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)     

Enhancement of stability of growth,structural and NLO properties of KDP crystals due to additive along with seed rotation

Potassium Acetate (CH₃COOK) and Potassium Citrate (K₃C₆H₅O₇) as new additives were added into the potassium dihydrogen phosphate (KDP) solutions in different molar ratios. The metastable zone width and induction period with and without these additives were determined and compared. Dielectric measurements on pure and doped KDP crystals at various temperatures ranging from 313 to 423 K were carried out by the conventional parallel plate capacitor method which results low dielectric constant value dielectrics in doped crystals. The high resolution XRD studies show that CH₃COOK doped KDP crystal and K₃C₆H₅O₇ doped KDP crystal do not contain any internal structural grain boundaries and indicates that the crystalline perfection is very good. Moreover, the addition of these potassium additives improves the quality of the crystal and yields highly transparent crystals with well defined features. The effect of additives on the growth, nucleation kinetics, structural, NLO and optical properties has been investigated. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study on crystallization kinetics and the crystal internal defects of HMX

In this paper, the solubility data of HMX (1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocane) in acetone from 323.15 K to 293.15 K were accurately measured by use of the laser‐monitoring observation technique. Intermittent dynamic method was utilized to study crystallization kinetics of HMX in acetone. The data of crystallization kinetics were obtained by moment analysis, and the parameters of the growth rate and nucleation rate equations were derived by using multiple linear least squares method. Subsequently, growth rate and nucleation rate at different conditions were calculated according to these equations. In addition, Optical Microscopy Images (qualitative) and Particle Apparent Density (quantitative) experiments were applied to study the crystal internal defects of HMX under different crystallization conditions. It can be found that the crystal apparent density of HMX is in the range of 1.8993 g·cm⁻³ to 1.9017 g·cm⁻³, very close to the theory density of HMX; the internal defects and the crystal size do not increase after 25 °C, from which we predict that the HMX crystal growth reaches the steady growth segment. These results suggest that the nucleation rate is a significant factor influencing the crystal internal defects, and larger nucleation kinetics can reduce crystal internal defects.     

Crystallization behavior of (GeS2)0.1(Sb2S3)0.9 glass

The crystal growth kinetics of antimony trisulfide in (GeS₂)_0.1(Sb₂S₃)_0.9 glass has been studied by microscopy and DSC. The linear crystal growth kinetics has been confirmed in the temperature range 492 ? T ? 515 K (E_G = 405 ± 7 kJ mol⁻¹). The applicability of standard growth models has been assessed. From the crystal growth rate corrected for viscosity plotted as a function of undercooling it has been found that the most probable mechanism is interface controlled 2D nucleated growth. The non-isothermal DSC data, corresponding to the bulk sample, can be described by the Johnson-Mehl-Avrami equation.     

Analysis of the kinetics of crystal growth and epitaxy in the framework of the multilayer model of mass crystallization

The method for calculating the kinetics of crystal growth and epitaxy based on the two-dimensional model of the mass crystallization in many atomic layers has been developed. The kinetics of crystal growth is analyzed with due regard for the initial (critical) size of two-dimensional nuclei, the dependence of the growth rate of two-dimensional nuclei on their size, and the non-steady-state frequency of the formation of two-dimensional nuclei. The effect of characteristic parameters of crystallization on the kinetics of formation of epitaxial films and structure is also studied.     

Growth Habit and Habit Variation of γ‐CuI Crystallites under Hydrothermal Conditions

The octahedra were observed in the γ CuI crystallites synthesized by hydrothermal method using 1.6g (C₂H₅OO)₂Cu and 2.66g KI as precursors at 200 °C for 12 hours in the de‐ionized water. The effect of additives on the morphology of γ‐CuI crystallites was investigated. Results show that the morphology of γ‐CuI crystallites prepared in the mixed solution of de‐ionized water and alcohol at 200 °C for 12 hours is the tetrahedron. In order to disclose the effect of the additive on the growth habit of γ‐CuI crystallites, the microcosmic growth mechanism of γ‐CuI crystal is investigated from the complex of I^‐ and Cu⁺ ions to each other. It is concluded that the effect of alcohol on the morphology of γ‐CuI crystallites is carried out through changing the relative rate of complex of anion and cation to each other at the interface. Based on the above analysis, the growth habit of γ‐CuI crystallites and the habit variation under hydrothermal conditions are explained reasonably.     

