallisation front, the radial gradient, tube geometry, stabilisation of temperature, mechanisms of zone travelling, partial pressures were changed. – Differential-thermal, X-ray, and spectral-chemical analysis were applied to initial substances and final crystal bodies. To decrease the influence of spontaneous crystallisation an optimal temperature gradient was applied approaching maximum undercooling at the liquid-solid interface. – Optically transparent proustite crystals resulted. In the range from 1 to 12 μm they show 80% transparency. Microhardness was measured along the growth direction which deviated from the c-axis about 25°.     

The crystallisation of alkaline-earth metal oxides from metal chloride melts: Solubility-temperature phase diagram analyses and preliminary experimental studies

The solubility v temperature phase diagrams for magnesium, calcium, strontium and barium oxide solutions, in lithium, sodium and potassium chloride melts and in the alkaline earth metal chloride melts, have been analysed. The solutions in the alkali metal chlorides are pseudo-binary reciprocal ternary mixtures; the more soluble barium and strontium oxides showed small deviations, calcium oxide showed larger deviations while the extremely sparingly-soluble magnesium oxide showed extensive deviations from ideality. These deviations were related to electrostatic interactions in solution, that depended in turn on some function of reciprocal solute and solvent caiton radii. The solutions in the alkalineearth metal chlorides are binary mixtures with MO · 4 MCl₂ solvate formation. — Some preliminary crystallisation experiments were carried out, by slow cooling of saturated solutions in the metal chloride melts: calcium and strontium oxide crystallisation from lithium chloride melts and barium oxide crystallisation from all three alkali metal chloride melts would be worth further investigation.     

Kinetics of crystal growth of strontium tungstate from solutions in sodium tungstate melts by continuous cooling

The crystallisation kinetics of strontium tungstate from unstirred saturated solutions in sodium tungstate melts was studied by continuous cooling from initial crystallisation temperatures T₀ = 1000° to 800°C to room temperature at cooling rates R_T = 0.67° to 3.3°C min⁻¹. The main crystal growth was diffusion rate-controlled; the final crystal growth was rate-controlled by the development rate of excess solute concentration. The estimated diffusion rate constant (k_D) values increased with cooling rates and initial crystallisation temperatures. They are higher than the rate constants for diffusion-controlled growth of calcium tungstate from sodium tungstate melts, but very much smaller than those for strontium tungstate from lithium chloride melts.     

Influence of solution constituents, solution conditioning and seeding on the crystalline phase of aluminium hydroxide using in situ X-ray diffraction

Filtering, drying and aging of crystalline solids can affect crystalline phase(s) and therefore ex situ X-ray diffraction is not necessarily indicative of the in situ crystalline components. This paper examines some of the factors affecting the crystallised phase of aluminium hydroxides in highly caustic solutions. Caustic aluminate solutions were prepared using several different methodologies. Where solutions were prepared from aluminium metal, gibbsite and bayerite were observed to be the crystallisation products. Where gibbsite was used as the aluminium source in the liquors, the crystallised phase was found to be a function of solution conditioning. Solutions prepared at 100°C and at atmospheric pressure crystallised to form only gibbsite. These same solutions subsequently heated to 160°C for 16 h crystallised as gibbsite and bayerite. It has been concluded from these results that the caustic aluminate solutions made using gibbsite were not dissolved on the molecular scale (although optically clear) if the solutions were heated to only 100°C. Further heating at elevated temperatures completed the dissolution process so that the species in solution were similar to those found in solutions made from aluminium metal. Solutions seeded with either bayerite or gibbsite crystallised to form only gibbsite. Only crystallisation in the bulk solution and not on the seed surfaces was recorded. In some cases seeding altered the expected crystallisation products, i.e. from gibbsite and bayerite to only gibbsite.     

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.     

Effect of V2O5 addition on the crystallisation of glasses belonging to the CaO–ZrO2–SiO2 system

The crystallisation of CaO–ZrO₂–SiO₂ glasses doped with V₂O₅ (0.1–5 mol%) has been investigated in terms of microstructure and thermal parameters. Results indicate that crystallisation is predominantly controlled by a surface nucleation mechanism, even though a partial bulk nucleation has been encountered in compositions containing more than 2 mol% of doping oxide. As detected from differential thermal analysis curves, glass transition temperature and crystallisation temperature, are strongly dependent upon V₂O₅ content varying from 0.0 to 2.0 mol%, while the crystallisation activation energy values decrease with a parabolic trend from B-glass (0.0 mol% V₂O₅ content, 495±7) to V-0.7 (0.7 mol% V₂O₅ content, 420±6) composition, increasing again to 442±5 kJ/mol K with higher amount of V₂O₅. The microstructure of the glass-ceramic materials clearly showed a marked dependence upon the amount of V₂O₅, also due to the presence of phase separation for content higher than 0.7 mol%. Wollastonite, CaO·SiO₂, and a calcia–zirconia–silicate, 2CaO·4SiO₂·ZrO₂, are the main crystalline phases whose ratio slightly varies with vanadium oxide content. The glass ceramics obtained from the studied materials are greenish and bluish coloured, so it is possible to use the studied glasses as coloured frits for tile glazes.     

Uncertainties in crystallization of hen‐egg white lysozyme: reproducibility issue

The reproducibility of biomacromolecular crystallization (tetragonal and orthorhombic lysozyme crystals) was studied by monitoring the evolution of protein concentration during the crystallization process using Mach‐Zehnder interferometer. It was found that formation of both tetragonal and orthorhombic crystals exhibited poor reproducibility. When the crystallization occurred under isothermal conditions, the protein concentration in the solution varied differently in different experiments under identical conditions (for both types of crystals). Moreover, in the case of orthorhombic lysozyme crystallization (under either isothermal or thermal gradient conditions), it is clear that the crystals could not be always readily formed. When formation of tetragonal lysozyme crystals was conducted at a temperature gradient condition, however, the evolution of concentration was reproducible. The phenomena found in this study revealed that biomacromolecular crystallization can be uncertain, which is probably caused by the process of nucleation. Such uncertainties will be harmful for the efforts of screening crystallization conditions for biomacromolecules. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Protein and solvent dynamics as studied by QENS and dielectric spectroscopy

We have investigated the dynamics of a protein (hemoglobin) in three different solvents by broadband dielectric spectroscopy and quasi-elastic neutron scattering (QENS). The solvents used were water, glycerol and methanol. From the dielectric measurements we were able to extract four relaxation processes, where the fastest process is due to solvent dynamics, and the three slower processes arise from protein motions of a different nature, and hence, visible on different time and temperature scales. The results from the mean square displacement (MSD) obtained by quasi-elastic neutron scattering indicate that the fast and local protein motions are strongly related (slaved) by the fastest and most local solvent motions in the case of water and glycerol. In contrast, for methanol we found the low temperature dynamics are dominated by the CH₃ group rotation, which does not promote any protein dynamics.     

Evaluation of degree of crystallization by optical microscopy and chemical analysis in crystallization of alkaline-earth metal tungstates from solutions in lithium chloride melts

A comparative study of the accuracy of optical microscopy and chemical analysis of residual solutions for evaluation of degree of crystallisation was carried out to ascertain their suitability for kinetics study of CaWO₄ and BaWO₄ crystallisation from LiCl melts (i) by continuous cooling at a constant cooling rate, and (ii) at constant temperature from a supersaturated solution. Chemical analysis of residual solution does not give desirable accuracy for the case (i) for α_t values <0.30, and for the case (ii) for α_t values <0.60. Optical microscopy was more accurate and suitable for both cases.