Effects of impurity ions on solubility and metastable zone width of phosphoric acid

Effects of two typical impurity ions as Fe²⁺ and SO₄^2– in phosphoric acid on solubility and metastable zone width (MZW) had been studied. It was shown that polythermal method was suitable for solubility measurement in this study. The solubility experimental data was correlated with a polynomial equation. Being compared with Fe²⁺, SO₄^2– had a greater impact on the phosphoric acid solubility; and the variation in phosphoric acid MZW was just opposite. Phosphoric acid apparent secondary nucleation order was calculated to be 3.50 by means of modified regression method. And also the influence of impurity ions on apparent secondary nucleation order was investigated in this paper. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of metastable zone width and induction time for a seeded aqueous solution of potassium sulfate

The metastable zone width (MSZW, ΔT_m) and induction time (t_ind) were determined with computer simulation for seeded batch crystallization of potassium sulfate from aqueous solution. The MSZW and induction time determined with simulation showed the same behavior as experimental values reported in the literature; log (ΔT_m) increased linearly with an increase in log R (R: cooling rate) and t_ind decreases in proportion to (ΔT)⁻ⁿ (ΔT: supercooling, n: nucleation order in the secondary rate expression of B=k_n(ΔT)ⁿ). The secondary nucleation parameters (k_n and n) were deduced both from the simulated MSZW and induction times by using the previously proposed model [J. Cryst. Growth, 2010, 312, 548–554]. The secondary nucleation rate calculated with the deduced parameters was in agreement with that calculated with the parameters input for simulation.     

Solubility and metastable zone width of DL‐tartaric acid in aqueous solution

Solubility and metastable zone width (MSZW) of DL‐tartaric acid (DL‐TA) in aqueous solution have been determined. Solubility of DL‐TA was measured in the temperature range from 0 to 50 °C at atmospheric pressure by means of the conventional polythermal method using Turbidity Monitoring Technique, which was verified by a gravimetric method. The dissolution enthalpy and entropy of DL‐TA were then calculated from the solubility data using van't Hoff equation. Two approaches was used to estimate the nucleation kinetics from the measured metastable zone width data, the self‐consistent approach and the approach based on 3D nucleation. In addition, the metastable zone width slightly decreases with increasing agitation rate and was independent of working volume.     

On the interpretation of metastable zone width in anti‐solvent crystallization

Considering nonlinear dependence of solute concentration on anti‐solvent–solvent composition a modified Nývlt‐like equation based on traditional power‐law relation between nucleation rate and developing supersaturation and a new equation based on the classical theory of three‐dimension nucleation are proposed to explain the dependence of anti‐solvent addition rate on metastable zone width defined as excessive anti‐solvent composition in anti‐solvent crystallization. The experimental data on the metastable zone width in anti‐solvent crystallization of benzoic acid are analyzed and discussed from the standpoint of these equations. It is found that the new approach based on the classical nucleation theory provides better insight into the processes involved in anti‐solvent crystallization. Analysis of the experimental results on anti‐solvent crystallization of benzoic acid [D. O'Grady, M. Barret, E. Casey, and B. Glennon, Trans. IChemE A 85 , 945, (2007)] revealed that: (1) the value of metastable zone width for a solvent–anti‐solvent system is determined by the solute–solvent and solute–anti‐solvent interactions, (2) the dependence of the metastable zone width on stirring is associated with the enthalpy of mixing, and (3) the new approach predicts a threshold anti‐solvent addition rate associated with the setting up of an equilibrium between solvent and anti‐solvent and a maximum anti‐solvent addition rate connected with the induction period t_ind for the onset of crystallization. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nucleation kinetics of paracetamol–ethanol solutions from metastable zone widths

A study of the nucleation kinetics for a cooling crystallisation of paracetamol–ethanol solutions in a batch reactor is described in this paper. Metastable zone width (MSZW) experiments were conducted in order to estimate the nucleation kinetics of the system. Measured MSZWs can be affected by numerous process parameters, such as cooling rate, concentration, agitation rate, and working volume. Two theoretical approaches were employed to estimate the nucleation kinetics, the classical mass based approach of Nývlt, and a more recent approach by Kubota, which also considers number density. Both approaches were found to produce similar estimates for the nucleation rates of the paracetamol–ethanol solutions as a function of supersaturation for an assumed nucleus size of 10 μm. The theory of Kubota was found to predict satisfactory estimates for the induction time of the nucleation process from MSZW data. The induction time was observed to be independent of the solution temperature as suggested by Kubota’s theory. This is a novel finding and serves to validate the induction time theory of Kubota. In this investigation, MSZWs were observed to decrease with increased levels of agitation and found to be independent of working volume.     

