The melt temperature change influence on the crystallization rate in czochralski growth system

This paper opens a series of publications about growth system parameters change influence on the crystallization rate. The influence of crucible melt temperature fluctuations and mechanical instability will be investigated. In approximation of one-dimensional heat transfer the behaviour of crystallization rate in case of crucible melt temperature small change is investigated in this paper. As an example characteristic time values and system sensitivity are given for fluorite and silicon crystals.     

The effect of mechanical instability on crystallization rate in czochralski growth system

The effect of mutual displacement of crucible and crystal or melt level change on crystallization rate is described in one-dimensional heat-transfer approximation. It is found that Czochralski growth system is very sensitive to mechanical instability and crystallization rate follows the jitter pattern. As an example crystallization rate behaviour is examined for fluorite and silicon crystal growth.     

Influence of crystallization conditions on the mechanism and rate of crystal growth of potassium sulphate

Growth rate of potassium sulfate crystals was studied in a fluidized bed crystallizer. Higher growth rates were observed at larger bed heights. Larger crystals grow faster than smaller size crystals due to the changed fluid dynamics. The growth rate was found to be very sensitive to the pH value of the solution. The growth rate increases with increasing the pH value and the increase of growth in the acidic medium is faster than in the basic medium. The presence of small amounts of Cr³⁺ ions reduces the growth rate of potassium sulfate dramatically. The presence of Cr³⁺ ions lowers the saturation temperature and increases the width of the metastable zone, i.e. shifts the metastability of the solution to be at lower level of supersaturation.     

The estimation of crystallization kinetics from linear in n(L) versus L steady-state data including growth rate dispersion

A discussion of modelling of nucleation and crystal growth kinetics is presented for those mixedsuspension, mixed product removal (MSMPR) crystallizer data available in the literature, for which log population density data appears to be a linear function of crystal size. The modelling crystallization kinetics is done twice – once assuming that the system is obeying McCabe's Δ law, and again when the crystals exhibit growth rate dispersion (GRD). In the latter case the gamma, inverse gamma, log-normal, beta, Fisher, sum of two gammas, sum of two inverse gammas, sum of two log-normal, and sum of two constant rates of growth rate dispersion models are used for crystal growth rate estimation. Finally, McCabe's and GRD predictions are compared with the size-dependent growth rate estimations.     

Differential thermal analysis studies on the crystallization of strontium tungstate melts. Variation of rate constants with crystallization temperatures and cooling rates

Kinetics of strontium tungstate crystallization from sodium tungstate melts were studied in platinum crucibles (by DTA) by continuous cooling from initial crystallization temperatures T₀ = 800° to 1000° to below the eutectic temperature at cooling rates R_T = 0.67° to 3.3° min⁻¹. Heterogeneous nuclei first formed slowly onto metal platinate particles within the solution during induction periods (t ); the main crystal growth then started after the development of some exces solute concentration (ΔC ) at the induction temperature (T ). The actual growth after t was diffusion rate-controlled. The diffusion rate-constants (k_Dt) for growth after the induction periods along the major axis were estimated; the increased with T₀ and R_T. These values were higher than those for diffusion-controlled crystal growth of strontium tungstate from sodium tungstate melts in alumina crucibles but much smaller than the real diffusion rate-constants (k_Dl)_real.     

Aligned crystallization in glasses: An analysis of heat transport and interface kinetics

An analysis of heat flow effects which are significant in the development of aligned microstructures in thermally crystallizable glasses is presented. Microstructures developed by heat treatment of a representative glass composition in the CdGeAs system have been interpreted on the basis of a heat flow analysis model developed in this work. The utility and limitations of the current analysis in problems related to interfacial kinetics and microstructure evolution in directionally crystallized glasses are discussed.     

On the dependence of the critical crystallization rate on the initial impurity concentration in melt

The dependence of the critical crystallization rate on the initial impurity concentration in melt is derived by determining the condition at which a nonplanar solution to the stationary diffusion problem arises. It is suggested that the conditions at which defects arise at the interface differ from those obtained when crystallization becomes stationary. The initial transient process of binary melt solidification under crystal pulling at a constant rate has been studied numerically within a 1D model. It is shown that the character of the time dependence of the crystallization rate is determined by the ratio of the crystal pulling rate to solidification rate V _c, when a constitutional supercooling zone is formed in the melt.     

