Calculation of the Suspension Volume of Crystallizers with Non-ideally Mixed Suspension

For the calculation of the suspension volume of crystallizers with non-ideally mixed suspension the material balance was derived. The model of complete segregation and the cell modell were used to describe the micro-mixing of solid phase. Testing was carried out in a laboratory crystallizer. The residence time distribution and the weight increase of the crystals were measured. The results showed that the model of complete segregation is suitable for describing the flow behaviour of the solid phase in crystallizers.     

Monte Carlo Simulation of Transient Crystal Size Distribution in a Continuous Crystallizer Using the ASL Model

A Monte Carlo simulation scheme is proposed for transient crystal size distribution in a continuous crystallizer to account for size-dependent growth rate. Crystal growth rates are described by Abegg , Stevens and Larson (ASL) model. The proposed model is used to predict the transient and steady state crystal size distribution from potassium carbonate crystallizer. The agreement between theory and available data confirms the validity of the model.     

Continuous reaction crystallization of struvite from phosphate(V) solutions containing calcium ions

Continuous reaction crystallization of struvite from water solutions containing phosphate(V) (1.0 mass%) and calcium ions (from 0.01 to 0.20 mass%) was investigated. Process was carried out in temperature 298 K in continuous DT MSMPR type crystallizer with internal circulation of suspension. Influence of pH (from 9 to 11) and mean residence time of suspension in crystallizer (from 900 to 3600 s) on product crystal size distribution, mean size, population homogeneity and shape of crystals, as well as chemical composition of solid phase was tested. Within the investigated process parameter ranges struvite crystals of mean size from 18 to ca. 50 μm were produced. With the increase in calcium ions concentration in a feed mean crystal size decreased from 34.2 to 18.4 μm (pH 9, τ 900 s). Coexistence of struvite and hydroxyapatite crystals in the solid product was confirmed analytically (Ca content in solid product from 0.3 to 8.4 mass%). Presence of calcium ions favoured crystallization of struvite in a form of tubular crystals, characterized by lengthwise cracks and irregular edges. Co–precipitated hydroxyapatite particles showed relatively small sizes, even below 1 μm, forming agglomerates on the surface of larger struvite crystals and individual agglomerates. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Graphical Representation of Various Models for Crystal Size Distribution in Continuous Flow Crystallizers

Plots of crystal size distribution of the following crystallizer models are compared: an ideal continuous-flow MSMPR (mixed suspension, mixed product removal) crystallizer with a zero as well as non-zero initial crystal size, an MSMPR crystallizer with size dependent growth of crystals, an MSMPR crystallizer with missing fines, an MSMPR crystallizer with agglomerative growth, and a series of MSMPR crystallizers simulating a crystallizer with nonideal agitation. The shape of the individual size distribution curves can serve as a diagnostic criterion in determination of the most probable model of crystallization.     

ASL model for prediction of CSD in a continuous crystallizer

A Monte Carlo simulation scheme is proposed for crystal size distribution (CSD) in a continuous crystallizer for size dependent growth rate. Crystal growth rates are described by Abegg, Stevens, and Larson (ASL) model. The proposed model is used to predict CSD from potassium carbonate crystallizer. The agreement between theory and available data confirms the validity of the model.     

Optimierung der Kühlungskristallisation mittels Vermischung einer kalten und einer warmen Lösung

Heated saturated solutions were directly mixed with cold ones in a fluidization crystallizer. Crystals were continuously drawn from the fluid layer, and the outflowing mother liquor of the upper part of this layer recooled and inflown into the crystallizer again. A model enabled to determine that optimum common temperature referring to the given initial solutions, and the temperature of the outflowing mother liquor, when the main part of the crystals precipitates. — The portions of crystals referring to the theoretically found optimum common temperature of the solution in the crystallizer and to the whole circulation process, were determined. We examined the validity of the theoretically found values by experiment and the influence of cooling parameters on crystal size distribution as well as on the productivity of the crystallizer.     

Mathematical model of particle size distribution of crystals taking into account the growth dispersion

This paper presents a mathematical model to describe the effect which the growth dispersion has on the particle-size distribution of crystals which are formed in a crystallizer with an ideally mixed suspension and ideal product discharge (MSMPR crystallizer). This model starts from a number density distribution of crystals, which shows dependence on the process duration, the rate of crystal growth and the crystal size. The model differs from the diffusion model. The distribution data calculated are in agreement with distribution data measured and published by a number of other authors. The influence of the two parameters b and r_LH on the mathematically determined frequency distributions is being studied.     

