Counteracting input uncertainty effects of crystallization process in achieving consistent crystal size distribution

Organic-free synthesis of ZSM-5 with narrow crystal size distribution using two-step temperature process

Crystal size and size distribution in precision controlled precipitations is modeled using the balanced nucleation-growth (BNG) process model. The BNG model predicts the experimental result that many crystallization processes lead to a limited number of crystals during a nucleation period followed by growth. The crystal size distribution, maximum crystal size, L m , number of crystals, N m , and nucleation time, t e , are modeled as a function of molar reactant addition rate during nucleation, R a , nucleation efficiency, F n , critical nucleus size, L n , and crystal maximum growth rate, G m . The model predicts that the maximum crystal size, L m , is independent of addition rate, R a , and nucleation efficiency, F n . It increases with nucleus size, L n , and crystal maximum growth rate, G m . The nucleation time, t e , is independent of addition rate, R a . It increases with increasing nucleus size, L n , and decreases with increasing nucleation efficiency, F n , and growth rate, G m . The crystal size distribution is independent of addition rate, R a , and growth rate, G m . The small size crystal population increases with increasing nucleus size, L n , and at low growth rates, G m . The crystal size distribution narrows with increasing nucleation efficiency, F n . In combination of effects, each variable has its own fingerprint and may be experimentally discerned from the others.

The ideal requirements for highly efficient evaporative crystallization in batch or semi-batch type operations are a high crystal growth rate, a high density of suspended crystalline particles in a slurry and a sharp crystal size distribution. On the other hand, the initial seed crystal conditions are also very important because they affect the crystal size and distribution during the entire period of operation. In the present study, the influence of seeding conditions (average diameter and mass) and heating rate on both the crystal growth rate of sodium chloride (NaCl) and the crystal size distribution were investigated in an optimal design draft-tube stirred vessel containing high suspension density slurries of sodium chloride particles up to 30 vol%. In order to determine the optimal seeding conditions to simultaneously achieve a high crystal growth rate and narrow size distribution, an optimal operation index Iop has been defined based on a comparison of the experimental data and a model calculation with the assumption of ideal crystal growth. The results show that Iop correlate with the particle number of seed crystals and have a maximum value. With Iop correlation, the appropriate seeding conditions for achieving a high crystal growth rate and sharp size distribution have been determined.

An assessment of calcite crystal growth mechanisms based on crystal size distributions

holocrystalline under a wide spectrum of cooling regimes implies batch system. Instead, the CSDs of each system reflect a combination that cooling and crystallization can be uncoupled and considered of kinetic and dynamic influences on crystallization. Heterogeneous separately. This is tantamount to realizing that the Avrami number nucleation and annexation of small crystals by larger ones, enis large in most igneous systems. Crystallization automatically trainment of earlier grown and ripened crystals, rate of solidification adjusts through nucleation and growth to the cooling regime, and front advance, and protracted transit of a well-established mush all aspects of the ensuing crystal population reflect the relative roles column are some of the eVects revealed in the observed CSDs. There of nucleation and growth, which reflect the cooling regime. The may be an overall CSD evolution, reflecting the maturity of characteristic scales of crystal size, crystal number, and crys- the magmatic system, from simple straight nonkinked CSDs in tallization time are intimately tied to the characteristic rates of monogenetic systems to multiply kinked, piecewise continuous CSDs nucleation and growth, but it is the crystal size distributions (CSDs) in well-established systems such as Hawaii and Mount Etna. This that provide fundamental insight on the time variations of nucleation is not unlike the evolution of CSDs in some industrial systems. and growth and also on the dynamics of magmatic systems. Crystal Finally, the fact that comagmatic CSDs are not often captured size distributions for batch systems are calculated by employing evolving systematically through large changes in nucleation rates, the Johnson‐Mehl‐Avrami equation for crystallinity related to even in low crystallinity systems, may suggest that magma is always exponential variations in time of both nucleation and growth. The laced with high population densities of nuclei, supernuclei, and slope of the CSD is set by the diVerence a ‐ b, where a and b crystallites or clusters that together set the initial CSD at high are exponential constants describing, respectively, nucleation and characteristic population densities. Further evolution of the CSD growth. The batch CSD has constant slope and systematically occurs through sustained heterogeneous nucleation and rapid anmigrates to larger crystal size (L) with increasing crystallinity. The nealing at all crystallinities beginning at the liquidus itself and diminution in nucleation with loss of melt is reflected in the CSD operating under more or less steady (not exponentially increasing) at late times by a strong decrease in population density at small rates of nucleation. crystal sizes, which is rarely seen in igneous rocks themselves. Observed CSDs suggest that a ‐ b ~6‐10 and that b ~0. That is, growth rate is approximately constant and nucleation rate apparently increases exponentially with time. Correlations among CSD slope, intercept, and maximum crystal size for both batch and open systems suggest that certain diagnostic relations may be useful in interpreting the CSD of comagmatic sequences. These systematics are explored heuristically and through the detailed

Growth histories and residence times of crystals in magmatic systems can be revealed by studying crystal sizes, size distributions and shapes. In this contribution, serial sectioning has been employed on a sample of porphyritic rhyolite from a Permo-Carboniferous laccolith from the Halle Volcanic Complex, Germany, to reconstruct the distribution of felsic phenocrysts in three dimensions in order to determine their true shapes, sizes and three-dimensional size distributions. A model of all three phenocryst phases (quartz, plagioclase, K-feldspar) with 217 crystals, and a larger model containing 1599 K-feldspar crystals was reconstructed in three dimensions. The first model revealed a non-touching framework of crystals in three dimensions, suggesting that individual crystals grew freely in the melt prior to quenching of the texture. However, crystal shapes are complex and show large variation on a Zingg diagram (intermediate over long axis plotted against short over intermediate axis). They often do not resemble the crystallographic shapes expected for phenocrysts growing unhindered from a melt, indicating complex growth histories. In contrast, the three-dimensional size distribution is a simple straight line with a negative slope. Stereologically corrected size distributions from individual sections compare well with stereologically corrected size distributions obtained previously from the same sample. However, crystal size distribution (CSD) data from individual sections scatter considerably. It is shown that CSDs can be robustly reproduced with a sampling size of greater than � 200 crystals. The kind of shape assumed in stereological correction of CSDs, however, has a large influence on the calculation and estimation of crystal residence times.

