Crystal Nucleation Rate Research Articles

Crystallization of Calcium Sulphate During Phosphoric Acid Production: Modeling Particle Shape and Size Distribution

A key unit operation in the production of phosphoric acid is the filtration needed to separate calcium sulphate dihydrate (CaSO4·2H2O, gypsum) crystals from an acid slurry. The filtration efficiency depends on the shape and size distribution (SSD) of the gypsum crystals produced from the upstream reactive crystallization. This article describes the construction of a first-principles model and computationally efficient numerical solver for the prediction of SSD during the reactive crystallization of gypsum while taking non-ideal phase equilibria and the effects of impurities (i.e., metal ions) into account.A population balance model couples the impurity compositions in the feed streams to the SSD for given process conditions, with the independent dimensions of the crystals being their length and width. Such a population balance model with two independent dimensions is able to represent rod-like crystals with varying aspect ratios (length/width). The compositions of all species in solution and the supersaturation driving force for crystal nucleation and growth are described using a mixed solvent electrolyte model that accounts for long-range, short-range, and ionic interactions. OLI software for computing the compositions is integrated with a Matlab implementation of the population balance model that is solved using the method of characteristics, which transforms the partial differential equations of the population balance model into a system of ordinary differential equations. This simulation method does not exhibit the numerical diffusion or dispersion common in other simulation methods, while being more computationally efficient.The crystal nucleation and growth rates are measured in a series of mixed-suspension mixed-product-removal experiments of various acid concentration, temperature, and impurity levels. A variety of models for the effects of impurities on the growth rates along the width and length dimensions are compared in terms of their ability to describe experimental observations.

Interfacial Effects on the Spherulitic Morphology of Isotactic Polystyrene Thin Films on Liquid Substrates

The influence of interfaces on the morphology of flat spherulites of isotactic polystyrene (iPS) grown in thin films on liquid substrates was investigated. Amorphous iPS thin films spin-cast from a solution were annealed for cold crystallization on glycerol and silicone oil (nonsolvents for iPS). The number density of grown spherulites was revealed to be higher on the glycerol substrate than on the silicone oil substrate. This implies that the primary nucleation rate of crystallization is greater at the iPS/glycerol interface than at the iPS/silicone oil interface. The results may be consistent with the previous findings that concern the molecular interaction between atactic polystyrene and nonsolvents at the interface. In some cases, holes were formed in the thin films during the cold crystallization due to dewetting, which also significantly affect the spherulite morphology via, for example, transcrystallization.

Lattice mold technique for the calculation of crystal nucleation rates.

We present a new simulation method for the calculation of crystal nucleation rates by computer simulation. The method is based on the use of molds to induce crystallization in state points where nucleation is a rare event. The mold is a cluster of potential energy wells placed in the lattice positions of the solid. The method has two distinct steps. In the first one the probability per unit volume of forming a sub-critical crystal cluster in the fluid is computed by means of thermodynamic integration. The thermodynamic route consists in gradually switching on an attractive interaction between the wells and the fluid particles. In the second step, the frequency with which such cluster becomes post-critical is computed in Molecular Dynamics simulations with the mold switched on. We validate our method with a continuous version of the hard sphere potential and with the sodium chloride Tosi-Fumi model. In all studied state points we obtain a good agreement with literature data obtained from other rare event simulation techniques. Our method is quite suitable for the study of both crystal nucleation of arbitrarily complex structures and the competition between different polymorphs in the nucleation stage.

The effect of elastic stresses on the thermodynamic barrier for crystal nucleation

For a variety of oxide glass-forming liquids, the thermodynamic barrier for homogeneous crystal nucleation, Wc, exhibits an unusual increase with a decrease in temperature below the maximum nucleation rate. Such behavior differs from the predictions made using the classical nucleation theory. In this article, we seek possible explanations for the increasing Wc by analyzing whether it is caused by internal elastic stresses that arise due to density misfits between the crystal and liquid phases. For this purpose, crystal nucleation rates and induction time data for two glasses that display significantly different density misfits, lithium and barium disilicates, are employed to determine the work of critical cluster formation. To explain the results, quantitative estimates of the effect of the elastic strain energy on the work required to form a critical nucleus are performed for both glasses. The interplay between stress development and relaxation is accounted for. The computations were performed, taking into account not only the possibility of precipitation of the most stable crystal phase but also that different metastable phases may form during the early stages of nucleation. We show that elastic stresses do indeed reduce the thermodynamic driving force for crystallization, and thus increase the barrier to nucleation. However, the sole effect of elastic strain energy cannot explain the aforementioned unusual behavior of the thermodynamic barrier. Hence, a comprehensive explanation to this phenomenon remains an open issue.