Diffusion induced segregation in the case of the ternary system sphalerite,chalcopyrite and cubanite

A mathematical model for describing natural and experimental diffusion induced segregation (DIS) in the case of a (Zn,Fe)S single crystal with three coexisting phases is derived. As main result, a new and quite general segregation principle for ternary systems is discovered where one phase has a flat free energy density and serves as catalyst for the segregation of the other two phases. The model includes also a stochastic noise term to represent fluctuations of the copper concentration. Numerical simulations in 2‐d underline the physical significance of the model and allow to make quantitative predictions. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Seed loading effects on the mean crystal size of acetylsalicylic acid in a continuous‐flow crystallization device

This study investigates the effects of seed loading on the mean crystal size of the model substance, acetylsalicylic acid, crystallized from ethanol in a continuously seeded tubular crystallizer. A hot, highly concentrated ethanolic acetylsalicylic acid solution was mixed with an acetylsalicylic acid‐ethanol seed suspension. Subsequent cooling of the slurry in the tubing promoted supersaturation and hence crystal growth. The tubular shape of the 15 m‐long crystallizer with an inner diameter of 2 mm enabled narrow residence time distributions of the crystals in the pipe and excellent temperature control in the radial direction and along the tubing. Crystals entering the crystallizer had both identical growth conditions in each section and about the same time for crystal growth. Narrow crystal size distributions were achieved with decreasing differences in the volume‐mean‐diameter sizes of the seed and product crystals as seed loadings increased. Decreasing the seed size had a similar effect as increasing the seed loading, since in that case the same amount of seed mass resulted in more individual seed particles. Altering the arrangement of the coiled crystallizer with respect to spatial directions (horizontal, vertical) did not lead to a significantly different outcome. All experiments produced considerably larger product crystals in comparison to the seeds despite relatively short crystallization times of less than 3 min. Moreover, product mass gains of a few hundred percent at a g/min‐scale were achieved. Similarities in product crystal samples taken at different times at the outlet of the crystallizer showed that steady‐state conditions were rapidly reached in the continuous flow crystallization device. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Continuous Recrystallization in a Double Crystallizer

This paper deals with a simple model of steady state recrystallization in a double crystallizer. Equations describing the particle size distribution are formulated and solved. The relations between resulting particle size distribution and working conditions of the double crystallizer are discussed.     

Effect of mixing on the crystal size distribution of borax decahydrate in a batch cooling crystallizer

The effect of the impeller speed upon the metastable zone width, supersaturation level, crystal growth and the crystal size distribution of borax decahydrate have been investigated to find operating conditions of a batch cooling crystallizer. The importance of impeller speed was studied in baffled stirred crystallizer with a volume of about 2 dm³, equipped with four straight blade turbine (4-SBT) cooling at a constant cooling rate. The metastable zone width was determined by visual method, while concentration changes during the process were monitored in line using ion-selective electrode. The crystal size distribution was determined by optical microscope and sieve analysis respectively. The power consumption measurements were performed for all impeller speeds examined as well. On the basis of the experimental results and observations it is evident that in an agitated batch crystallizer the above mentioned parameters are significantly influenced by hydrodynamic regime in the system determined by impeller used and its revolution speed.     

ACRT forced convection and its effects on solute segregation and heat and mass transfer during single crystal growth

A numerical simulation study was carried out for CdZnTe vertical Bridgman method crystal growth with the accelerated crucible rotation technique (ACRT). The convection, heat and mass transfer in front of the solid‐liquid interface, and their effects on the solute segregation of the grown crystal can be characterized with the following. ACRT brings about a periodic forced convection in the melt, of which the intensity and the incidence are far above the ones of the natural convection without ACRT. This forced convection is of multiformity due to the changes of the ACRT parameters. It can result in the increases of both the solid‐liquid interface concavity and the temperature gradient of the melt in front of the solid‐liquid interface, of which magnitudes vary from a little to many times as the ACRT wave parameters change. It also enhances the mass transfer in the melt in a great deal, almost results in the complete uniformity of the solute distribution in the melt. With suitable wave parameters, ACRT forced convection decreases the radial solute segregation of the crystal in a great deal, even makes it disappear completely. However, it increases both the axial solute segregation and the radial one notably with bad wave parameters. An excellent single crystal could be gotten, of which the most part is with no segregation, by adjusting both the ACRT wave parameters and the crystal growth control parameters, e.g. the initial temperature of the melt, the temperature gradient, and the crucible withdrawal rate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

溶胶-凝胶法制备高Mg含量Zn1-x MgxO薄膜

采用溶胶-凝胶法在石英玻璃基板上制备了ZB1-xMgxO薄膜,研究退火温度对高Mg含量Zn0.5Mg0.5O薄膜的相组成、相偏析及紫外-可见透过光谱中吸收边移动的影响,当退火温度≤500℃时,Zn0.5Mg0.5O薄膜未发生相偏析现象,且400℃退火处理制备的Zn0.5Mg0.5O薄膜的紫外-可见透过光谱中吸收边蓝移最大.因此,对于高Mg含量Zn0.5Mg0.5O薄膜,退火温度是影响Mg2+在ZnO中固溶度的关键因素,且400℃是其理想的退火温度.在此条件下研究了不同Mg含量对Zn1-xMgO(x=0～0.8)薄膜带隙调节的影响,随着Mg含量的增加,其紫外-可见透过光谱中紫外光区吸收边呈现规律性蓝移,光学带隙值Eg从纯ZnO的3.3 eV调节至4.2 eV.     

