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)     

A novel self‐consistent Nývlt‐like equation for metastable zone width determined by the polythermal method

Using a power‐law relation between three‐dimensional nucleation rate J and dimensionless supersaturation ratio S, and the theory of regular solutions to describe the temperature dependence of solubility, a novel Nývlt‐like equation of metastable zone width of solution relating maximum supercooling ΔT_max with cooling rate R is proposed in the form: ln(ΔT_max/T₀) = Φ + β lnR, with intercept Φ = {(1–m)/m }ln(ΔH_s/R_GT_lim) + (1/m)ln(f/KT₀) and slope β = 1/m. Here T₀ is the initial saturation temperature of solution in a cooling experiment, ΔH_s is the heat of dissolution, R_G is the gas constant, T_lim is the temperature of appearance of first nuclei, m is the nucleation order, and K is a new nucleation constant connected with the factor f defined as the number of particles per unit volume. It was found that the value of the term Φ for a system at saturation temperature T₀ is essentially determined by the constant m and the factor f. The value of the factor f for a solute–solvent system at initial saturation temperature T₀ is determined by solute concentration c₀. Analysis of the experiment data for four different solute‐water systems according to the above equation revealed that: (1) the values of Φ and m for a system at a given temperature depend on the method of detection of metstable zone width, and (2) the value of slope β = 1/m for a system is practically a temperature‐independent constant characteristic of the system, but the value of Φ increases with an increase in saturation temperature T₀, following an Arrhenius‐type equation with an activation energy E_sat. The results showed, among others, that solubility of a solute is an important factor that determines the value of the nucleation order m and the activation energy E_sat for diffusion. In general, the lower the solubility of a solute in a given solvent, the higher is the value of m and lower is the value of E_sat. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of concentration and supersaturation ratio of CuI·HI on CuI crystal growth by decomplexation method

The fundamental role of solubility and supersaturation of solute for crystal growth from solution has been widely realized. In order to optimize the process of CuI crystal growth by CuI·HI decomplexation in HI acid, the solubility and supersaturation curves of CuI in HI‐H₂O mixed solvent were measured, and then a modified concentration programming scheme was designed, which could grow high quality CuI single crystals of 2.5 mm on edge successfully. In this scheme, the concentration distribution of CuI·HI complex and HI acid in silica gel along their diffused direction were measured with spectrophotometer, and the evolution of CuI·HI complex supersaturation ratio was analysed. It was found that the excess CuI·HI complex concentration would lead to the high supersaturation ratio and the formation CuI dendrites. The condition for regular CuI single crystal growth in silica gel was measured as follow: when the crystal nuclei appears, the CuI·HI complex concentration in HI‐H₂O solvent should be kept in the range of 0.033–0.050 mol/L and its corresponding supersaturation ratio is 1.24–1.45, and then they should be respectively declined to a range of 0.025–0.033 mol/L and 1.14–1.26 at the stage of crystal growth. The results may provide a useful clue for further improvement of the experimental scheme. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the origin of supersaturation barriers during the growth of single crystals from aqueous solutions containing impurities – a review

A generalised treatment of the appearance of supersaturation barriers σ_d, σ* and σ** during the growth of single crystals is outlined from the standpoint of well‐defined critical values of relative step velocities on a face. The final theoretical expressions are based on the premise that: (1) there are critical values of the relative step velocities associated with different average distances between adsorbed impurity particles during instantaneous, time‐dependent and time‐independent adsorption of the impurity on the growing surface, (2) the growth rate of a face is proporptional to velocity of steps on the growing face, and (3) Freundlich and Langmuir adsorption isotherms apply for different impurities. The theoretical expressions are then used to critically analyse the experimental data on supersaturation barriers observed during the growth of ammonium oxalate monohydrate and potassium dihydrogen phosphate single crystals from aqueous solutions containing different impurities. It was found that: (1) Langmuir adsorption isotherm is more practical for the analysis of the experimental data of the dependence of supersaturation barriers σ_d, σ* and σ** on the concentration c_i of an impurity, and (2) the ratios σ_d/σ* and σ*/σ** of successive supersaturation barriers for an impurity either increases or remains constant with an increase in impurity concentration c_i, and may be explained in terms of the mechanism of adsorption of impurity particles. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth kinetics of ammonium oxalate monohydrate single crystals from aqueous solutions containing Co(II) and Ni(II) impurities

