Journal articles: 'Crystal Size Distribution (CSD)'

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Chou, S. T., and J. P. Hsu. "Stochastic analysis of the Transient Behavior of an msmpr Crystallizer." Probability in the Engineering and Informational Sciences 1, no. 4 (1987): 383–404. http://dx.doi.org/10.1017/s0269964800000474.

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The transient crystal size distribution (CSD) in a continuous mixed suspension, mixed product removal crystallizer has been modeled through a stochastic approach. Effects of the seed size distribution and size-dependent growth rate on both the transient and steady-state CSD have been investigated. It has been found that the seed size distribution causes a maximum in the steady-state CSD and the size-dependent growth rate results in an upward curvature at the lower end in a semilogarithmic plot of steady-state CSD against crystal size. Under appropriate conditions, the mean CSD of the present stochastic model reduces to the results predicted by the corresponding deterministic population balance model.

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Neher, Sigmund H., Helmut Klein, and Werner F. Kuhs. "FXD-CSD-GUI: a graphical user interface for the X-ray-diffraction-based determination of crystallite size distributions." Journal of Applied Crystallography 52, no. 6 (2019): 1437–39. http://dx.doi.org/10.1107/s1600576719012159.

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Bragg intensities can be used to analyse crystal size distributions in a method called FXD-CSD, which is based on the fast measurement of many Bragg spots using two-dimensional detectors. This work presents the Python-based software and its graphical user interface FXD-CSD-GUI. The GUI enables user-friendly data handling and processing and provides both graphical and numerical crystal size distribution results.

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Neher, Sigmund H., Helmut Klein, and Werner F. Kuhs. "A fast X-ray-diffraction-based method for the determination of crystal size distributions (FXD-CSD)." Journal of Applied Crystallography 51, no. 5 (2018): 1352–71. http://dx.doi.org/10.1107/s1600576718010567.

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A procedure for a fast X-ray-diffraction-based crystal size distribution analysis, named FXD-CSD, is presented. The method enables the user, with minimal sample preparation, to determine the crystal size distribution (CSD) of crystalline powders or polycrystalline materials, derivedviaan intensity scaling procedure from the diffraction intensities of single Bragg spots measured in spotty diffraction patterns with a two-dimensional detector. The method can be implemented on any single-crystal laboratory diffractometer and any synchrotron-based instrument with a fast-readout two-dimensional detector and a precise sample scanning axis. The intensity scaling is achievedviathe measurement of areferencesample with known CSD under identical conditions; the only other prerequisite is that the structure (factors) of bothsampleandreferencematerial must be known. The data analysis is done with a software package written in Python. A detailed account is given of each step of the procedure, including the measurement strategy and the demands on the spottiness of the diffraction rings, the data reduction and the intensity corrections needed, and the data evaluation and the requirements for the reference material. Using commercial laboratory X-ray equipment, several corundum crystal size fractions with precisely known CSD were measured and analysed to verify the accuracy and precision of the FXD-CSD method; a comparison of known and deduced CSDs shows good agreement both in mean size and in the shape of the size distribution. For the used material and diffractometer setup, the crystal size application range is one to several tens of micrometres; this range is highly material and X-ray source dependent and can easily be extended on synchrotron sources to cover the range from below 0.5 µm to over 100 µm. FXD-CSD has the potential to become a generally applicable method for CSD determination in the field of materials science and pharmaceutics, including development and quality management, as well as in various areas of fundamental research in physics, chemistry, chemical engineering, crystallography, the geological sciences and bio-crystallization. It can be used also underin situconditions for studying crystal coarsening phenomena, and delivers precise and accurate CSDs, permitting experimental tests of various theories developed to predict their evolution.

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Wirz, Dominic, Marc Hofmann, Heike Lorenz, Hans-Jörg Bart, Andreas Seidel-Morgenstern, and Erik Temmel. "A Novel Shadowgraphic Inline Measurement Technique for Image-Based Crystal Size Distribution Analysis." Crystals 10, no. 9 (2020): 740. http://dx.doi.org/10.3390/cryst10090740.

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A novel shadowgraphic inline probe to measure crystal size distributions (CSD), based on acquired greyscale images, is evaluated in terms of elevated temperatures and fragile crystals, and compared to well-established, alternative online and offline measurement techniques, i.e., sieving analysis and online microscopy. Additionally, the operation limits, with respect to temperature, supersaturation, suspension, and optical density, are investigated. Two different substance systems, potassium dihydrogen phosphate (prisms) and thiamine hydrochloride (needles), are crystallized for this purpose at 25 L scale. Crystal phases of the well-known KH2PO4/H2O system are measured continuously by the inline probe and in a bypass by the online microscope during cooling crystallizations. Both measurement techniques show similar results with respect to the crystal size distribution, except for higher temperatures, where the bypass variant tends to fail due to blockage. Thiamine hydrochloride, a substance forming long and fragile needles in aqueous solutions, is solidified with an anti-solvent crystallization with ethanol. The novel inline probe could identify a new field of application for image-based crystal size distribution measurements, with respect to difficult particle shapes (needles) and elevated temperatures, which cannot be evaluated with common techniques.

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Higgins, Michael D. "Closure in crystal size distributions (CSD), verification of CSD calculations, and the significance of CSD fans." American Mineralogist 87, no. 1 (2002): 171–75. http://dx.doi.org/10.2138/am-2002-0118.

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Nanev, Christo N. "On some aspects of crystallization process energetics, logistic new phase nucleation kinetics, crystal size distribution and Ostwald ripening." Journal of Applied Crystallography 50, no. 4 (2017): 1021–27. http://dx.doi.org/10.1107/s1600576717007105.