Solidification Atmosphere and Glass-Forming Ability of Engineering Important Fe- and Zr-Based Bulk Glassy Alloys

It is important to clarify the best solidification condition for the formation of bulk glassy alloys in Fe- and Zr-based alloy systems with engineering values. The effectiveness of atmosphere during injection casting changes in the order of O2 > Air > N2 > Ar > He for Fe76Si9B10P5 bulk glassy alloy and 105 Pa He > 105 Pa Ar > 103 Pa Ar > vacuum for Zr65Al7.5Ni10Cu17.5−xPdx (x = 0–17.5 %) bulk glassy alloys. The effectiveness of oxygen atmosphere is due to the suppression of crystal nucleation rate caused by the increase in surface tension of liquid by the dissolution of oxygen in case of Fe-based alloy. In case of Zr-based bulk glassy alloys, the He atmosphere is effective due to the maintenance of cleanness of alloy liquid as well as the increase in the cooling rate. The opposite tendency of the effectiveness for helium atmosphere in the same injection casting is important for further development of the production techniques for large-scale Fe- and Zr-based bulk glassy alloys.

Energy-saving continuous fractionation and deep purification of organic materials by zonal melting

Energy-saving continuous fractionation and deep purification of organic material by zonal melting is considered. This approach permits the combination of various purification methods: fractionation by directional and/or counterflow solidification; and deep purification by single-zone or multizone melting. Simplified (for engineering use) and more detailed mathematical descriptions of the solidification of a binary melt with a stable phase boundary are considered. The rates of crystal nucleation and growth in binary melts are taken into account, as well as the influence of mass transfer on the heat transfer, the thermal diffusion, and the need for considerable temperature gradients. The mathematical descriptions employ effective distribution coefficients of the components that take account of the change in boundary-layer thickness on solidification (melting). The discrepancy between practical experience and the calculation results is no more than 10%, with 95% probability. An industrial system for continuous deep purification by zonal melting is proposed. It is based on a roller crystallization unit. A general mathematical description of the solidification of a binary melt is formulated and provides the basis for a simplified mathematical description and an algorithm for its solution in engineering calculations.

Influence of preformed nuclei on crystal nucleation kinetics in soda–lime–silica glass

An unusual form of the time-dependence of the number N(t, Tn) of nucleated at a temperature Tn crystals was obtained for a soda–lime–silica glass of the composition 22.4Na2O·28.0CaO·49.6SiO2 (mol.%). The crystals are solid solutions based on the Na2O·2CaO·3SiO2 compound. The analysis of the nucleation kinetics was performed for a nucleation temperature Tn located well below the temperature of the maximum of the steady-state crystal nucleation rate. Following to the development method, supercritical clusters formed at the temperature Tn have been developed at a temperature Td>Tn in order to reach measurable sizes. A large number of crystals, N(t, Tn, Td)=No, was detected by this method already at t=0. With an increasing nucleation time, the number of developed crystals gradually increases with a temporary tendency towards saturation. After this transient stage, the crystal number gradually increases again and a linear N(t, Tn, Td)-dependence corresponding to the steady state nucleation rate is established. These uncommon features are the consequence of the growth at the nucleation temperature of the nuclei preformed in the course of glass preparation with sizes between critical sizes corresponding to the nucleation Tn and development Td temperatures.