Metastable zone width for secondary nucleation and secondary nucleation inside the metastable zone

This study presents an evaluation of a new method, called zero growth activation free energy, used to determine the metastable zone width for the secondary nucleation case. It predicts the metastable zone width with a maximum error of 5‐10%. Estimation of the metastable zone width for different isothermal crystallization conditions can be modeled according to a chosen reference set of growth experiments carried out in the volume diffusion regime at different initial supersaturations, using seed crystals of a certain characteristic size. Moreover, the activation free energy of the secondary nucleation was estimated. The role of the enthalpy of immersion in the formation of secondary nucleation events inside the metastable zone was pointed out, as well as its effect in causing extra‐fast growth rate. Furthermore, sucrose crystal surface free energy was estimated. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of metastable zone width of ammonium oxalate aqueous solutions

The metastable zone width of pure ammonium oxalate aqueous solutions, as represented by maximum supercooling ΔT_max, is investigated as functions of cooling rate R and saturation temperature T₀ by the polythermal method. The experimental results are discussed by using two recently advanced approaches: (1) self‐consistent Nývlt‐like approach based on a power‐law relationship between nucleation rate J and maximum supersaturation lnS_max, and (2) a novel approach based on the relationship between J and lnS_max described by the classical three‐dimensional nucleation theory. Analysis of the experimental data revealed that both approaches describe the experimental data on metastable zone width by the polythermal method reliably and provide useful information about the physical processes and parameters involved in nucleation kinetics. The values of various physical quantities predicted by both of these approaches are reasonable for a fairly‐soluble compound. A careful examination of the data on ΔT_max as a function of T₀ obtained by polythermal method and from density measurements showed that ΔT_max has a slight tendency to decrease with increasing saturation temperature T₀. The values of lnS_max at saturation temperature 303 K suggest that the metastable zone width of ammonium oxalate aqueous solutions is determined by primary nucleation in the polythermal method and by secondary nucleation during density measurements. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nucleation, growth and characterization of L-tartaric acid—nicotinamide NLO crystals

The solubility, metastable zone width and nucleation parameters of organic nonlinear optical material L-tartaric acid–nicotinamide (LTN) have been determined. The crystals of LTN are grown by the slow cooling method. The grown crystals are morphologically interpreted. The crystalline powder of the grown crystals has been examined by X-ray diffraction and thermogravimetric analysis. The different modes of vibrations present in the crystal are identified by the Fourier infrared spectroscopy analysis. The powder SHG efficiency of LTN is comparable with that of KDP.     

Study of the metastable region in the growth of GaN using the Na flux method

It was revealed that the metastable region, in which liquid phase epitaxy (LPE) of GaN single crystals proceeds without the generation of polycrystals, expands with growth temperature in the Na flux method. The metastable region appears when LPE growth proceeds at temperatures above 1073 K, although generation of polycrystals inevitably occurs on a crucible at temperatures less than 1073 K. The highest growth rate of 14 μm/h in a small experimental setup was achieved at a temperature of 1163 K with a nitrogen pressure of 5.5 MPa due to complete suppression of the growth of polycrystals on a crucible, even though the supersaturation at this condition reached a fairly high level.Also, an LPE crystal with a flat surface could easily be obtained under high-temperature conditions.     

In situ determination of metastable zone width by a simple optical probe

The metastable zone width (MSZW), which denotes the region between the solubility curve and the onset of nucleation, is an important control parameter for successful operation of a solution crystallization process as it defines an operating boundary for the crystallization process. The MSZW can be approximated as the gap between the loci of cloud points that correspond to onset of nucleation and clear points that closely represent solubility. This work presents the design and application of a simple optical probe consisting of a line laser source, a light‐dependent resistor, and a simple processing circuit for in situ determination of onset of nucleation of a crystallization process. Three different crystallization processes, namely, cooling crystallization of glycine, cooling crystallization of L‐asparagine monohydrate, and anti‐solvent crystallization of glycine, are investigated to assess the performance of the in situ probe. In all the cases, the cloud points and clear points are conveniently detected by sharp changes in output voltage of the probe with reasonable accuracy. The presented optical probe can be used as a simple and inexpensive alternative tool in the area of crystallization process monitoring.     

The effect of calcium cations on the precipitation of barium sulfate 2: calcium ions in the presence of organic additives

Calcium ions have been implicated in changing the precipitation of barium sulfate when organic additives are present, although whether it inhibits or promotes nucleation and/or growth has been disputed in the literature. We conducted a thorough investigation into the effect of calcium when additives are present and show that calcium cations do indeed promote nucleation of barium sulfate particles when compared to the appropriate control. This result is independent of the analytical method (conductivity or turbidity) used to assess precipitation. The nucleation promotion produces no change in the crystal morphology, thus morphology is not always a good indicator of nucleation or growth behavior. The extent of nucleation promotion depends on the functional group of the additive.     

Nucleation of AlN on SiC substrates by seeded sublimation growth

The nucleation of aluminum nitride (AlN) on silicon carbide (SiC) seed by sublimation growth was investigated. Silicon-face, 8 off-axis 4H-SiC (0 0 0 1) and on-axis 6H-SiC (0 0 0 1) were employed as seeds. Initial growth for 15 min and extended growth for 2 h suggested that 1850 °C was the optimum temperature of AlN crystal growth: on an 8 off-axis substrate, AlN grew laterally forming a continuous layer with regular “step” features; on the on-axis substrate, AlN grew vertically as well as laterally, generating an epilayer with hexagonal sub-grains of different sizes. The layer's c-lattice constant was larger than pure AlN, which was caused by the compression of the AlN film and impurities (Si, C) incorporation. Polarity sensitive and defect selective etchings were performed to examine the surface polarity and dislocation density. All the samples had an Al-polar surface and no N-polar inversion domains were observed. Threading dislocations were present regardless of the substrate misorientation. Basal plane dislocations (BPDs) were revealed only on the AlN films on the 8 off-axis substrates. The total dislocation density was in the order of when the film was 20– thick.     