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Nucleation, nucleus number densities, and the respective supersaturation dependence, crystal growth and Ostwald ripening are reconsidered from the energetics perspective. Supersaturation-dependent critical nucleus sizes are calculated accordingly. It is argued that the logistic time-dependent nucleation resembles one period of a harmonic oscillation. The general conclusion is that a crystallizing system adapts to the distorting influence of the supersaturation imposed, and during crystal nucleation and growth, the system gradually consumes this supersaturation to reach a new equilibrium state at the end of Ostwald ripening (completely exhausted supersaturation). This is an indication that the system responds to the change in its energetic status according to the well known Le Châtelier–Braun principle. The extent to which the nucleation process affects the crystal size distribution (CSD) is also discussed. Slightly altered by the crystal growth, the CSD also preserves some trace of the nucleation stage shape during Ostwald ripening.

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Rusi, M., and P. Hoxha. "CSD correction as a tool for estimating 3d block size distribution." Bulletin of the Geological Society of Greece 47, no. 4 (2013): 1854. http://dx.doi.org/10.12681/bgsg.11065.

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For the headrace Moglicë-Grabovë, part of Devoll Hydropower Project in Albania, two different techniques of tunnelling are planned: DS TBM for the Flysch series starting in Moglicë and Drill & Blast for the Ophiolite section, starting in Grabovë. A major question concerning the tunnelling seems to find the point where DS-TBM excavation from the Moglicë side should stop to “wait” for the Drill&Blast excavation from the Shemsit access tunnel side. Assumed that the so called “block in matrix” rock mass is very unfavourable, respectively disqualifying for TBM excavation. These mixtures of hard blocks embedded in weaker and finer matrix that are very difficult to characterize, frequently challenge the engineering geologists with the characterization, design and construction problems associated with them. Evaluating Block Size Distribution in the BiM rock zone of this project area has been only the first step in characterizing all the geological and geotechnical parameters of the rock mass which will influence a decision that has major economic consequences. CSDCorrections 1.39 is the program used to convert the two dimensional data gathered from thin sections, outcrops, photographs etc. to true three dimensional crystal size distributions (CSD).

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Shao, Lixiong, Jiang Diao, Wang Zhou, Tao Zhang, and Bing Xie. "Non-isothermal crystallization behavior of spinel crystals in FeO-SiO2-TiO2-V2O3-Cr2O3 slag." Metallurgical Research & Technology 116, no. 1 (2018): 110. http://dx.doi.org/10.1051/metal/2018033.

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The growth behaviour of spinel crystals in vanadium slag with high Cr2O3 content was investigated and clarified by statistical analyses based on the Crystal Size Distribution (CSD) theory. The results indicate that low cooling rate and Cr2O3 content benefit the growth of spinel crystals. The chromium spinel crystals firstly precipitated and then acted as the heterogeneous nuclei of vanadium and titanium spinel crystals. The growth mechanisms of the spinel crystals at the cooling rate of 5 K/min consist two regimes: firstly, nucleation control in the temperature range of 1873 to 1773 K, in which the shapes of CSD curves are asymptotic; secondly, surface and supply control within the temperature range of 1773 to 1473 K, in which the shapes of CSD curves are lognormal. The mean diameter of spinel crystals increases from 3.97 to 52.21 µm with the decrease of temperature from 1873 to 1473 K.

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Synowiec, Piotr Maria, and Magdalena Stec. "Analysis of CaF2 Precipitation Process in the Selected Static Mixers." Journal of Chemistry 2019 (February 11, 2019): 1–20. http://dx.doi.org/10.1155/2019/6728492.

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In the paper, the analysis of the precipitation process of calcium fluoride in the selected static mixers was made. The Kenics and Koflo static mixers, as well as an empty pipe as a background, have been taken into consideration. The Kenics and Koflo types have been chosen as their inner shapes convenient for the realization of continuous precipitation processes as incrustation phenomenon and dangerousness of flow blocking are not as high as in other solutions. The main tasks were focused on the recognition of the precipitation kinetics (to get the knowledge of the relative supersaturation, nucleation sources, and mechanisms controlling the crystal growth), determination of conversion efficiency of the chemical reaction by which CaF2 is precipitated, the fluid dynamic conditions on crystal size distribution (CSD), and the identification of particles’ destruction sources as well. This paper is a primary work dedicated to the possibilities of a special treatment of the solid phase during its formation in order to obtain the required crystal size distribution (CSD) and to avoid the agglomeration when necessary. The results are very promising. As it will be shown, the special treatment of the precipitated solid substances in static mixers enables to create crystals with the required size and to eliminate the agglomeration phenomenon.

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10

Rohani, S. "Dynamic study and control of crystal size distribution (CSD) in a KCL crystallizer." Canadian Journal of Chemical Engineering 64, no. 1 (1986): 112–16. http://dx.doi.org/10.1002/cjce.5450640116.

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Cashman, Katharine V., and John M. Ferry. "Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization." Contributions to Mineralogy and Petrology 99, no. 4 (1988): 401–15. http://dx.doi.org/10.1007/bf00371933.

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Marsh, Bruce D. "Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization." Contributions to Mineralogy and Petrology 99, no. 3 (1988): 277–91. http://dx.doi.org/10.1007/bf00375362.

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13

Hash, Juliana, and Ogbonnaya C. Okorafor. "Crystal size distribution (CSD) of batch salting-out crystallization process for sodium sulfate." Chemical Engineering and Processing: Process Intensification 47, no. 4 (2008): 622–32. http://dx.doi.org/10.1016/j.cep.2006.12.006.

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Ruan, Chunlei, Kunfeng Liang, Xianjie Chang, and Ling Zhang. "Weighted Essentially Nonoscillatory Method for Two-Dimensional Population Balance Equations in Crystallization." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/125128.

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Population balance equations (PBEs) are the main governing equations to model the processes of crystallization. Two-dimensional PBEs refer to the crystals that grow anisotropically with the change of two internal coordinates. Since the PBEs are hyperbolic equations, it is necessary to build up high resolution schemes to avoid numerical diffusion and numerical dispersion in order to obtain the accurate crystal size distribution (CSD). In this work, a 5th order weighted essentially nonoscillatory (WENO) method is introduced to compute the two-dimensional PBEs. Several numerical benchmark examples from literatures are carried out; it is found that WENO method has higher resolution than HR method which is well established. Therefore, WENO method is recommended in crystallization simulation when the crystal size distributions are sharp and higher accuracy is needed.

