Investigation of nucleation kinetics and crystal defects of HMX

The nucleation kinetics of HMX (cyclotetramethylene tetranitramine, C₄H₈N₈O₈) in γ‐butyrolactone was studied in cooling process by induction time method. The laser scattering method was used to measure the solubility data and metastable region of HMX in γ‐butyrolactone. The induction time was measured over a range of supersaturation at different temperatures. Then, the nucleation mechanism of HMX in γ‐butyrolactone was investigated by analysis the relationships between induction time and supersaturation. The results indicated homogeneous nucleation dominated at high supersaturation of S >1.35, while the heterogeneous nucleation dominated at low supersaturation of S < 1.35. The values of interfacial tension at different final temperatures were calculated to indicate the ability of HMX to be crystallized. The growth mechanism of HMX was investigated by the data fitting applying different growth mechanism models and identified as two‐dimensional nucleation‐mediated (2D) growth. Finally, the effects of supersaturation and temperature on the crystal defects were analyzed based on the nucleation kinetics. When the temperature is below 303.15K, homogeneous nucleation dominated the nucleation process at higher supersaturation. Fine HMX crystals with more defects were produced. On the contrary, heterogeneous nucleation mechanism dominated at lower supersaturation. large regular HMX crystals with fewer defects were formed when the temperature is above 318.15K.     

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kg LAA crystals m^–3h^–1) crystal product population of mean size L_m from 0.2 to 0.3 mm and CV from 66.6 to 49% is withdrawn.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)     

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)     

Single‐crystal sapphire microstructure for high‐resolution synchrotron X‐ray monochromators

We report on the growth and characterization of sapphire single crystals for X‐ray optics applications. Structural defects were studied by means of laboratory double‐crystal X‐ray diffractometry and white‐beam synchrotron‐radiation topography. The investigations confirmed that the main defect types are dislocations. The best quality crystal was grown using the Kyropoulos technique. Therein the dislocation density was 10²–10³ cm⁻² and a small area with approximately 2*2 mm² did not show dislocation contrast in many reflections. This crystal has suitable quality for application as a backscattering monochromator. A clear correlation between growth rate and dislocation density is observed, though growth rate is not the only parameter impacting the quality.     

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.     

Rate of homogeneous nucleation in alkali disilicate glasses

Rates of crystal nucleation in alkali disilicate glasses were measured by counting the number of crystals under an optical microscope. The viscosities of these glasses were measured by the method of beam-bending and penetration. Using the data of rate of nucleation and viscosity obtained in the present study and the data of free energy measured by Takahashi and Yoshio, crystal-glass interfacial energies for alkali disilicate systems were estimated on the basis of homogeneous nucleation theory as follows: 196 erg/cm² for Li₂O·2SiO₂, 126–144 erg/cm² for Na₂O·2SiO₂ and 88–104 erg/cm² for K₂O·2SiO₂. The effects of the viscosity of glass, the free energy difference between crystal and glass and crystal-glass interfacial energy on the rate of nucleation were discussed, and the remarkably higher rate of crystal nucleation in the Li₂O·2SiO₂ glass was attributed to the larger free energy difference.     

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)     

Precipitation kinetics of sodium bicarbonate in an industrial bubble column crystallizer

Sodium bicarbonate is a substance which is produced in the middle stages of the soda ash production process. In this precipitation process, carbon dioxide gas is continuously injected into the bubble column reactor which contains carbonate and bicarbonate solutions. To elucidate the key parameters affecting precipitation kinetics, an experimental study was conducted to understand nucleation and growth in conditions of industrial reactor. The composition of the solution is followed during the crystallization process by titration. Magma density is also monitored and crystal size distribution (CSD) is obtained by sieving. The method of moments was used to determine nucleation and growth rates of crystals. The nucleation and growth rate correlations for sodium bicarbonate precipitation in industrial scale were correlated by empirical power laws as B = 26.685M_T^0.42Δw^1.31 and G = 1.381×10^–4Δw^1.53. The nucleation and growth rate correlations obtained in this study can be used to simulate the crystallization of sodium bicarbonate plants. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of reactive crystallization kinetics of 5‐(difluromethoxy)‐2‐mercapto‐1H‐benzimidazole in a batch crystallizer