Influence of polyethylenimine on the precipitation process of lead sulfate crystals

Crystals of lead sulfate were precipitated in a solution of polyethylenimine (PEI) using a double-jet crystallizer. PEI controlled both the nucleation rate and the growth rate, and enabled to produce fine monodispersed crystals. This effect is considered to be due to a complexation between PEI and lead ion. The on-line measurement of the variation in the lead ion concentration indicated PEI lost its effect when a certain amount of reactants was supplied. And the duration in which PEI could control the precipitation rate and the amount of PEI had a strong correlation. In addition, it was suggested that their relationship could be utilized in order to produce monodispersed particles.     

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)     

Effect of molecular weight of polystyrensulfonic acid sodium salt polymers on the precipitation kinetics of sodium bicarbonate

This paper analyzes the effect of polystyrensulfonic acid sodium salt (NaPSS), obtained by kinetic precipitation from solutions of polymers of molecular weight 245 000 and 38 000 g mol⁻¹ in sodium bicarbonate (NaHCO₃) itself precipitated from synthetic brine. Crystal size, shape and the additive adsorbed are reported. X shaped and hexagonal prisms crystals with different aspect ratios were obtained. The results show that with increasing polymer concentration the crystal size decreases, from 0.27 to 0.48 mm. Additionally, the higher molecular weight polymer shows both higher adsorption capacity and higher crystal habit modification. Crystal shape patterns were similar for both polymers; however, the higher molecular weight material induced changes at lower concentration. It was observed that the precipitation rate reached a minimum with increasing additive concentration.     

Crystallization of zinc lactate in presence of malic acid

The influence of malic acid, which acts as an impurity on the cooling crystallization of zinc lactate is investigated in this paper by monitoring the relative supersaturation and the number of crystals during crystallization. The presence of malic acid increases the solution solubility and makes the metastable zone wider; it also changes the habit of the crystal. The purity of the final products is shown to be influenced by the amount and size of seed crystals, cooling rate, seeding temperature and final temperature, but appears to depend mainly on the particle size and level of supersaturation. Residual supersaturation thresholds are observed that depend on the final temperature. A model is proposed to predict the steady-state supersaturation value from the final temperature at a given impurity concentration. This model is based on Kubota and Gibbs equations.     

Investigations on the nucleation kinetics of bis glycine sodium nitrate

The nucleation parameters such as, energy per unit volume, radius of critical nucleus, critical free energy barrier, number of molecules in the critical nucleus and nucleation rate have been evaluated for bis glycine sodium nitrate single crystals. The interfacial energy of the solution at various temperatures has been estimated from existing solubility data. The metastable zone width and induction period measurements have been carried out experimentally.     

Solidification behavior of falling germanium droplets produced by pulsated orifice ejection method

In order to clarify containerless solidification mechanism of falling semiconductor microdroplets, the monosized droplets of germanium in the size range from 200 to 500 μm were ejected by pulsated orifice ejection apparatus method. The density of grains in the resultant particles was dramatically reduced by decreasing the ejection temperature, i.e. initial temperature. A surface observation and orientation imaging microscopy analysis proposed that such microstructural transition was derived from the dependency of preferred growth direction on the undercooling level: the initial temperature determined the solidification undercooling. Numerical calculation with the classical nucleation theory was performed to discuss this phenomenon, but could not sufficiently elucidate the effect of initial temperature obtained experimentally.     

Calcite crystallization on oxadiazole-terpyridine copolymer

The nucleation and further crystallization of calcite on oxadiazole-terpyridine copolymer were investigated by the constant composition method. The apparent order of the crystallization process was found to be 2.3±0.2 indicative of a surface diffusion-controlled spiral growth mechanism. The number of ions forming the critical nucleus was found experimentally to be (n^*=) 3 in accordance with the simulation by the PM3 method included in the MOPAC program package. The surface energy of the growing phase was found to be 29.5 mJ m⁻².     

Effect of various precipitants on the nucleation rate of tetragonal hen egg-white lysozyme crystals in an AC external electric field

It was observed that the effect of an external electric field on the nucleation rate of tetragonal hen egg-white lysozyme crystals varied depending on the precipitant used (NaCl, NiCl₂ or YbCl₃) and that the electric double layer (EDL) played an important role in generating an external electric field of the necessary strength to control the nucleation rate. This phenomenon depended on the ionic strength of the precipitant used; that is, a precipitant of greater ionic strength resulted in a thinner EDL and increased the effect of the external electric field as the driving force for nucleation. The dependence of the nucleation rate on the precipitant was attributed to the magnitudes of the external electric fields generated in EDLs of varying thickness which were formed in the presence of different precipitants.