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MAGEE, C., B. O'DRISCOLL, and A. D. CHAMBERS. "Crystallization and textural evolution of a closed-system magma chamber: insights from a crystal size distribution study of the Lilloise layered intrusion, East Greenland." Geological Magazine 147, no. 3 (2010): 363–79. http://dx.doi.org/10.1017/s0016756809990689.

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AbstractThe recognition that postcumulus processes significantly modify primary textures in layered mafic intrusions has thrown into question many early observations on which classical crystallization theories are based. Petrographic observations combined with quantitative textural analysis of samples from various stratigraphic levels of the Lilloise intrusion, East Greenland, demonstrate that postcumulus textural modification of cumulates, formed during the solidification of a closed system magma chamber, may be detected. Crystal size distribution (CSD) measurements of Lilloise cumulates and the resulting CSD profiles are compared to predicted theoretical closed system CSD profiles. Similarities between the measured CSD profiles and published predicted CSD profiles support Lilloise magma evolving in a closed system chamber and indicate that primary crystallization processes can be distinguished using quantitative textural techniques. Textural coarsening driven by syn-magmatic deformation is suggested to be the dominant postcumulus process affecting CSD plot morphology. CSD slope values and profiles (plot shapes) remain relatively constant for a given liquidus mineral (particularly olivine and clinopyroxene), so that the number of phases on the liquidus at any one time affects mineral modal abundances. As a result, CSDs generally exhibit overall smaller grainsizes and progressively lower nucleation densities at higher levels in the intrusion.

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LENTZE, RACHEL C. F., and Harry Y. McSWEEN. "Crystallization of the basaltic shergottites: Insights from crystal size distribution (CSD) analysis of pyroxenes." Meteoritics & Planetary Science 35, no. 5 (2000): 919–27. http://dx.doi.org/10.1111/j.1945-5100.2000.tb01481.x.

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Orehek, Jaka, Matic Češnovar, Dušan Teslić, and Blaž Likozar. "Mechanistic crystal size distribution (CSD)-based modelling of continuous antisolvent crystallization of benzoic acid." Chemical Engineering Research and Design 170 (June 2021): 256–69. http://dx.doi.org/10.1016/j.cherd.2021.04.007.

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Wang, Xiang Tian, Jian Hai Zhao, Xing Fu Song, Jin Wang, and Jian Guo Yu. "Preparation of Anhydrous Magnesium Chloride from Bischofite (MgCl₂·6H₂O) I. Reaction Crystallization of Magnesium Chloride Hexammoniate." Materials Science Forum 488-489 (July 2005): 57–60. http://dx.doi.org/10.4028/www.scientific.net/msf.488-489.57.

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Magnesium chloride hexammoniate (MgCl2·6NH3) is an intermediate product for preparation anhydrous magnesium chloride by reaction crystallization method. An experiment study of a semi-batch reaction crystallization is presented. In a single feed operation, magnesium chloride solution is fed to a stirred methanol solution mixed with ammonia to crystallize magnesium chloride hexammoniate. The median crystal size of product increases with increasing stirring rate, reaches a maximum, and then decreases again. Decreasing feed rate or decreasing stirring time increases the crystal size significantly. The reaction temperature and concentration of magnesium ion can also influence the crystal size distribution (CSD). A double feed operation can create larger crystal size than that of single feed operation. The relationship between crystal size and the content of water of the product is discussed.

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Synowiec, Piotr. "How to improve the crystal size distribution (CSD) in crystallizers with the inner suspension circulation." Chemical Engineering and Processing: Process Intensification 41, no. 7 (2002): 585–93. http://dx.doi.org/10.1016/s0255-2701(01)00178-7.

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Tang, Mingliang, Xuerun Li, Yusheng Shen та Xiaodong Shen. "Kinetic model for calcium sulfate α-hemihydrate produced hydrothermally from gypsum formed by flue gas desulfurization". Journal of Applied Crystallography 48, № 3 (2015): 827–35. http://dx.doi.org/10.1107/s1600576715007141.

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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.

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Lormand, Charline, Georg F. Zellmer, Károly Németh, et al. "Weka Trainable Segmentation Plugin in ImageJ: A Semi-Automatic Tool Applied to Crystal Size Distributions of Microlites in Volcanic Rocks." Microscopy and Microanalysis 24, no. 6 (2018): 667–75. http://dx.doi.org/10.1017/s1431927618015428.

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AbstractCrystals within volcanic rocks record geochemical and textural signatures during magmatic evolution before eruption. Clues to this magmatic history can be examined using crystal size distribution (CSD) studies. The analysis of CSDs is a standard petrological tool, but laborious due to manual hand-drawing of crystal margins. The trainable Weka segmentation (TWS) plugin in ImageJ is a promising alternative. It uses machine learning and image segmentation to classify an image. We recorded back-scattered electron (BSE) images of three volcanic samples with different crystallinity (35, 50 and ≥85 vol. %), using scanning electron microscopes (SEM) of variable image resolutions, which we then tested using TWS. Crystal measurements obtained from the automatically segmented images are compared with those of the manual segmentation. Samples up to 50 vol. % crystallinity are successfully segmented using TWS. Segmentation at significantly higher crystallinities fails, as crystal boundaries cannot be distinguished. Accuracy performance tests for the TWS classifiers yield high F-scores (>0.930), hence, TWS is a successful and fast computing tool for outlining crystals from BSE images of glassy rocks. Finally, reliable CSD’s can be derived using a low-cost desktop SEM, paving the way for a wide range of research to take advantage of this new petrological method.

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Cashman, Katharine V., and Bruce D. Marsh. "Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization II: Makaopuhi lava lake." Contributions to Mineralogy and Petrology 99, no. 3 (1988): 292–305. http://dx.doi.org/10.1007/bf00375363.

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Svetov, Sergei A., Svetlana Y. Chazhengina, and Alexandra V. Stepanova. "Geochemistry and Texture of Clinopyroxene Phenocrysts from Paleoproterozoic Picrobasalts, Karelian Craton, Fennoscandian Shield: Records of Magma Mixing Processes." Minerals 10, no. 5 (2020): 434. http://dx.doi.org/10.3390/min10050434.