5‐(difluromethoxy)‐2‐mercapto‐1H‐benzimidazole (DMB) was crystallized via the reaction between sodium salt of DMB and acetic acid. In this work, we firstly measured the solubility data of DMB in binary ethanol‐water mixture at different temperatures. Then, the reactive crystallization kinetics of DMB was determined in the batch crystallizer. Based on the population balance and mass balance, the kinetics model of reactive crystallization process of DMB was established. And the nucleation rate, size‐independent crystal growth and agglomeration kernel were determined by method of classes. Finally, based on the population balance, numeric simulation was done using the above crystallization kinetics in order to verify its reliability.     

Nanocrystallization of fresnoite glass. I. Nucleation and growth kinetics

We determined the internal nucleation, crystal growth and overall crystallization kinetics of fresnoite crystal (2BaO · TiO₂ · 2SiO₂) in an almost stoichiometric fresnoite glass. Due to the extremely high nucleation rates (10¹⁷ m⁻³ s⁻¹) that limit the maximum crystal size to 700 nm the nucleation densities and crystal sizes were estimated by scanning electron microscopy (SEM). The volume fraction crystallized was measured by X-ray diffraction. The nucleation rates obtained directly from SEM measurements reasonably agree with those calculated from the combination of overall crystallization with crystal growth kinetics. The activation enthalpies for viscous flow, transport of structural units across the nucleus/melt interface (nucleation) and crystal growth: ΔH_η, ΔH_τ and ΔH_U respectively, follow a similar trend to that observed for other stoichiometric silicate glasses that nucleate internally: ΔH_η=294>ΔH_τ=87>ΔH_U=61 kJ/mol. Fresnoite glass displays the highest internal nucleation rates so far measured in inorganic glasses. These rates are comparable to some metallic glasses and can lead to nanostructured glass-ceramics.     

A Stochastic Model for Nucleation Kinetics Determination in Droplet-Based Microfluidic Systems

The measured induction times in droplet-based microfluidic systems are stochastic and are not described by the deterministic population balances or moment equations commonly used to model the crystallization of amino acids, proteins, and active pharmaceutical ingredients. A stochastic model in the form of a Master equation is formulated for crystal nucleation in droplet-based microfluidic systems for any form of nucleation rate expression under conditions of time-varying supersaturation. An analytical solution is provided to describe the (1) time evolution of the probability of crystal nucleation, (2) the average number of crystals that will form at time t for a large number of droplets, (3) the induction time distribution, and (4) the mean, most likely, and median induction times. These expressions are used to develop methods for determining the nucleation kinetics. Nucleation kinetics are determined from induction times measured for paracetamol and lysozyme at high supersaturation in an evaporation-based high-throughput crystallization platform, which give low prediction errors when the nucleation kinetics were used to predict induction times for other experimental conditions. The proposed stochastic model is relevant to homogeneous and heterogeneous crystal nucleation in a wide range of droplet-based and microfluidic crystallization platforms.     

Study of lactose crystallization in water‐acetone solutions

This paper describes a study on the process of lactose crystallization using a water‐acetone solution. The selection of lactose was based on its significance for the pharmaceutical and food industries and on the fact that the crystallization of this organic compound has been little studied and is, unlike inorganic compounds, complex. The objective was to achieve lactose batch crystallization of solutions by analyzing the crystal growth under different operating conditions. To determine solubility curves, the experiments were carried out based on gravimetric methods. All the crystallization experiments were performed according to the methodology proposed by Nývlt in 1985, who uses the temperature at which the first crystals appear (nucleation) to establish the width of the metastable zone and the induction time. The results showed that crystals with different average diameters, shape factors, and recovered mass were obtained for different water‐acetone compositions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Size-dependent nucleation and growth kinetics model for potassium chloride—Application in Qarhan salt lake