The growth kinetics of different faces of ammonium oxalate monohydrate (AO) single crystals from aqueous solutions containing different concentrations of Co(II) and Ni(II) ions at a constant temperature are described and discussed. It was found that: (1) at a given supersaturation σ, both Co(II) and Ni(II) ions lead to a decrease in the growth rates R of different faces of AO crystals, (2) the growth of a particular face of the crystals occurs above a critical supersaturation σ_d, but there is also another supersaturation barrier σ* when the rate abruptly increases with σ, and (3) the values of σ_d and σ* increase with increasing concentration c_i of the impurity. The experimental R(σ) data for different concentrations c_i of the impurities were analysed according to the model involving complex source of cooperating screw dislocations and concepts of instantaneous and time‐dependent impurity adsorption. Analysis of the data showed that: (1) adsorption of Co(II) and Ni(II) impurities occurs on the surface terrace of AO crystals, (2) there is a simple relationship between Langmuir constant K and the impurity concentration c_i* corresponding to maximum surface coverage, and (3) the ratio σ_d/σ* of the supersaturation barriers observed in the presence of both impurities increases with an increase in impurity concentration c_i, and may be explained from the standpoint of the mechanism of adsorption of impurity particles at kinks and ledges. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth mechanism of corundum crystals from cryolite (Na3AlF6) flux

Using the experimental data of the velocity versus supersaturation, υ(σ), relation and estimated values of liquid viscosity and density, flow velocity, and crystal density, the diameter of solute particles in solution in the growth of Al₂O₃ crystals from cryolite flux was estimated on the hard sphere model to be 11.8 Å. The step heights of single spiral layers on the (0001) face were measured by means of phase contrast microscopy and multiple-beam interferometry, which gave the values of 26 and 53 Å in two cases. Both values are in fair agreement in order of magnitude. It is suggested that the solute exists in the supersaturated solution in the form of culsters rather than ionic or molecular entities. Both from υ(σ) relation and diffusion coefficient values, the rate-controlling process in this case is considered to be volume diffusion through the unstirred boundary layer.     

Study of growth kinetics of ammonium oxalate monohydrate crystals from aqueous solutions

Experimental results of the dependence of linear growth rates of ammonium oxalate monohydrate [(NH₄)₂C₂O₄ · H₂O; AO] single crystals on solution supersaturation are presented. The AO crystals were grown by constant-temperature, constant-supersaturation method at 30 and 40 °C in the supersaturation range of 1–9%. It was observed that the supersaturation dependence of growth rates follows the parabolic growth law. Analysis of the supersaturation dependence of linear growth rates of AO crystals showed (1) that growth models involving surface diffusion and direct incorporation of growth units give kinetic parameters similar to those reported for other compounds grown from solutions, and (2) that the the BCF model of cooperating screw dislocations is also applicable. An inverse relationship between the estimated values of the length, L, of the line containing the dislocations and growth rate, R, and a direct relationship between L and interplanar distance, d_hkl, of the face {hkl} were found. Both these relationships are associated with the process of generation of screw dislocations in the growing layer.     

Effect of supersaturation on the crystallization of phenylbutazone polymorphs

The article describes the effect of degree of supersaturation, σ, on the crystallization of specific polymorphs of phenylbutazone from its methanolic solution at 20 °C. At low initial supersaturation, σ ≤ 2.0, the fraction of the metastable α polymorph in the crystallized product exceeds that of the δ polymorph, while at σ ≥ 5.0, the fraction of the stable δ polymorph increases in the crystallized product. The results are explained by the effect of supersaturation on the relative rates of nucleation and crystal growth of the polymorphs. Furthermore, the mechanism of nucleation and crystal growth also change with supersaturation. Supersaturated methanolic solutions of phenylbutazone exhibit a critical temperature at which the nucleation rates of the polymorphs decrease drastically. This effect is partly explained by the decreased mobility of phenylbutazone molecules at lower temperatures. Nucleation is most rapid when the crystallization temperature is close to the transition temperature, T_t(α ⟷ δ), between the polymorphs, α and δ. The nucleation rate decreases as the temperature difference between T_t(α ⟷ δ) and the crystallization temperature increases. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystal structures and spectroscopic characterization of chiral and racemic 4‐phenyl‐1,3‐oxazolidin‐2‐one