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This paper presents an integrated major and trace element data and crystal size distribution analysis for zoned clinopyroxene phenocrysts hosted in variolitic and massive picrobasalts of the Suisaari Formation, Karelian Craton, Eastern Fennoscandian Shield. Clinopyroxenes in variolitic and massive lavas occur as unzoned, reverse, and normally zoned crystal. Oscillatory-zoned clinopyroxenes are only observed in variolitic lavas. The obtained data were examined in order to evaluate the contribution of magmatic processes such as magma mixing, contamination and fractional crystallization to the formation of various zoning patterns of clinopyroxene phenocrysts. Clinopyroxene phenocrysts in both variolitic and massive lavas originate from similar primary melts from a single magmatic source. The obtained data on composition and texture of clinopyroxene phenocrysts together with the crystal size distribution (CSD) analysis suggest that crystallization of the massive lavas mainly involves fractionation in a closed magmatic system, whereas the crystallization of the variolitic lavas is determined by processes in an open magmatic system. The results provide novel information on the evolution of Paleoproterozoic magmatic systems in the Karelian Craton.

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Hojjati, Hossein, and Sohrab Rohani. "Cooling and seeding effect on supersaturation and final crystal size distribution (CSD) of ammonium sulphate in a batch crystallizer." Chemical Engineering and Processing: Process Intensification 44, no. 9 (2005): 949–57. http://dx.doi.org/10.1016/j.cep.2004.11.003.

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Zheng, Dan, Jie Yan, Jun Chen, and Zeqin Wang. "The Reaction Extraction Combining Crystallization for Growth of Sodium Chloride in a Spray Fluidized Bed Crystallizer." Journal of Chemistry 2020 (November 27, 2020): 1–12. http://dx.doi.org/10.1155/2020/8307847.

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At present, the crystal size of sodium chloride prepared by a traditional crystallization process (such as stirred crystallization) is inhomogeneous, and it has a great quantity of fine grains in crystallizer. This work presents a novel approach for the growth of sodium chloride from supersaturated solutions by reaction-extractive crystallization in a spray fluidized bed crystallizer (SFBC), in which sodium sulfate solution is transformed into potassium chloride and sulphuric acid based on a reactive extraction-crystallization process using triisooctylamine (TOL) in n-octanol as the extraction system. This paper mainly studies the effect of operating conditions (e.g., circulation flow rate, velocity ratio of oil and aqueous phases, crystallization temperature, hydraulic residence time, and feed velocity) on the crystal size distribution (CSD) during the crystallization process of sodium chloride in a SFBC. Experimental results show that the optimum conditions are 1.0362 m/s as the best circulation flow rate, 9.5 : 8.5 as the best velocity ratio of oil and aqueous phases, 313 K as the best temperature, 4320 s as residence time, and 8 mL.min−1 as the best feed velocity. Meanwhile, the proposed extraction kinetic model about extraction rates is developed and validated against data from the SFBC. And it proves that the reactive extraction system is controlled by diffusion and chemical reaction. Analysis of the extraction kinetic model and comparison with experiments reveal that the extraction kinetic model results are in well agreement with experiments. Furthermore, the uniform and large crystals can be obtained in a spray fluidized bed crystallizer without special concentration since extraction and crystallization are carried out in the same equipment. In addition, all of the sodium chloride products prepared under the optimal conditions in SFBC show a better CSD performance than the stirred crystallization. This research demonstrates that this process enables controlling the crystal size in a rather wide range, thus further underlining the potential of this technique for applications in the crystallization industry.

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Öner, Merve, Francis Tran, Gitte Holm Jensen, et al. "Independent Validation of an In Silico Tool for a Pilot-Scale Pharmaceutical Crystallization Process Development." Processes 9, no. 4 (2021): 640. http://dx.doi.org/10.3390/pr9040640.

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There are many published models for predicting crystal size distribution (CSD) in the literature. However, none of them have been independently and comprehensively tested, which is important for industrial acceptance and confidence of these models. Therefore, in this study, using solubility and kinetic data from the literature, an in silico tool for predicting the crystallization process performance of a model compound system (paracetamol in ethanol) was developed and challenged by independent experiments at the 50 L pilot scale. The solute concentration was tracked, and the final CSD was quantified using three measurement techniques including a novel image analysis tool. The reported parameter uncertainties were also addressed using Monte Carlo simulations. The results showed that, when the models were used within their validity range (e.g., suspended solids), they were able to describe the observed process trends/dynamics (CSD and solute concentration) under varying experimental conditions (cooling time and seed mass) with R2 ranging from 0.72 and 0.90. Overall, the results indicate that, using Monte Carlo simulations to account for known parametric uncertainties, the models can support model-based approaches for crystallization process development from scale-down to scale-up studies as well as control evaluation.

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Díaz Azpiroz, M. "Characterization of tectono-metamorphic events using crystal size distribution (CSD) diagrams. A case study from the Acebuches metabasites (SW Spain)." Journal of Structural Geology 25, no. 6 (2003): 935–47. http://dx.doi.org/10.1016/s0191-8141(02)00081-0.

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Higgins, Michael D., and Julie Roberge. "Three magmatic components in the 1973 eruption of Eldfell volcano, Iceland: Evidence from plagioclase crystal size distribution (CSD) and geochemistry." Journal of Volcanology and Geothermal Research 161, no. 3 (2007): 247–60. http://dx.doi.org/10.1016/j.jvolgeores.2006.12.002.

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Neumann, Andreas M., Sean K. Bermingham, Herman J. M. Kramer, and Gerda M. van Rosmalen. "The effect of the impeller speed on the product crystal size distribution (CSD) a 22 liter draft tube (DT) crystallizer." Journal of Crystal Growth 198-199 (March 1999): 723–28. http://dx.doi.org/10.1016/s0022-0248(98)01193-2.