The nucleation process and crystallization kinetics of KCl were studied in order to investigate the problems in KCl production in Qarhan salt lake. The correlation between particle size and KCl crystal growth rate was studied in a continuous mixed-suspension mixed-product removal (MSMPR) crystallizer. Classical theory of primary nucleation was used to study the homogeneous and heterogeneous nucleation mechanism of KCl crystallization. Several size-independent growth models and size-dependent growth models, such as Bransom, C-R, MJ2, ASL, and MJ3, were examined by the population balance theory. Results showed that MJ3 model closely fitted the experimental data, the mean relative deviation was 0.94%, the crystal growth rate G=2068{1−exp[−1.081×10−5(L+961.882)]}.     

Crystal growth,quality characterization and THz properties of DAST crystals

4‐N, N‐diethylamino‐4’‐N’‐methyl‐stilbazolium tosylate (DAST) crystals were grown by slope nucleation method (SNM). The crystal structure of grown DAST crystals was characterized by single crystal X‐ray diffraction with demonstrating X‐ray diffraction main peaks. The crystal defects were analyzed by the synchrotron radiation X‐ray topography. It was found that the unbalanced temperature gradient, the Teflon groove and the super saturation fluctuation were primary causes of crystal defects. Furthermore, widely tunable THz waves ranging from 1.16 to 16.71 THz were generated from 1 mm‐thick DAST crystal using the optical parametric oscillator (OPO). It was obtained that the THz output energy was 27.4 nJ (peak power of 2.74 W) and the highest conversion efficiency was 1.37 × 10⁻⁵ at 3.8 THz.     

The induction time,interfacial energy and growth mechanism of maltitol in batch cooling crystallization

Maltitol is crystallized with seeds by cooling mode in industry, often with large amount of fine crystals and wide crystal size distribution. To eliminate the fine nucleation, it's necessary to understand the nucleation kinetics. In this work, the solubility of maltitol in water was measured by the gravimetric method, the nucleation kinetics of maltitol in batch cooling crystallization was investigated using focus beam reflectance measurement (FBRM), and a novel method was proposed to determine the induction time from the trend of the crystal median chord given by FBRM. Based on the relationship between the induction time and the supersaturation, the nucleation mechanism was obtained, including homogenous nucleation at high supersaturation and heterogenous nucleation at low supersaturation. Additionally, combining the classical nucleation theory (CNT) and Arrhenius’ principle, the crystal‐solution interfacial energy and the energy barrier of homogenous nucleation were calculated. From the scanning electron microscope (SEM) images, the growth mechanism of maltitol was identified as surface nucleation growth and the surface entropy factor calculated from the kinetic analyses of t_ind data corroborated this growth mechanism.     

Nucleation Catalysis in Metastable Liquids: Inborn Active Sites

A simple formalism is developed in order to analyze the nucleation activity of inborn “week” or “strong” active sites in metastable liquids which can play in nucleation kinetics a role, similar to this of heterogeneous nucleation cores. As examples are examined the influence of Bernal holes and fluctuatively formed Frenkel voids on bubble nucleation, of athermal supercritical nuclei and heterophase fluctuations, frozen‐in in the thermal prehistory of the system on any process of phase formation, and of structural defects, due to change of composition or created in redox processes on crystallization. The analysis is performed in analogy with the known treatment of the influence of heterogeneous foreign cores on nucleation kinetics. Different changes of the metastable liquid are investigated, considering both isobaric thermal quenches and change of pressure at isothermal conditions. The effect of inborn active sites on both steady nucleation rate Iss and on nucleation time lag τ^# is investigated. In this way the whole kinetics of nucleation is constructed using the known approximative solutions of the more general, transient theory of nucleation.     