Preparation and Antiscaling Application of Superhydrophobic Anodized CuO Nanowire Surfaces

Antiscaling technology is necessary in order to prevent the performance loss and blockage of heat exchangers. In this research, a superhydrophobic CuO nanowire layer was prepared and utilized for antiscaling process of CaCO3 on the surface of copper. Modified with 1H,1H,2H,2H-perfluorodecyltriethoxysilane (FAS-17), the water contact angle on the CuO surface increased sharply from 4.5° ± 1° after anodization to 154° ± 2°, since the surface free energy decreased from 74.8 mJ/m2 for the hydrophilic surface to 0.2 mJ/m2 for the superhydrophobic surface. The scale inhibition performance of the surface of superhydrophobic CuO nanowires was confirmed since the corresponding scaling weight of deposited CaCO3 decreased significantly from 0.6322 mg/cm2 to 0.1607 mg/cm2. This attractive antiscaling effect of the modified superhydrophobic CuO nanowire surface should ascribe to the slow CaCO3 crystal nucleation rate, because of the low surface energy, low adhesion strength of CaCO3 crystal, and air film retained on th...

Fabrication of composite particles through single pass using a coaxial tube reactor

Composite particles were prepared by liquid–liquid interfacial crystallization in a coaxial tubular reactor. A microfluidic channel was utilized for controlling particle properties and fabricating composite particles via a single pass in a continuous flow process. Changes in flow patterns with Weber number were investigated by visualizing flow patterns in the reactor; four types of flow patterns were observed. Particle size distributions of sodium chloride (NaCl) in the reactor were optimized by controlling flow patterns. Crystal nucleation rates and growth rates were calculated using the Rosin–Rammler distribution, which is also used in conventional crystallizers. Indomethacin (IMC) crystals with a fibrous morphology were obtained in any of three flow patterns by ultrasonic irradiation of the tube reactor; however, precipitation of IMC did not occur without ultrasonic irradiation. Composite particles of NaCl and IMC were produced by ultrasonic irradiation in a dispersed flow. The process involving dispersed flow could be used to continuously fabricate composite particles in a single pass through the reactor.

Kinetic model for calcium sulfate α-hemihydrate produced hydrothermally from gypsum formed by flue gas desulfurization

Modeling of the kinetics of the synthesis process for calcium sulfate α-hemihydrate from gypsum formed by flue gas desulfurization (FGD) is important to produce high-performance products with minimal costs and production cycles under hydrothermal conditions. In this study, a model was established by horizontally translating the obtained crystal size distribution (CSD) to the CSD of the stable phase during the transformation process. A simple method was used to obtain the nucleation and growth rates. A nonlinear optimization algorithm method was employed to determine the kinetic parameters. The model can be successfully used to analyze the transformation kinetics of FGD gypsum to α-hemihydrate in an isothermal batch crystallizer. The results showed that the transformation temperature and stirring speed exhibit a significant influence on the crystal growth and nucleation rates of α-hemihydrate, thus altering the transformation time and CSD of the final products. The characteristics obtained by the proposed model can potentially be used in the production of α-hemihydrate.

On the reaction coordinate for seeded crystallisation

Small pre-structured seeds introduced into an undercooled fluid are known to increase the crystal nucleation rate by some orders of magnitude, if the structure of the seeds is commensurate with the bulk crystalline phase. The presence of such seeds also alters the crystallisation mechanism by favouring particular structures at the early stages of the nucleation process. Here, we study with computer simulations the effect of small face-centred cubic and body-centred cubic seeds on the crystallisation of a Lennard-Jones liquid in the strongly undercooled regime. We find that seeds with body-centred cubic structure lead to a larger enhancement of the crystallisation rate than face-centred cubic seeds. An analysis of recurrence times reveals that the size of the largest crystalline cluster used as reaction coordinate is affected by pronounced memory effects, which depend on the particular seed structure and point to the importance of structural information in the definition of a good reaction coordinate for crystallisation.

Shape- and size-dependent catalysis activities of iron-terephthalic acid metal-organic frameworks

Precise control of the size and morphology of metal-organic frameworks (MOFs) presents an important direction for extending these inorganic-organic materials to many more advanced applications. However, because of the limit of the crystal-growth rule and mechanism, good-control of the size and morphology of MOFs remains challenging. In this contribution, an iron-terephthalic acid metal-organic framework with different shapes (octahedron, spindle and bipyramidal hexagonal) was easily and reproducibly synthesized via a solvothermal method. Sodium acetate and glycerol were used as modulators. Mechanism studies showed that the crystal nucleation rate and orientational growth both play important roles in determining the final shape of the MOFs. Further investigations showed that the as prepared MOFs exhibit shape-dependent catalytic activities, which means that MOFs can be designed to perform different catalytic functions. This investigation not only provides an effective guideline for the precise control of the size and morphology of metal-organic frameworks, but also extends MOFs to much more advanced applications in terms of catalyst chemistry.