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Ruan, Chunlei. "Chebyshev Spectral Collocation Method for Population Balance Equation in Crystallization." Mathematics 7, no. 4 (2019): 317. http://dx.doi.org/10.3390/math7040317.

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The population balance equation (PBE) is the main governing equation for modeling dynamic crystallization behavior. In the view of mathematics, PBE is a convection–reaction equation whose strong hyperbolic property may challenge numerical methods. In order to weaken the hyperbolic property of PBE, a diffusive term was added in this work. Here, the Chebyshev spectral collocation method was introduced to solve the PBE and to achieve accurate crystal size distribution (CSD). Three numerical examples are presented, namely size-independent growth, size-dependent growth in a batch process, and with nucleation, and size-dependent growth in a continuous process. Through comparing the results with the numerical results obtained via the second-order upwind method and the HR-van method, the high accuracy of Chebyshev spectral collocation method was proven. Moreover, the diffusive term is also discussed in three numerical examples. The results show that, in the case of size-independent growth (PBE is a convection equation), the diffusive term should be added, and the coefficient of the diffusive term is recommended as 2G × 10−3 to G × 10−2, where G is the crystal growth rate.

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MOCK, A., and D. A. JERRAM. "Crystal Size Distributions (CSD) in Three Dimensions: Insights from the 3D Reconstruction of a Highly Porphyritic Rhyolite." Journal of Petrology 46, no. 8 (2005): 1525–41. http://dx.doi.org/10.1093/petrology/egi024.

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Rodriguez-Navarro, Alejandro, and Krzysztof Kudłacz. "Determination of crystal size distribution by two-dimensional X-ray diffraction." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C1131. http://dx.doi.org/10.1107/s2053273314088688.

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Polycrystalline materials properties and behaviour are ultimately determined by their crystallinity, phase composition and microstructure (i.e., crystal size, preferential orientation). Two-dimensional (2D) diffraction patterns collected with an area detector (i.e., CDD), available in modern X-ray diffractometers, contain detailed information about all these important material characteristics. Furthermore, recent advances in detector technologies permits the collection of high resolution diffraction patterns in which the microstructure of the material can be directly imaged. If the size of beam relative to the crystal size in the sample is adequately choosen, the diffraction pattern produced will have spotty rings in which the spots are the diffracted images of individual grains. The resolution of the image is mainly dependent on the characteristics of the X-ray beam (i.e., diameter, angular divergence), which can be modulated by X-ray optics, sample to detector distance, the pixel size of the detector and the sharpness of the point spread function. From these patterns, the crystal size distribution of different crystalline phases present in the sample can be independently determined using specialized software capable of extracting and combining the information contained in these patterns. This technique is applicable to materials with crystal sizes ranging from submicron to mm sizes and is complementary to techniques based on peak profile analyses (i.e., Scherrer method) which are applicable only to nanocrystalline materials. Finally, given the high sensitivity of current detectors, crystal size evolution can be followed in real-time to study important transformation processes such as crystallization, annealing, etc. The use of 2D X-ray diffraction as applied to microstructure characterization will be illustrated through several examples.

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Nugroho, R. P., T. Disando, I. A. Kurniawan, and M. Abdurrachman. "Crystal size distribution (CSD) of plagioclase phenocryst-microphenocryst and the calculation of crystal resident times in the continuous central eruption sequences of Mount Lasem, Central Java, Indonesia." Journal of Physics: Conference Series 1363 (November 2019): 012041. http://dx.doi.org/10.1088/1742-6596/1363/1/012041.

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Moschini, Piergiorgio, Silvio Mollo, Mario Gaeta, et al. "Parameterization of clinopyroxene growth kinetics via crystal size distribution (CSD) analysis: Insights into the temporal scales of magma dynamics at Mt. Etna volcano." Lithos 396-397 (September 2021): 106225. http://dx.doi.org/10.1016/j.lithos.2021.106225.

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Higgins, Michael D. "Origin of megacrysts in granitoids by textural coarsening: a crystal size distribution (CSD) study of microcline in the Cathedral Peak Granodiorite, Sierra Nevada, California." Geological Society, London, Special Publications 168, no. 1 (1999): 207–19. http://dx.doi.org/10.1144/gsl.sp.1999.168.01.14.

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36

Bond, Andrew D. "A survey of thermal expansion coefficients for organic molecular crystals in the Cambridge Structural Database." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 77, no. 3 (2021): 357–64. http://dx.doi.org/10.1107/s2052520621003309.

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Typical ranges of thermal expansion coefficients are established for organic molecular crystals in the Cambridge Structural Database. The CSD Python API is used to extract 6201 crystal structures determined close to room temperature and at least one lower temperature down to 90 K. The data set is dominated by structure families with only two temperature points and is subject to various sources of error, including incorrect temperature reporting and missing flags for variable-pressure studies. For structure families comprising four or more temperature points in the range 90–300 K, a linear relationship between unit-cell volume and temperature is shown to be a reasonable approximation. For a selected subset of 210 structures showing an optimal linear fit, the volumetric expansion coefficient at 298 K has mean 173 p.p.m. K−1 and standard deviation 47 p.p.m. K−1. The full set of 6201 structures shows a similar distribution, which is fitted by a normal distribution with mean 161 p.p.m. K−1 and standard deviation 51 p.p.m. K−1, with excess population in the tails mainly comprising unreliable entries. The distribution of principal expansion coefficients, extracted under the assumption of a linear relationship between length and temperature, shows a positive skew and can be approximated by two half normal distributions centred on 33 p.p.m. K−1 with standard deviations 40 p.p.m. K−1 (lower side) and 56 p.p.m. K−1 (upper side). The distribution for the full structure set is comparable to that of the test subset, and the overall frequency of biaxial and uniaxial negative thermal expansion is estimated to be < 5% and ∼30%, respectively. A measure of the expansion anisotropy shows a positively skewed distribution, similar to the principal expansion coefficients themselves, and ranges based on suggested half normal distributions are shown to highlight literature cases of exceptional thermal expansion.