Influence of emulsion types on nucleation kinetics and growth habit in the cooling crystallization

Experiments on unseeded batch cooling crystallization were made to investigate the influence of emulsion [solution in non‐solvent (S/NS) emulsion and non‐solvent in solution (NS/S) emulsion] on crystal size and growth habit of various materials such as hexahydro‐1,3,5‐trinitro‐1,3,5‐triazine, ammonium sulfate, potassium dihydrogen phosphate (KDP), and γ‐glycine. Size of crystals obtained from the S/NS emulsions was found to be significantly larger than that obtained from the NS/S emulsions. Those results were explained by broad induction time distribution of nucleation in the isolated solution droplets and subsequent seeding effect by free movement of early‐induced crystals by vigorous agitation. As a result, the population density of crystals was shown to be smaller in the S/NS emulsions than that in the NS/S emulsions. In the S/NS emulsions, desupersaturation rate should be slow and high supersaturation is subsequently generated during crystal growth stage. Therefore, it may be concluded that crystal morphology of the materials with supersaturation dependent growth habit, such as ammonium sulfate, KDP and γ‐glycine, can be controlled by selection of emulsion type.     

An overview of gallium nitride growth chemistry and its effect on reactor design: Application to a planetary radial-flow CVD system

In this paper, gallium nitride (GaN) growth chemistry is characterized by two competing reaction pathways. An overview of GaN gas-phase and surface-phase chemistry is used to generate a comprehensive model for epitaxial GaN growth from the commonly used precursors, trimethylgallium ((CH₃)₃Ga) and ammonia (NH₃). The role of reactor geometry in controlling the selectivity among the competing reaction pathways is explored in the context of a planetary radial-flow CVD system. Finally, application of a geometrically based uniformity criterion is presented for film uniformity optimization.     

Kinetic studies on the influence of temperature and growth rate history on crystal growth

Crystallization experiments of sucrose were performed in a batch crystallizer to study the effect of temperature and growth rate history on the crystal growth kinetics. In one of the growth methods adopted, the isothermal volumetric growth rate (R_V) is determined as a function of supersaturation (S) at 35, 40 and 45 ºC. In the other, crystals are allowed to grow at constant supersaturation by automatically controlling the solution temperature as the solute concentration decreased. Using the latter method R_V is calculated as the solution is cooled. The obtained results are interpreted using empirical, engineering and fundamental perspectives of crystal growth. Firstly, the overall activation energy (E_A) is determined from the empirical growth constants obtained in the isothermal method. The concept of falsified kinetics, widely used in chemical reaction engineering, is then extended to the crystal growth of sucrose in order to estimate the true activation energy (E_T) from the diffusion‐affected constant, E_A. The differences found in the isothermal and constant supersaturation methods are explained from the viewpoint of the spiral nucleation mechanism, taking into account different crystal surface properties caused by the growth rate history in each method. Finally, the crystal growth curve obtained in the batch crystallizer at 40 ºC is compared with the one obtained in a fluidized bed crystallizer at the same temperature. Apparently divergent results are explained by the effects of crystal size, hydrodynamic conditions and growth rate history on the crystallization kinetics of sucrose. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of the rate of supersaturation generation on polymorphic crystallization of m-hydroxybenzoic acid and o-aminobenzoic acid

Effects of the rate of supersaturation generation on polymorphic crystallization have been investigated through evaporation and cooling crystallization experiments of m-hydroxybenzoic acid (m-HBA) in methanol, acetone and ethyl acetate, and o-aminobenzoic acid (o-ABA) in ethanol. The rate of supersaturation generation has been altered by systematically changing either the cooling rate or the evaporation rate of solvent using a jacketed crystallizer and a microfluidic evaporation device, respectively. The results have revealed that the rate of supersaturation generation and the tendency of the formation of the less stable polymorph are positively correlated. Kinetic effects are dominant when the rate of supersaturation generation is high, thereby producing the metastable polymorphs (orthorhombic m-HBA; Form II of o-ABA); on the contrary, more stable polymorphs (monoclinic m-HBA; Forms III and I of o-ABA) are formed when the rate of supersaturation generation is low and the thermodynamic effects are prevailing.     