Growth of KDP crystals from solutions with mechanical impurities

Growth of KDP crystals from aqueous solutions with SiO₂ particles whose size ranges from 10^–2 to 400 μm in the static and dynamic modes has been studied. The effect of mother-solution supersaturation and particle size and concentration on the process of particle capture by a growing crystal is considered as well as types of inhomogeneities formed in the crystal under the influence of these factors. It is shown that the larger the particle size, the higher the probability of particle capture by a crystal. The influence of supersaturation, growth rate, face morphology, and particle concentration on particle capture and defect formation in crystals is also discussed.     

Growth of a polyhedral crystal from solution and its morphological stability

When a polyhedral crystal grows from solution in a stable way, the supersaturation is not uniform over its interface. The rate of stable growth of a cubic crystal is determined by taking account of three-dimensional diffusion field surrounding it and growth kinetics on the interface. It depends on both supersaturation σ∞ at infinity and crystal size L. Then, the shape stability of the growing polyhderal crystal is discussed, and the curve of stability limit, σ⁷∞ versus L, is obtained by numerical calculations.     

Autodeformation bending of gypsum crystals grown under the conditions of counterdiffusion

The dynamics and kinetics of growth-induced bending of gypsum crystals grown from solution have been studied. Crystallization was performed by the method of chemical reaction under the conditions of component counterdiffusion. It is established that autodeformation bending occurs in the [001] direction at the growth front and is caused by cationic impurities. The crystal curvature depends on the anisotropy of growth rate and increases at lower supersaturations. The mechanism of growth-induced crystal bending is suggested which takes into account the heterometry stresses providing the appearance of a bending moment at the growth front.     

Crystallization of vitamin C in a continuous DT MSMPR crystallizer – Size independent growth kinetic model approach

The experimental results concerning continuous mass crystallization process in L(+)‐ascorbic acid – water system are presented and discussed. Influence of L(+)‐ascorbic acid concentration in a feeding solution and mean residence time of suspension in laboratory DT MSMPR crystallizer on product crystal size distribution as well as nucleation and growth kinetics were determined. Kinetic parameter values were evaluated on the basis of size–independent growth (SIG) kinetic model (McCabe's ΔL law). It was observed, that within the examined range of crystallizer productivity (120–1600 kg LAA crystals m^–3h^–1) crystal product population of mean size L_m from 0.2 to 0.3 mm and CV from 66.6 to 49% is withdrawn. Linear growth rate values present decreasing trend (from ca. 7 · 10^–8 to ca. 6 · 10^–8 m s^–1) with the productivity increase (assuming constant mean residence time of suspension τ = 900 s). Occurrence of secondary nucleation within the circulated and mixed suspension, resulting from crystal attrition and breakage, was observed. The parameter values in design equation connecting linear growth rate and suspension density with nucleation rate were determined. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth rate of α-calcium sulfate hemihydrate in K–Ca–Mg–Cl–H2O systems at elevated temperature

Kinetics of calcium sulfate hemihydrate (HH) crystal growth plays an important role in mineralization of calcium sulfate phases in nature. HH crystal growth and the conversion of calcium sulfate phases form the basis for the production and application of gypsum based building material. α-HH crystals have been grown in 3.74 M CaCl₂ solutions at a fixed initial ratio of calcium to sulfate under atmospheric pressure. The variations of sulfate ions were determined to obtain the α-HH crystal growth kinetics information. Effects of Mg²⁺ and K⁺ ions on α-HH growth were investigated to find an optimal composition of solution for α-HH preparation. The orders of α-HH growing in the CaCl₂ solution were found, in most cases, to be near 2.0 in presence or in absence of Mg²⁺ and K⁺ ions. Mg²⁺ ions enhance the growth of α-HH in CaCl₂ solution mainly due to initial supersaturation enhancing effects. K⁺ ions also improve the growth rate, which has been attributed to the reduction of interfacial energy. In a Ca (3.74 M)–Mg (0.20 M)–K (0.09 M) chlorides solution, the growth rate of α-HH increases with temperature from 80 to 100 °C, and the activation energy was calculated to be 40 kJ/mol.     