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37

ZEH, A. "Crystal Size Distribution (CSD) and Textural Evolution of Accessory Apatite, Titanite and Allanite during Four Stages of Metamorphism: an Example from the Moine Supergroup, Scotland." Journal of Petrology 45, no. 10 (2004): 2101–32. http://dx.doi.org/10.1093/petrology/egh049.

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38

Meldrum, A., E. Sonder, R. A. Zuhr, et al. "A transmission electron microscopy investigation of sulfide nanocrystals formed by ion implantation." Journal of Materials Research 14, no. 12 (1999): 4489–502. http://dx.doi.org/10.1557/jmr.1999.0610.

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Ion implantation was used to form compound semiconductor nanocrystal precipitates of ZnS, CdS, and PbS in both glass and crystalline matrices. The precipitate microstructures and size distributions were investigated by cross-sectional transmission electron microscopy techniques. Several unusual features were observed, including strongly depth-dependent size variations of the ZnS precipitates and central void features in the CdS nanocrystals. The morphology and crystal structure of the nanocrystal precipitates could be controlled by selection of the host material. The size distribution and microstructural complexity were significantly reduced by implanting a low concentration of ions into a noncrystalline host, and by using multi-energy implants to give a flat concentration profile of the implanted elements.

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39

Abdel-Rahman, Zaid, and Zeyad Abdullah. "Utilization of CO2 in Flue Gas for Sodium Bicarbonate Production in a Bubble Column." Tikrit Journal of Engineering Sciences 26, no. 2 (2019): 28–38. http://dx.doi.org/10.25130/tjes.26.2.05.

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Utilization of CO2 in flue gases for the production of sodium bicarbonate is an environmentally friendly process. A mathematical model was constructed for the design and simulation of utilizing a low concentration CO2 (2-18%) in flue gas to produce sodium bicarbonate in a bubble column reactor. The model is based on the mass balance equations for three phases (gas, liquid, and solid). Danckwerts theory for mass transfer from the gas phase to the liquid phase coupling with chemical reaction, and crystallization mechanism was used. The effect of process variables; gas molar velocity or flux (G=2.5-10 mole/m2.s), liquid mass flow rate (mL=2800-3400 kg/h), sodium bicarbonate concentration (x1=0.04-0.1), CO2 gas mole fraction (y=0.02-0.18), column height (h=11-33 m), and column diameter (dR=1-3 m) on the objective variables; solid molar velocity (S), CO2 conversion, precipitation zone height (Zi), and crystal size distribution (CSD) were studied. The conversion of CO2 varied from 34% to 71% whereas the particle size range varied from 0 to 400 μm. The particle size range and the CO2 absorption efficiency of about 50% for 20 m column height are in agreement with the literature.

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Majumder, Aniruddha. "Modeling and Simulation Studies of a Novel Coupled Plug Flow Crystallizer for the Continuous Separation of Conglomerate-Forming Enantiomers." Processes 6, no. 12 (2018): 247. http://dx.doi.org/10.3390/pr6120247.

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Separation of enantiomers is a major concern in pharmaceutical industries due to the different therapeutic activities exhibited by the enantiomers. Preferential crystallization is an attractive means to separate the conglomerate-forming enantiomers. In this work, a simulation study is presented for a proposed novel preferential crystallization configuration that involves coupled plug flow crystallizers (PFCs). The PFCs are coupled through liquid phase exchange which helps the enrichment of the preferred enantiomer in the liquid phase. A set of coupled population balance equations (PBEs) are used to describe the evolution of the crystal size distribution (CSD) in the PFCs. The PBEs and the relevant mass balance equations are solved using the high-resolution finite-volume method. The simulation results predict that the proposed configuration has higher productivity compared to the currently used crystallization configurations while maintaining the same level of purity. Moreover, the effect of process variables, such as the extent of liquid phase change and the location of the PFC where liquid phase exchange occurs, are studied. The insights obtained from this simulation study will be useful in design, development, and optimization of such novel crystallization platforms.

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Rangel-Chávez, L. G., M. I. Neria-González, A. Márquez-Herrera, et al. "Synthesis of CdS Nanocrystals by Employing the By-Products of the Anaerobic Respiratory Process ofDesulfovibrio alaskensis6SR Bacteria." Journal of Nanomaterials 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/260397.

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A novel methodology for the direct synthesis of CdS nanoparticles, using a biological agent that avoids the extracellular processing, and the results of the characterization of CdS nanocrystals are presented. The by-products of the anaerobic respiratory process ofDesulfovibrio alaskensis6SR along with aqueous solutions of Cd salts were successfully employed to produce CdS nanocrystals with mixed cubic and hexagonal phases. Nanocrystal size has a narrow size distribution with little dependence on the Cd concentration. Both the presence of the crystallographic cubic phase and the crystalline order decrease as Cd concentration increases. The band gap values obtained from optical transmission measurements are lower than those of the bulk crystal. Raman spectroscopy characterization agrees with electron transmission microscopy images and X-ray diffraction results indicating that the method promotes the formation of high structural quality nanocrystals when low concentrations of the Cd salt are used.

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Li, Qing Yun, and Xue Zhong Wang. "Population Balance and CFD Simulation of Particle Aggregation and Growth in a Continuous Confined Jet Mixer for Hydrothermal Synthesis of Nanocrystals." Crystals 11, no. 2 (2021): 144. http://dx.doi.org/10.3390/cryst11020144.

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Population balance and computational fluid dynamics models are built and integrated to carry out a simulation study of the reactive crystallisation process in a confined jet mixer (CJM) for the continuous flow synthesis of TiO2 nanoparticles at a supercritical water condition. In the population balance model, the crystal growth in size is modelled as being due to combined nanocrystal aggregation as well as surface growth. A free molecular model is used to predict the particle aggregation. The performance of the combined aggregation and surface growth models is compared with models that only consider surface growth as the only mechanism for particle size enlargement. It was found that the combined model gives a more accurate prediction of particle size distribution.

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Kaszkur, Zbigniew, Maciej Zieliński, and Wojciech Juszczyk. "The real background and peak asymmetry in diffraction on nanocrystalline metals." Journal of Applied Crystallography 50, no. 2 (2017): 585–93. http://dx.doi.org/10.1107/s1600576717003235.