Statistical analysis of bubble and crystal size distributions: Formulations and procedures

One of the main specification of crystallisation process is the crystal size distribution (CSD). In order to achieve the desired CSD, supersaturation or temperature control is applied to maintain the concentration or temperature at the required set-point trajectory which lies within the metastable zone. The set-point trajectory can be determined using the analytical CSD estimator where both the supersaturation/concentration set-point and batch time needed to achieve the desired target CSD can be estimated. The current analytical CSD estimator is applicable only for growth dominated phenomena and neglects the effects of agglomeration and breakage phenomena. Both phenomena occurs during crystallisation operation and may influences the CSD. Both agglomeration and breakage phenomena need to be considered during crystallisation operation in order to provide an accurate set-point trajectory and also to identify the effects of both phenomena on the performance of CSD. The objective of this work is to extend the analytical CSD estimator to cover the effects of agglomeration and breakage phenomena. Here the agglomeration and breakage phenomena are represented by kinetic power law equation and incorporated into the extended analytical CSD estimator. The application of this work is highlighted through a sucrose batch cooling crystallisation process case study where based on the identified target CSD, the extended analytical estimator is capable to generate the required setpoint trajectory. The proposed controller is successfully maintained the operation at the desired set-point and achieving the target CSD in the case of agglomeration and breakage.

Modeling and control of ibuprofen crystal growth and size distribution

New perspectives for the on-line monitoring of pharmaceutical crystallization processes using in situ infrared spectroscopy

In situ monitoring and closed‐loop control of the solution crystallization process are the modern trends for pharmaceutical development, in which the critical process parameters (CPPs) as well as the product critical quality attributes (CQAs) can be regulated and guaranteed during the manufacturing process. In this study, an in situ image monitoring methodology based on a state‐of‐the‐art deep‐learning model was developed to track the CQAs such as polymorph ratio, two‐dimensional crystal size, and crystal shape in a solvent‐mediated polymorphic transformation (SMPT) process. Coupled with the multidimensional process information, a 2D population balance model (PBM) was developed and validated using the results of the in situ image‐based CQAs analysis. The 2D‐PBM was solved using a high‐resolution finite volume method (HR‐FVM) which could provide a high dimensional particle‐size distribution. Through the validation between the process image analysis and the 2D‐PBM, the accuracy of image analysis was discussed, and the potential and challenges of in situ image analysis were proposed. This work aims to integrate the crystal polymorphism and two‐dimensional crystal size distribution (2D‐CSD) information in the SMPT process using intelligent microscopic image analysis and then to validate the results of neural network processing by solving the numerical solution of the multidimensional PBM.

Effects of different seed forms on crystal size distribution for seeded batch crystallization process

A series of controlled abiotic syntheses of magnetite nanocrystals were carried out to explore the possibility of using morphological criteria, crystal size distributions, and shape ratio as tools for identifying nanocrystals that would be specifically produced by magnetotactic bacteria. High-quality magnetite crystals synthesized with various controlled total iron concentrations were shown to have cubo-octahedral shapes and sizes varying from 4 to 24 nm. The mean particle size of the population was found to be 10.5 ± 0.7 nm and no significant effect of the total iron concentration on the particle size was observed. Systematical analyses of size and morphology also allowed for the determination of crystal size and shape ratio distributions. Crystal sizes were observed to follow log-normal distributions. Shape factors are bounded by one, with maxima between 0.80 to 1.00. Their distributions are asymmetric, with a cut off toward the high values. Crystal morphologies and shape factors appear not to be a powerful diagnostic tool for the differentiation of abiotic vs. biotic particles. However, crystal size distributions of abiotic crystals are significantly different from those of biotic populations. Indeed, opposite asymmetry of the size distributions from biogenic and non biogenic crystals was observed, with cut off toward larger sizes for biogenic nanocrystals and with cut off toward smaller sizes for abiogenic nanocrystals. This therefore constitutes a potential diagnostic tool for deciphering magnetite origin.

Introducing uncertainty analysis of nucleation and crystal growth models in Process Analytical Technology (PAT) system design of crystallization processes

Manganese sulphate crystals can be produced in laboratory‐scale batch crystallisers by either heating or by salting‐out crystallisation. However, manganese sulphate produced through heating forms monohydrate while salting‐out mode will form the tetrahydrate. The effects of various operating conditions including supersaturation, temperature and seed dosage on growth rate of these hydrates were studied. The crystal size distribution of manganese sulphate crystals was determined by Malvern Mastersizer laser diffraction and by using a Nikon microscope with digital camera attached. The growth rate was determined from the time shft of the crystal size distribution expressed in population density numbers and by the moments method. The measurements of the growth of the crystals from ex situ microscopy supported the calculated growth rate. Salting‐out crystallisation resulted in relatively large cubic crystals, and their size and size distribution can be improved by careful control of the operating conditions. However, heating crystallisation produced irregular crystals where controlling the operating conditions has little effect on the final crystal size and size distribution with almost no observable growth.