Unsteady-state transfer of impurities during crystal growth of sucrose in sugarcane solutions

In this work, we present growth rate data of sucrose crystals in the presence of impurities that can be used by both sugar technologists and crystal growth scientists. Growth rate curves measured in a pilot-scale evaporative crystallizer suggest a period of slow growth that follows the seeding of crystals into supersaturated technical solutions. The observed trend was enhanced by adding typical sugarcane impurities such as starch, fructose or dextran to the industrial syrups. Maximum growth rates of sucrose resulted at intermediate rather than high supersaturation levels in the presence of the additives. The effects of the additives on the sucrose solubility and sucrose mass transfer in solution were taken into account to explain the observed crystal growth kinetics. A novel mechanism was identified of unsteady-state adsorption of impurities at the crystal surface and their gradual replacement by the crystallizing solute towards the equilibrium occupation of the active sites for growth. Specifically designed crystallization experiments at controlled supersaturation confirmed this mechanism by showing increasing crystal growth rates with time until reaching a steady-state value for a given supersaturation level and impurity content.     

Determination of Mass Transfer Coefficients for Crystal Growth of Nitrate Salts

In this paper, the crystal growth of sodium nitrate and potassium nitrate from aqueous solutions, in a perfectly stirred batch crystallizer, has been studied considering the effect of temperature, supersaturation degree, and the size of seed crystal growth rate. The mass transfer coefficients obtained correlated with Re, Sc and NL dimensionaless numbers. Supersaturation curve determination using a 0.5 mW He-Ne laser, connected to an automated data acquisition system, was the first stage of the study. The supersaturation and saturation curves were closely parallel with average DT value of 4.1 and 6.8 °C for KNO₃ and NaNO₃ respectively. For the growth kinetics order, unit values were found for both salts, with diffusion as a controlling stage.     

Part 1: Kinetics and mechanism of the crystallization process

The kinetics of spontaneous crystallization of sodium chloride from aqueous‐ethanol solutions were studied. During the crystallization the electrical conductance and optical transmission of the supersaturated solutions were measured automatically. For monitoring of the total surface of growing potassium chloride crystals at the crystallization the turbidimetric method was used. The growth rate and activation energy were determined. The crystal growth rate was proportional to supersaturation. When the volume fraction of ethanol in solution increased from 14.85 to 29.72%, the activation energy of the growth process did not change and was about 50 kJ· mol^‐1. Aggregation of the crystals was found. The aggregation kinetics of the crystals may be described approximately by the famous Smoluchowski equation for coagulation of colloidal particles. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

CFD modelling of single crystal growth of potassium dihydrogen phosphate (KDP) from binary water solution at 30 °C

Crystal growth rate depends on both diffusion and surface reaction. In industrial crystallizers, there exist conditions for diffusion-controlled growth and surface reaction-controlled growth. Using mathematical modelling and experimental information obtained from growth studies of single crystals, it is possible to separate these phenomena and study how they are affected by concentration, slip velocities of particles, temperature and finally estimate the parameters for crystal growth models.In this study, a power-law growth model using activity-based driving force is created. Computational fluid dynamics (CFD) was used to evaluate the thickness of a diffusion layer around the crystal. Parameters of the crystal growth model were estimated using a non-linear optimization package KINFIT. Experimental data on growth rate of the (1 0 1) face of a potassium dihydrogen phosphate (KDP) single crystal and simulated data on the thickness of a diffusion layer at the same crystal face were used in parameter estimation. The new surface reaction model was implemented into the CFD code. The model was used to study the effect of flow direction on growth rate of the whole crystal with various slip velocities and solute concentrations.The developed method itself is valid in general but the parameters of crystal growth model are dependent on the system. In this study, the model parameters were estimated and verified for KDP crystal growth from binary water solution.     

The catalytic effect of impurity. The effect of benzene, acetone, organic acids, iron, and chromium on growth of KH2PO4 and C8H5O4K crystals

The effect of benzene, acetone, acetic, formic, and oxalic acids, iron, and chromium on the growth kinetics of KH₂PO₄ and C₈H₅O₄ K crystal faces has been studied. It is found that low concentrations of organic impurities increase growth rates of some crystal faces (the so-called catalytic effect of impurity). This effect is rather weak in the case of organic acids, however, it is clearly seen in the presence of inorganic impurity (Fe³⁺). The analysis of two models of growth (dislocation-free and B + S) under the assumption that the main cause of the catalytic effect is a decrease in the step energy showed that the calculated and experimental data are consistent only under certain assumptions that should be additionally verified both theoretically and experimentally.     