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A method to analytically calculate the column length distribution (CLD) from a single reflection of a strain-free nanocrystalline metal is proposed. It involves precise estimation of the peak background level using a physical criterion – the positivity of the CLD. The method can be applied to materials showing a dependence of the lattice constant on the crystal size, because of which the diffraction peaks display asymmetry. The analysis can provide an estimation of this dependence. Results for platinum and gold nanocrystals are presented, showing and explaining the different asymmetry of their peaks. By applying the proposed method to diffraction patterns of in situ treated gold nanocrystals, it is shown that the nanocrystal shape changes in response to changing environment.

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44

Sarangi, B., S. G. Aggarwal, D. Sinha, and P. K. Gupta. "Aerosol effective density measurement using scanning mobility particle sizer and quartz crystal microbalance with the estimation of involved uncertainty." Atmospheric Measurement Techniques Discussions 8, no. 12 (2015): 12887–931. http://dx.doi.org/10.5194/amtd-8-12887-2015.

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Abstract. In this work, we have used scanning mobility particle sizer (SMPS) and quartz crystal microbalance (QCM) to estimate the effective density of aerosol particles. This approach is tested for aerosolized particles generated from the solution of standard materials of known density, i.e. ammonium sulfate (AS), ammonium nitrate (AN) and sodium chloride (SC), and also applied for ambient measurement in New Delhi. We also discuss uncertainty involved in the measurement. In this method, dried particles are introduced in to a differential mobility analyzer (DMA), where size segregation was done based on particle electrical mobility. At the downstream of DMA, the aerosol stream is subdivided into two parts. One is sent to a condensation particle counter (CPC) to measure particle number concentration, whereas other one is sent to QCM to measure the particle mass concentration simultaneously. Based on particle volume derived from size distribution data of SMPS and mass concentration data obtained from QCM, the mean effective density (ρeff) with uncertainty of inorganic salt particles (for particle count mean diameter (CMD) over a size range 10 to 478 nm), i.e. AS, SC and AN is estimated to be 1.76 ± 0.24, 2.08 ± 0.19 and 1.69 ± 0.28 g cm−3, which are comparable with the material density (ρ) values, 1.77, 2.17 and 1.72 g cm−3, respectively. Among individual uncertainty components, repeatability of particle mass obtained by QCM, QCM crystal frequency, CPC counting efficiency, and equivalence of CPC and QCM derived volume are the major contributors to the expanded uncertainty (at k = 2) in comparison to other components, e.g. diffusion correction, charge correction, etc. Effective density for ambient particles at the beginning of winter period in New Delhi is measured to be 1.28 ± 0.12 g cm−3. It was found that in general, mid-day effective density of ambient aerosols increases with increase in CMD of particle size measurement but particle photochemistry is an important factor to govern this trend. It is further observed that the CMD has good correlation with O3, SO2 and ambient RH, suggesting that possibly sulfate secondary materials have substantial contribution in particle effective density. This approach can be useful for real-time measurement of effective density of both laboratory generated and ambient aerosol particles, which is very important for studying the physico-chemical property of particles.

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Afchine, Armin, Christian Rolf, Anja Costa, et al. "Ice particle sampling from aircraft – influence of the probing position on the ice water content." Atmospheric Measurement Techniques 11, no. 7 (2018): 4015–31. http://dx.doi.org/10.5194/amt-11-4015-2018.

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Abstract. The ice water content (IWC) of cirrus clouds is an essential parameter determining their radiative properties and thus is important for climate simulations. Therefore, for a reliable measurement of IWC on board research aircraft, it is important to carefully design the ice crystal sampling and measuring devices. During the ML-CIRRUS field campaign in 2014 with the German Gulfstream GV HALO (High Altitude and Long Range Research Aircraft), IWC was recorded by three closed-path total water together with one gas-phase water instrument. The hygrometers were supplied by inlets mounted on the roof of the aircraft fuselage. Simultaneously, the IWC is determined by a cloud particle spectrometer attached under an aircraft wing. Two more examples of simultaneous IWC measurements by hygrometers and cloud spectrometers are presented, but the inlets of the hygrometers were mounted at the fuselage side (M-55 Geophysica, StratoClim campaign 2017) and bottom (NASA WB57, MacPex campaign 2011). This combination of instruments and inlet positions provides the opportunity to experimentally study the influence of the ice particle sampling position on the IWC with the approach of comparative measurements. As expected from theory and shown by computational fluid dynamics (CFD) calculations, we found that the IWCs provided by the roof inlets deviate from those measured under the aircraft wing. As a result of the inlet position in the shadow zone behind the aircraft cockpit, ice particle populations with mean mass sizes larger than about 25 µm radius are subject to losses, which lead to strongly underestimated IWCs. On the other hand, cloud populations with mean mass sizes smaller than about 12 µm are dominated by particle enrichment and thus overestimated IWCs. In the range of mean mass sizes between 12 and 25 µm, both enrichment and losses of ice crystals can occur, depending on whether the ice crystal mass peak of the size distribution – in these cases bimodal – is on the smaller or larger mass mode. The resulting deviations of the IWC reach factors of up to 10 or even more for losses as well as for enrichment. Since the mean mass size of ice crystals increases with temperature, losses are more pronounced at higher temperatures, while at lower temperatures IWC is more affected by enrichment. In contrast, in the cases where the hygrometer inlets were mounted at the fuselage side or bottom, the agreement of IWCs is most frequently within a factor of 2.5 or better – due to less disturbed ice particle sampling, as expected from theory – independently of the mean ice crystal sizes. The rather large scatter between IWC measurements reflects, for example, cirrus cloud inhomogeneities and instrument uncertainties as well as slight sampling biases which might also occur on the side or bottom of the fuselage and under the wing. However, this scatter is in the range of other studies and represent the current best possible IWC recording on fast-flying aircraft.