Crystal structures of (R)‐ and (rac)‐4‐phenyl‐1,3‐oxazolidin‐2‐one (4‐POO) have been determined by X‐ray diffraction and characterized by the solid state ¹³C NMR and IR spectra. Molecular geometries and intermolecular interactions in (R)‐ and (rac)‐4‐POO crystals are very similar to each other; 4‐POO molecules are linked via the N‐H…O intermolecular hydrogen bonds to form the chained structure. Chemical shifts of the solid state ¹³C NMR spectra are very similar to each other, whereas the ¹H spin‐lattice relaxation times (T_1H) value for (R)‐4‐POO is five times as large as that for (rac)‐4‐POO, reflecting the more restricted mobility of the (R)‐4‐POO chain. Although both crystals contain an unique molecule in the asymmetric unit, a doublet feature is observed for the C=O stretching mode in the IR spectra of (R)‐ and (rac)‐4‐POO crystals. The frequency gap of the C=O bands are correlated with the strength of the dipole‐dipole interactions between the neighboring C=O groups. © 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Concentration distribution in crystallization from solution under microgravity

Concentration distribution in crystallization from solution under microgravity is numerically studied. A quasi-steady state growth and dissolution in a 2D rectangular enclosure filled with sodium chlorate (NaClO₃) aqueous solution, in which one wall is the growth surface of the crystal and the opposite one is the dissolution surface, is considered. The solute transport process at the growth surface is described by the diffusion-reaction theory with finite interface kinetics coefficient. The results show that the concentration at the growth surface is supersaturated and the supersaturation distribution is of non-uniformity, i.e. the supersaturation in a region facing an incoming flow is high. On the other hand, the non-uniformity of supersaturation at the growth surface is closely related to the gravity level even under microgravity, it exponentially increases as the thermal Rayleigh number on behalf of the gravity level rises.     

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)     

Solution Growth and Characterisation of L‐alanine Single Crystals

Single crystals of L‐alanine have been grown from buffered aqueous solutions and characterised as to their optical quality via wavefront distortion analysis, electrooptical response and harmonic generation efficiency. Refraction indices as well as phase matching loci were found in satisfactory agreement with previously published data for crystals grown in non buffered solution. Estimates for the electro‐optical response are reported for the first time. The experimentally observed crystal habit is discussed in terms of morphological importance (M.I.), which was found to be in disagreement with the predictions of crystallographic criteria based on the interplanar distance d_hkl, on the periodic bond chains (PBC) and the attachment energy E_att. This disagreement is tentatively attributed to the presence of impurities and non‐appropriate supersaturation conditions.     

Synthesis and crystallographic characterization of a chiral complex of (R)‐2‐(pyridin‐2‐ylmethylene)amino‐2′‐hydroxy‐1,1′‐binaphthyl(L) with hydrated nickel(II) acetate

A chiral complex of (R)‐2‐((pyridin‐2‐ylmethylene)amino)‐2′‐hydroxy‐1,1′‐binaphthyl ( L ) with hydrated nickel (II) acetate has been synthesized and spectroscopically characterized. The crystal structure of [NiL₂(CH₃OH)(CH₃COO)]CH₃COO·CH₃OH has been determined by single‐crystal X‐ray diffraction. The complex crystallizes in the orthorhombic space group P 2(1) 2(1) 2(1) with cell constants a = 15.1035 (19), b = 17.836 (2), c = 18.730 (2)Å, α = β = γ = 90.00°, Z = 4. The structure was solved by direct methods and refined to R = 0.0346 (wR₂ = 0.0863). The analytical result of the crystal structure indicates that a pair of L ligands chelate to a Ni (II) atom in an asymmetric fashion with one Ni‐N bond being longer than the other, the Ni (II) atom is further coordinated by one methanol molecule and one acetate anion to form a distorted octahedral geometry. In the crystal of the complex, the coordination cation [NiL₂(CH₃OH)(CH₃COO)]⁺, the uncoordinated methanol molecule and uncoordinated acetate anion are further assembled into one‐dimensional chain structure via intermolecular hydrogen bonds along the a‐axis. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spontaneous crystallization of sodium chloride from aqueous‐ethanol solutions – Part 2: Mechanism of aggregation and coalescence of crystals

Published data on aggregation kinetics of sodium chloride crystals at its spontaneous crystallization from supersaturated aqueous‐ethanol solutions were analysed. It was found that the crystals coalesced through contact nucleus‐bridges between them according to the mechanism proposed by Polak. The kinetics of aggregation were described by the Smoluchowski equation for coagulation of colloidal particles. The kinetic coefficient of aggregation process depended on supersaturation, temperature of solution and other characteristics of the system. The specific surface energy of sodium chloride 0.95 mJ/m² was found. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spontaneous crystallization of potassium chloride from aqueous and aqueous‐ethanol solutions Part 1: Kinetics and mechanism of the crystallization process