Transmission X-Ray Microscopy of the Galvanostatic Growth of Lead Sulfate on Lead: Impact of Lignosulfonate

The galvanostatic growth of PbSO4 on Pb in H2SO4 was studied using scanning electron microscopy and in situ transmission X-ray microscopy (TXM). Images from the TXM are used to investigate the effects of sodium lignosulfonate on the PbSO4 formation and the initial growth of the PbSO4 crystals. Sodium lignosulfonate is shown to retard, on average, the growth of the PbSO4 crystals, yielding a film with smaller crystals and higher crystal densities. In addition, results from experiments with and without sodium lignosulfonate indicate an increase in the nucleation rate of the PbSO4 crystals when the oxidation current is applied, which was attributed to an increase in the supersaturation of the electrolyte. Furthermore, an analysis of the growth rates of individual, large crystals showed an initial rapid growth which declined as the PbSO4 surface coverage increased. It was concluded that the increase in PbSO4 provides additional sites for precipitation and reduces the precipitation rate on the existing crystals. Finally, the potential-time transient at the beginning of oxidation is suggested to result from the relaxation of a supersaturated solution and the development of a PbSO4 film with increasing resistance.

Computing the crystal growth rate by the interface pinning method.

An essential parameter for crystal growth is the kinetic coefficient given by the proportionality between supercooling and average growth velocity. Here, we show that this coefficient can be computed in a single equilibrium simulation using the interface pinning method where two-phase configurations are stabilized by adding a spring-like bias field coupling to an order-parameter that discriminates between the two phases. Crystal growth is a Smoluchowski process and the crystal growth rate can, therefore, be computed from the terminal exponential relaxation of the order parameter. The approach is investigated in detail for the Lennard-Jones model. We find that the kinetic coefficient scales as the inverse square-root of temperature along the high temperature part of the melting line. The practical usability of the method is demonstrated by computing the kinetic coefficient of the elements Na and Si from first principles. A generalized version of the method may be used for computing the rates of crystal nucleation or other rare events.

Measuring induction times and crystal nucleation rates

A large variation is observed in induction times measured under equal conditions in 1 ml solutions. Ruling out experimental errors, this variation originates from the nucleation process. The induction time distribution is explained by the stochastic nature of nucleation if the number of nuclei formed is approaching 1 per vial. Accurate heterogeneous crystal nucleation rates were determined from the induction time distributions on a 1 ml scale for racemic diprophylline in two solvents. The difference in nucleation behaviour in the two solvents originates from the energy barrier for nucleation, which is much higher in the solvent in which induction times are much longer. In addition the pre-exponential factor for the crystal nucleation rate in both solvents is rather low compared to predictions using Classical Nucleation Theory. Unfortunately, concentration and surface characteristics of the effective heterogeneous particles are not known which clouds a further molecular interpretation.

Nucleation of crystals in sodium-calcium-silicate glasses of the metasilicate section

Nucleation of crystals in sodium-calcium-silicate glasses of the quasi-binary metasilicate section CaO · SiO2-Na2O · SiO2 has been investigated by the development method. The maximal stationary rate of crystal nucleation in the composition range Na2O · 2CaO · 3SiO2-Na2O · CaO · 2SiO2 increases substantially with the increase of the sodium oxide content. It was assumed that in this range, along with nucleation of crystals of solid solutions based on Na2O · 2CaO · 3SiO2, nucleation of crystals 2Na2O · CaO · 3SiO2 could occur as well. Nucleation of crystals of the above two phases in glass of the composition 28.4Na2O · 21.2CaO · 50.4SiO2 (mol %) from the middle of the range Na2O · CaO · 2SiO2-2Na2O · CaO · 3SiO2 has been studied.