Re-examination of effects of nucleation temperature and time on glass crystallization

The effects of nucleation temperature and time on the kinetics of non-isothermal glass crystallization have been re-examined to demonstrate the limitations of some approximate solutions used to extract kinetic parameters from differential thermal analysis (DTA) experiments. Those features were analyzed by numerical solutions of equations describing the dependence of fraction crystallized on the rates of nucleation and growth, and the corresponding transient time, reported for lithium disilicate. It was shown that the temperature of maximum nucleation rate varies on changing the nucleation time. Some guidelines were established to assist the selection of suitable conditions to perform crystallization studies by DTA, and to extract the values of activation energy and dimensionality of growth from the dependences of crystallization peak temperature on heating rate, and nucleation time. The main limitations of these methods were identified and discussed.     

Growth and characterization of calcium hydrogen phosphate dihydrate crystals from single diffusion gel technique

Calcium hydrogen phosphate dihydrate (CaHPO₄·2H₂O, CHPD) a dissolved mineral in urine is known to cause renal or bladder stones in both human and animals. Growth of CHPD or brushite using sodium metasilicate gel techniques followed by light and polarizing microscopic studies revealed its structural and morphological details. Crystal identity by powder x‐ray diffraction confirmed the FT‐IR and FT‐Raman spectroscopic techniques as alternate methods for fast analysis of brushite crystals which could form as one type of renal stones. P‐O‐P asymmetric stretchings in both FT‐IR (987.2, 874.1 and 792 cm^‐1) and FT‐Raman (986.3 cm^‐1, 1057.6 cm^‐1 and 875.2 cm^‐1) were found as characteristics of brushite crystals. Differential Scanning Calorimetry (DSC) analysis revealed brushite crystallization purity using gel method by studying their endothermic peaks. This study incorporated a multidisciplinary approach in characterizing CHPD crystals grown in vitro to help formulate prevention or dissolution strategy in controlling urinary stone growth. Initial studies with 0.2 M citric acid ions as controlling agent in the nucleation of brushite crystals further support the presented approach. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Advancements (and challenges) in the study of protein crystal nucleation and growth; thermodynamic and kinetic explanations and comparison with small-molecule crystallization

This paper reviews advancements and some novel ideas (not yet covered by reviews and monographs) concerning thermodynamics and kinetics of protein crystal nucleation and growth, as well as some outcomes resulting therefrom. By accounting the role of physical and biochemical factors, the paper aims to present a comprehensive (rather than complete) review of recent studies and efforts to elucidate the protein crystallization process. Thermodynamic rules that govern both protein and small-molecule crystallization are considered firstly. The thermodynamically substantiated EBDE method (meaning equilibration between the cohesive energy which maintains the integrity of a crystalline cluster and the destructive energies tending to tear-up it) determines the supersaturation dependent size of stable nuclei (i.e., nuclei that are doomed to grow). The size of the stable nucleus is worth-considering because it is exactly related to the size of the critical crystal nucleus, and permits calculation of the latter. Besides, merely stable nuclei grow to visible crystals, and are detected experimentally. EBDE is applied for considering protein crystal nucleation in pores and hydrophobicity assisted protein crystallization. The logistic functional kinetics of nucleation (expressed as nuclei number density vs. nucleation time) explains quantitatively important aspects of the crystallization process, such as supersaturation dependence of crystal nuclei number density at fixed nucleation time and crystal size distribution (CSD) resulting from batch crystallization. It is shown that the CSD is instigated by the crystal nucleation stage, which produces an ogee-curve shaped CSD vs. crystal birth moments. Experimental results confirm both the logistic functional nucleation kinetics and the calculated CSD. And even though Ostwald ripening modifies the latter (because the smallest crystals dissolve rendering material for the growth of larger crystals), CSD during this terminal crystallization stage retains some traces of the CSD shape inherited from the nucleation stage. Another objective of this paper is to point-out some biochemical aspects of the protein crystallization, such as bond selection mechanism (BSM) of protein crystal nucleation and growth and the effect of electric fields exerted on the process. Finally, an in-silico study on crystal polymorph selection is reviewed.