Measurement and analysis of the dextran partition coefficient in sucrose crystallization

The effect of crystallization conditions on the dextran partition coefficient between impure syrup and sugar crystal has been investigated in a batch crystallizer. The crystallizer is operated isothermally at temperatures of 30, 40, and 50 °C, at constant relative supersaturations of 0.05, 0.07, and 0.09, and with mother liquor dextran concentrations of 1000 and 2000 ppm/Brix. The dextran content has been determined by the CSR method. A 1:1 mass ratio of high-fraction dextran (approximately 250,000 Da) and low-fraction dextran (60,000-90,000 Da) is used to represent a wide range of dextran contamination. It is seen that the dextran partition coefficient in sucrose crystallization increases with both increasing supersaturation and increasing crystallization temperature. However it appears that these are secondary effects, with the partition coefficient strongly correlating with crystal growth rate alone, despite the regressed data having large variations in temperature, mother liquor dextran content, and supersaturation. Dextran incorporation into the sugar crystal results from both dextran adsorption onto the crystal surface and mother liquor inclusions. The explanation for the variation in the dextran content in sugar crystal with respect to the growth rate is due to increased adsorption due to the higher surface roughness of crystals grown at high growth rates. Although the dextran concentration in the solution affects the dextran content in the crystal, it does not strongly affect the dextran partition coefficient.     

Determination of kinetic parameters of crystal growth rate of borax in aqueous solution by using the rotating disc technique

Growth rate of polycrystalline disc of borax compressed at different pressure and rotated at various speed has been measured in a rotating disc crystallizer under well-defined conditions of supersaturation. It was found that the mass transfer coefficient, K, increased while overall growth rate constant, K_g, and surface reaction constant, k_r, decreased with increasing smoothness of the disc. It was also determined that kinetic parameters (k_r,r,K,g) of crystal growth rate of borax decreased with increasing rotating speed of the polycrystalline disc. The effectiveness factor was calculated from the growth rate data to evaluate the relative magnitude of the steps in series bulk diffusion through the mass transfer boundary layer and the surface integration. At low rotating speed of disc, the crystal growth rate of borax is mainly controlled by integration. However, both diffusion and integration steps affect the growth rate of borax at higher rotating speed of polycrystalline disc.     

Study of the effect of crystallization parameters on gaseous inclusions in sapphire ribbons grown by the Stepanov method

Crystallography Reports - The effect of growth parameters on the two main types of gaseous inclusions in sapphire ribbons—bubbles in the crystal bulk and near-surface pores—have been...     

Effect of process parameters on crystal size and morphology of lactose in ultrasound‐assisted crystallization

α‐lactose monohydrate is widely used as a pharmaceutical excipient. Drug delivery system requires the excipient to be of narrow particle size distribution with regular particle shape. Application of ultrasound is known to increase or decrease the growth rate of certain crystal faces and controls the crystal size distribution. In the present paper, effect of process parameters such as sonication time, anti‐solvent concentration, initial lactose concentration and initial pH of sample on lactose crystal size, shape and thermal transition temperature was studied. The parameters were set according to the L₉‐orthogonal array method at three levels and recovered lactose from whey by sonocrystallization. The recovered lactose was analyzed by particle size analyzer, scanning electron microscopy and differential scanning calorimeter. It was found that the morphology of lactose crystal was rod/needle like shape. Crystal size distribution of lactose was observed to be influenced by different process parameters. From the results of analysis of variance, the sonication time interval was found to be the most significant parameter affecting the volume median diameter of lactose with the highest percentage contribution (74.28%) among other parameters. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of addition of 5 at% sulphur or tellurium to selenium on its electrical properties and on its rate of crystallization

The characteristic properties of selenium: density d, logarithm of electrical conductivity logσ, and the activation energy ΔE_g with addition of 5 at% sulphur and tellurium was measured for the glassy state and for the crystalline state. The process of transition of the amorphous into crystalline selenium was followed by measuring these quantities for all intermediate stages. Both S and Te decrease the rate of crystallization of selenium. In the crystalline state, the presence of S and Te increases the energy of activation of the conductivity process.     

The impact of pressure and temperature on growth rate and layer uniformity in the sublimation growth of AlN crystals

To effectively design a large furnace for producing large-size AlN crystals, a fully coupled compressible flow solver was developed to study the sublimation and mass transport processes in AlN crystal growth. Compressible effect, buoyancy effects, flow coupling between aluminum gas and nitrogen gas, and Stefan effect are included. Two sets of experimental data were used to validate the present solver. Simulation results showed that the distributions of Al and N₂ partial pressures are opposite along the axial direction due to constant total pressure and Stefan effect, with the Al and nitrogen partial pressures being highest at the source and seed crystals positions, respectively. The distributions of species inside the growth chamber are obviously two-dimensional, which can curve a flat crystal surface. Simulation results also showed that AlN crystal growth rate can be increased by reducing total pressure or by increasing seed temperature or by increasing source-seed temperature difference. High nitrogen pressure causes decrease in growth rate, but it is beneficial for obtaining uniform growth rate in the radial direction. Results of simulation also showed that there is an optimized temperature difference (40 °C) in the present furnace for obtaining good homogeneity of growth rate.