Facile synthesis and enhanced visible-light photocatalytic activity of micro/nanostructured Ag2ZnGeO4 hollow spheres

Micro/nanostructured Ag2ZnGeO4 hollow spheres were successfully synthesized by a one-step and low-temperature route under ambient pressure. The micro/nanostructured Ag2ZnGeO4 hollow spheres have a diameter of 1–2 μm and their shells are composed of numerous nanoparticles and nanorods. The growth process of the micro/nanostructured Ag2ZnGeO4 hollow spheres was investigated in detail. The results indicated that the morphologies and composition of Ag2ZnGeO4 samples were strongly dependent on the dose of the AgNO3 and reaction time. Excessive AgNO3 was favorable for the nucleation and growth rate of Ag2ZnGeO4 crystals and the formation of pure Ag2ZnGeO4. Moreover, the formation mechanism of the micro/nanostructured Ag2ZnGeO4 hollow spheres is related to the Ostwald ripening. Under the same conditions, the photocatalytic activity of micro/nanostructured Ag2ZnGeO4 hollow spheres is about 1.7 times and 11 times higher than that of bulk Ag2ZnGeO4 and Degussa P25, respectively. These interesting findings could provide new insight on the synthesis of micro/nanostructured ternary-metal oxides with enhanced photocatalytic activity.

Effects of lithium oxide on the crystallization kinetics of Na2O·2CaO·3SiO2 glass

The crystal nucleation (I) and growth (U) rates of Na2O·2CaO·3SiO2 glasses with increasing additions of Li2O were measured for the primary crystalline phase over wide and overlapping temperature intervals. A partial section of the phase diagram Na2O·2CaO·3SiO2–Li2O was constructed via DSC analysis and shows a narrow range of solid solution formation that is close to that of Na2O·2CaO·3SiO2. In the four-component system (Na2O–Li2O–CaO–SiO2), a pseudo-binary eutectic system of Na2O·2CaO·3SiO2–Li2O·SiO2 exists. The role of Li2O in the formation of the crystalline phases was investigated using DSC and X-ray analyses. The addition of Li2O results in decreases in the glass transition (Tg) and liquidus (TL) temperatures. With increasing Li2O content, both the reduced glass transition temperature Tgr (Tgr=Tg/TL) and the fragility index, m, pass through a minimum. These findings extend and confirm the known inverse correlation between Tgr and Imax (lower values of Tgr correspond to higher values of Imax) and provide evidence for a similar correlation between m and Imax. When using the low temperature data for the crystal growth rate (U) the viscosity (η) and diffusivity (D) were decoupled at T<1.1 Tg. Next, a parameter (U·η at Tg) that characterized the decoupling phenomenon was proposed.

Controlled synthesis and visible light photocatalytic activity of Bi12GeO20 uniform microcrystals.

We successfully synthesized uniform Bi12GeO20 microspheres and microtetrahedrons enclosed by four {111} facets using a controlled hydrothermal method for the first time. The photocatalytic activity of these regular-shaped products was further investigated by the degradation of RhB and gaseous formaldehyde under visible light irradiation (λ>420 nm). The Bi12GeO20 microtetrahedrons (s) exhibited enhanced photocatalytic activity and stability which is closely related to the high capacity of exposed {111} facets for uptake of O2. The formation mechanism studies indicate that the Bi12GeO20 seeds were directed to grow into truncated microcubes, truncated microtetrahedrons, and then microtetrahedrons when the NaOH concentration was 5 M. The same batch of seeds only evolved into microspheres when the NaOH concentration was switched to 3 M. The difference in Bi12GeO20 morphology could be attributed to the rates of both crystal nucleation and crystal growth.

Emulsion-Based Technique To Measure Protein Crystal Nucleation Rates of Lysozyme

We measured the nucleation rates of lysozyme protein crystals using microfluidically produced emulsion drops containing supersaturated protein solution. The technique involves quenching several thousand independent nanoliter drops by rapidly lowering the temperature and then counting the number of drops that have not nucleated as a function of time at constant temperature. We fit the number distribution to a theoretical model developed by Pound and La Mer (J. Am. Chem. Soc. 1952, 74, 2323–2332) for heterogeneous nucleation and extract two nucleation rates and the number of nucleation sites per drop. We describe the technique in detail and present our analysis of the measured nucleation rates within the context of Classical Nucleation Theory, which adequately describes our observations. Of the two nucleation rates, one is a slow rate that varies with temperature and one is a fast rate independent of temperature. The nucleation barrier and kinetic prefactors are obtained for each rate. Notably, there is no detectable barrier for the fast rate. Both rates are inconsistent with the process of homogeneous nucleation and are consistent with heterogeneous nucleation.