Technological properties of CSK-1 crystallizer for material research in space

The crystallizer CSK-1 is based on a tubular furnace with five heating elements. The crystallizer operates in an automatic mode, i.e., the setting up of the temperature fields, setting of the sample position in the tube and of the rate and direction of their movement are controlled by a microprocessor running according to a program stored on a magnetic tape. The crystallizer is placed on the Soviet Orbital Laboratory “MIR”. Basic technological properties of the crystallizer were studied by means of an standard probe connected with a computer and of the special ARP device, respectively. The topic of the study was especially the creation of various types of axial temperature fields and of various temperature gradients, the rate of heating and spontaneous cooling of the furnace, the temperature stability, and so on.     

Optimization of control parameters of cadmium zinc telluride Bridgman single crystal growth

The temperature gradient within a furnace chamber and the crucible pull rate are the key control parameters for cadmium zinc telluride Bridgman single crystal growth. Their effects on the heat and mass transfer in front of the solid‐liquid interface and the solute segregation in the grown crystal were investigated with numerical modeling. With an increase of the temperature gradient, the convection intensity in the melt in front of the solid‐liquid interface increases almost proportionally to the temperature gradient. The interface concavity decreases rapidly at faster crucible pull rates, while it increases at slow pull rates. Moreover, the solute concentration gradient in the melt in front of the solid‐liquid interface decreases significantly, as does the radial solute segregation in the grown crystal. In general, a decrease of the pull rate leads to a strong decrease of the concavity of the solid‐liquid interface and of the radial solute segregation in the grown crystal, while the axial solute segregation in the grown crystal increases slightly. A combination of a low crucible pull rate with a medium temperature gradient within the furnace chamber will make the radial solute segregation of the grown crystal vanish. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Morphotropic phase boundary,segregation effect and crystal growth in the NBT–KBT system

Lead-free piezoelectric materials of sodium–potassium bismuth titanate, (1−x)NaBi(TiO₃)₂–xKBi(TiO₃)₂, ceramics and single crystals were prepared and their crystallographic and dielectric properties were measured. Single crystals with dimensions of several centimeters were grown by using the melt growth technique. The morphotropic phase boundary between rhombohedral and tetragonal symmetry determined by X-ray diffraction and Raman spectra was found at x=0.2. No coexistence of rhombohedral/tetragonal phases was found in the NKBT system. Compositions analyses showed that severe phase segregation occurred during the crystallization of the solid solution. From the segregation point, a homogeneous NKBT crystal near the MPB composition is difficult to grow.     

Crystallization kinetics of MgSO4·12H2O from different scales of batch cooling scraped crystallizers

For reliably scaling up of crystallizers, a full kinetic model is required in addition to heat, mass and population balances. A method for extracting nucleation and growth kinetic parameters for scaling‐up seeded batch cooling crystallization was developed and demonstrated with a 15 L and in a 115 L scraped crystallizer using MgSO₄·12H₂O as the model system. The method includes fitting the time resolved measured solute concentration and the crystal size distributions with a dynamic population‐based model. The kinetic parameters extracted from the bench‐scale crystallizer agree with those obtained from the pilot scale, confirming that they can be employed for design purposes. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nucleation and growth kinetics for the crystallization of ice from dextrose solutions in a continuous stirred tank crystallizer with supercooled feed

The crystallization of ice in aqueous dextrose solutions is studied in an adiabatic continuous stirred tank crystallizer with a supercooled feed stream. The effective diameter of the ice crystals was determined for various values of mean crystal residence time, feed supercooling, magma density, stirring rate, and dextrose concentration. For all process conditions the supercooling was measured at 9-12 different locations in the crystallizer. These local supercoolings were averaged algebraically to yield the bulksupercooling. From the experimental results growth and nucleation rates have been calculated. By comparing the experimental growth rates to growth rates calculated by means of a mathematical model kinetics for the inbuilding of water molecules into the ice lattice have been determined. The growth rate appears to be directly proportional to the interface supercooling. The rate constant decreases exponentially with increasing weight percentage of dextrose in the solution. The nucleation rate was found to be directly proportional to total crystal surface per unit volume of suspension and proportional to the bulksupercooling to the power 2.1. Nucleation is believed to occur by breakage of dendrites from the surface of parent crystals.     

Autoradiographic Investigations on the Incorporation of Ca Ions in KCl Crystals during Kyropoulos Growth

Ca doped KCl crystals were grown by the Kyropoulos method. 10⁻⁵ to 10⁻³ mole fractions of Ca (as CaCl₂ with a small amount of Ca-45 (β-emitter)) were added to the melt. By autoradiography of suitable cleavage planes the incorporation of the Ca ions was found to take place preferentially in a periodic manner parallel to the solid liquid interface. In the case of a rotating seed there is a segregation process in which only one zone of maximum Ca content is built up like a helix throughout the whole crystal, the axis being identical with the growth axis of the crystal and the slope of the helix corresponding to the growth rate per seed rotation, this leading to striations of long range periodicity on vertical cleavage planes. In the case of a non-rotating seed there is a different segregation process including a periodical incorporation too, but in discrete layers of relatively small separation parallel to the solid liquid interface in short range periodicity. Explanations for the segregation phenomena are given in terms of periodically varying effective growth rates related to periodic temperature fluctuations in the neighbourhood of the solid liquid interface.