A kinetic treatment of glass formation VII: Transient nucleation in non-isothermal crystallization during cooling

The analysis of crystallization statistics has been modified to allow for time-dependent (transient) nucleation. To establish its accuracy, the numerical analysis has been applied to isothermal crystallization kinetics and shown to yield crystallization versus time curves which compare very closely with curves calculated analytically with or without the inclusion of transient nucleation.The numerical analysis including transient has been used to calculate the critical cooling rates for glass formation in anorthite and o-terphenyl considering (1) only homogeneous nucleation and (2) homogeneous nucleation + heterogeneous nucleation for 10⁷ heterogeneities cm^?3 with contact angles between 40° and 100°. It has been shown that inclusion of time-dependent nucleation in the calculations does not change the critical cooling rates for glass formation calculated assuming steady-state homogeneous nucleation in both materials. The critical cooling rate in anorthite calculated including steady-state heterogeneous nucleation was found to be decreased only slightly by the inclusion of time-dependent nucleation; while the critical cooling rates calculated for o-terphenyl were not change at all by the inclusion of time-dependent nncleation.The lack of an effect of time-dependent nucleation on the critical cooling rates calculated assuming only homogeneous nucleation is explained by the relatively small transient times on the high temperature side of the nucleation peak (a temperature range which has an overwhelming effect on the overall crystallization process because of the relatively high crystal growth rates in this range).Although the critical cooling rates associated with heterogeneous nucleation are large, the nucleation here takes place at relatively small undercooling where the transient times are relatively small. Thus, transient nucleation causes only a temporary delay in the over all crystallization, and its effect on the critical cooling rate is small.     

Crystal growth of FeCO3 in mixed monoethylene glycol and water solvent

The transportation of natural gas in long subsea pipelines is a challenge when it comes to hydrate prevention, corrosion and mineral scaling. When monoethylene glycol (MEG) is injected into carbon steel pipelines to prevent formation of gas hydrates, the solubility of the corrosion products is altered. Understanding the kinetics of FeCO₃ precipitation may make it possible to avoid deposition in the gas liquid separation process and improve solids removal in MEG recovery units. In this work, the growth kinetics of iron carbonate (siderite) has been studied in seeded batch experiments in MEG‐water solutions with 0 and 40 wt% MEG at 50 and 70 °C. Precautions were taken to keep anaerobic conditions and avoid oxidation of ferrous ions. The growth rate (G) was measured as function of supersaturation (S) and fitted to the equation: G = k_r(S‐1)^g. The growth order (g) was approximately 2 independent of the MEG concentration at the two temperatures. The growth rate constant (k_r) was in the range of 6 × 10⁻¹¹ to 1 × 10⁻¹⁰ m/s. Temperature increase from 50 to 70°C had no measurable effect on the growth rate while in the presence of 40 wt% MEG the growth rate constant decreased.     

Growth habit of crystals of refractory compounds prepared from high temperature solutions

The growth habit of single crystal refractory compounds (borides, carbides and silicides) obtained using a solution-melt method involving various growth conditions is reviewed. The effect of external and internal factors on the growth habit is analyzed. The influence of such external factors as the cooling mode, the cooling rate, the effect of variation of solute concentration, the stoichiometry of the initial components, the presence of additives in the system, the change of the maximum soaking temperature, the nature of the initial components and the solvent metal and microgravity on the growth habit are described. Examples of various anisotrophic properties in crystals of refractory compounds as well as data on crystal michrohardness anisotropy, obtained by the authors, are given. In conclusion the comparative evaluation of the effect of external factors on growth habit is provided.     

Coarse crystal layer growth and liquid entrapment study with gradient freeze technology

The coarse crystal layer growth and liquid entrapment processes were investigated with gradient freeze technology in this paper. The research system was hemihydrate phosphoric acid (H₃PO₄·0.5H₂O) crystal‐phosphoric acid aqueous solution. The distribution coefficients of ions (Ca²⁺, Fe³⁺ and Na⁺) in this system were measured. The effect of supercooling degree gradient on layer growth and the effect layer growth rate on ions redistribution were studied. The result indicated that the layer growth rate increased with supercooling degree gradient as an exponential curve. The distribution coefficient tended to increase as an approximate ‘S’ curve when coarse crystal layer growth rate increased. The ‘three region’ theory was applied to explain this phenomenon. Each ion's diffusion parameter was obtained, which contributed to explain the separation differences between different ions. The work in this paper also indicated that layer crystallization was an effective separation technology for electronic grade phosphoric acid preparation.