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46

Sarangi, Bighnaraj, Shankar G. Aggarwal, Deepak Sinha, and Prabhat K. Gupta. "Aerosol effective density measurement using scanning mobility particle sizer and quartz crystal microbalance with the estimation of involved uncertainty." Atmospheric Measurement Techniques 9, no. 3 (2016): 859–75. http://dx.doi.org/10.5194/amt-9-859-2016.

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Abstract. In this work, we have used a scanning mobility particle sizer (SMPS) and a quartz crystal microbalance (QCM) to estimate the effective density of aerosol particles. This approach is tested for aerosolized particles generated from the solution of standard materials of known density, i.e. ammonium sulfate (AS), ammonium nitrate (AN) and sodium chloride (SC), and also applied for ambient measurement in New Delhi. We also discuss uncertainty involved in the measurement. In this method, dried particles are introduced in to a differential mobility analyser (DMA), where size segregation is done based on particle electrical mobility. Downstream of the DMA, the aerosol stream is subdivided into two parts. One is sent to a condensation particle counter (CPC) to measure particle number concentration, whereas the other one is sent to the QCM to measure the particle mass concentration simultaneously. Based on particle volume derived from size distribution data of the SMPS and mass concentration data obtained from the QCM, the mean effective density (ρeff) with uncertainty of inorganic salt particles (for particle count mean diameter (CMD) over a size range 10–478 nm), i.e. AS, SC and AN, is estimated to be 1.76 ± 0.24, 2.08 ± 0.19 and 1.69 ± 0.28 g cm−3, values which are comparable with the material density (ρ) values, 1.77, 2.17 and 1.72 g cm−3, respectively. Using this technique, the percentage contribution of error in the measurement of effective density is calculated to be in the range of 9–17 %. Among the individual uncertainty components, repeatability of particle mass obtained by the QCM, the QCM crystal frequency, CPC counting efficiency, and the equivalence of CPC- and QCM-derived volume are the major contributors to the expanded uncertainty (at k = 2) in comparison to other components, e.g. diffusion correction, charge correction, etc. Effective density for ambient particles at the beginning of the winter period in New Delhi was measured to be 1.28 ± 0.12 g cm−3. It was found that in general, mid-day effective density of ambient aerosols increases with increase in CMD of particle size measurement but particle photochemistry is an important factor to govern this trend. It is further observed that the CMD has good correlation with O3, SO2 and ambient RH, suggesting that possibly sulfate secondary materials have a substantial contribution in particle effective density. This approach can be useful for real-time measurement of effective density of both laboratory-generated and ambient aerosol particles, which is very important for studying the physico-chemical properties of particles.

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47

Génin, A., K. Essemiani, C. Lemoine, E. Barbier, and S. Logette. "Impact of hydrodynamics on the precipitation efficiency – application to HARDTAC reactor." Water Science and Technology 56, no. 11 (2007): 101–8. http://dx.doi.org/10.2166/wst.2007.772.

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Precipitation of gypsum is studied in a HARDTAC (High-Aspect Ratio, Draft-Tube, Agitated Crystallizer) reactor, which is considered as the core crystallization unit of lots of wastewater treatment systems. Coupling Computational Fluid Dynamics (CFD) and population balance modelling to simulate precipitation can be a useful tool to come to a decision about upstream and downstream units. In the present study, we aim to validate such approach by investigating gypsum precipitation in a HARDTAC pilot unit and comparing experiments results with simulation. Measured nucleation and growth kinetics are used to feed the model. A comparison between experiments and simulations is presented in the case of gypsum precipitation with a given set of operating conditions. Good agreement is obtained for species concentrations, gypsum mass fraction and volumetric mean diameter but some discrepancies still remain between measured and simulated crystal size distribution.

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Kupchak, I. M., D. V. Korbutyak, and N. F. Serpak. "Electronic characteristics of CdS quantum dots with defects." Технология и конструирование в электронной аппаратуре, no. 3-4 (2020): 28. http://dx.doi.org/10.15222/tkea2020.3-4.28.

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Using the density functional theory and the generalized gradient approximation, we calculated the atomic structure, the density of electronic states, and the optical absorption spectra of CdS quantum dots containing intrinsic defects — a cadmium vacancy VCd and an interstitial sulfur atom SI, and substitutional impurities — zinc and copper in place of the atom cadmium — ZnCd and CuCd, respectively. The calculations were performed for the Cd33S33 cluster corresponding to the so-called “magic” size of the quantum dot. This size has a minimum of dangling bonds at the surface and allows the using of such a cluster without the passivation. The structural relaxation during the formation of such defects and the distribution of the wave function of the state corresponding to the top of the valence band are analyzed in details. It has been shown that the cadmium vacancy forms local states in the band gap of CdS nanocrystals, and can serve as centers of radiative recombination. Other defects form energy levels in the depths of the valence band or near its top, but whose energy positions do not correspond to the band maxima in the experimental photoluminescence spectra of CdS quantum dots, both undoped and doped with zinc. The calculated optical absorption spectra demonstrate a strong peak in the region of fundamental absorption of CdS for a cluster containing a substitutional impurity of CuCd, in contrast to other systems where no such peaks are observed. In addition, the replacement of the cadmium atom with copper leads to a decrease in the number of chemical bonds to three and, accordingly, to the largest relaxation among the systems studied. This feature is caused by the crystal structure inhomogeneity of copper sulfide CuxS, which, depending on stoichiometry, can be either a semiconductor or a metal.

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49

Bao, Ying, Jinlong Zhang, Qiuxiang Yin, and Jingkang Wang. "Calibration for measured crystal size distribution." Powder Technology 161, no. 3 (2006): 242–47. http://dx.doi.org/10.1016/j.powtec.2005.11.003.

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50

Anderson, Tor, H. Scott Peters, Rosario A. Torres, Nancy A. Nagy, and Dale L. Schruben. "Wax crystal size distribution versus composition." Fuel 80, no. 11 (2001): 1635–38. http://dx.doi.org/10.1016/s0016-2361(01)00039-4.

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Journal articles on the topic 'Crystal Size Distribution (CSD)'

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