Kinetics of spontaneous crystallization of potassium chloride from aqueous and aqueous‐ethanol solutions were studied. During the crystallization of the salt 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 of the crystals were determined. The crystal growth rate was proportional to supersaturation. When the volume fraction of ethanol in the solution increased from 0 to 25.76%, the activation energy of the growth process did not change and was about 60 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. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the addition of alcoholic miscible co‐solvents on the properties of ascorbic acid in its supersaturated aqueous solution

In the current study results are presented on the influence of the solvent composition on the properties of ascorbic acid in its supersaturated aqueous solutions. In examining the role of addition of 20 wt.% ethanol or 1‐propanol to the ascorbic acid water system, it was emphasized that the solubility is reduced significantly due to the addition of alcoholic co‐solvents. Using UNIFAC simulation, tt was found that the addition of alcoholic co‐solvents to the aqueous ascorbic acid solution and in the state of equilibrium reduces significantly the activity coefficient of ascorbic acid. In the supersaturated ascorbic acid solutions, the calculated activity ratio (γ/γ_eqm) by means of UNIFAC simulations as a function of supersaturation ratio (x/x_eqm) point out that the addition of alcoholic co solvents lead to an increase in the thermodynamic driving force. The measured metastable zone widths in the presence of alcoholic co‐solvents displays that alcoholic co‐solvents acts on increasing the width of the metastable zone. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of Mn(II) ions on the growth of ammonium oxalate monohydrate crystals from aqueous solutions: II. Growth kinetics

The experimental results of the effect of concentration of Mn(II) ions on the growth kinetics of different faces of ammonium oxalate monohydrate single crystals from aqueous solutions at a constant temperature and different predefined supersaturations are described and discussed. It was observed that: (1) at a given supersaturation σ, Mn(II) ions lead to a decrease in the growth rates of different faces of AO crystals, (2) the growth of a particular face of the crystals occurs above a critical supersaturation σ_d but there is also another supersaturation barrier σ* when the rate abruptly increases with σ, (3) the values of σ_d and σ* increase with increasing concentration of the impurity, and (4) the values of σ_d depend on the growth kinetics of a face but those of σ* are independent of face growth kinetics. The experimental R(σ) data for different Mn(II) concentrations c_i were analysed according to the model involving complex source of cooperating screw dislocations and concepts of instantaneous and time‐dependent impurity adsorption. It was found that: (1) for a given face the differential heat of adsorption Q_diff is higher during instantaneous impurity adsorption than that during time‐dependent adsorption, and (2) the values of Q_diff involved during instantaneous adsorption are related with face growth kinetics but those during time‐dependent adsorption are independent of face growth kinetics.     

Total pressure‐controlled PVT SiC growth for polytype stability during using 2D nucleation theory

A total pressure‐controlled physical vapor transport growth method that stabilizes SiC polytype is proposed. The supersaturation of carbon during SiC growth changed as a function of the growth time due to changes in the temperature difference between the surfaces of the source and the grown crystal. Supersaturation also varied as a function of the pressure inside the furnace. Therefore, modification of the pressure as a function of growth time allowed for constant supersaturation during growth. The supersaturation was calculated based on classical thermodynamic nucleation theory using data for heat and species of Si₂C and SiC₂ transfer in a furnace obtained from a global model. Based on this analysis, a method for polytype‐stabilized SiC growth was proposed that involves decreasing the pressure as a function of growth time. The 4H‐SiC prepared using this pressure‐controlled method was more stable than that of 4H‐SiC formed using the conventional constant‐pressure method.     

Crystallization and Characterization of Orthorhombic β‐MgSO4 · 7H2O

In solution, the growth rate and the crystal habit are influenced by a number of factors such as supersaturation, temperature, pH of the solution, cooling rate, agitation, viscosity, initial state of the seed crystal and the presence of impurities. The crystallization of orthorhombic β‐MgSO₄ · 7H₂O, from low temperature aqueous solution by slow cooling process was studied. The metastable zone width, the induction periods (τ) for different supersaturations and the effect of pH on the growth rate of the crystals were investigated. The increase of pH yielded bigger crystals. The structural, optical, thermal and mechanical properties of β‐MgSO₄ · 7H₂O have been studied using FT‐IR, X‐ray diffraction, TGA‐DTG and micro hardness analyses.