scholarly journals Reactive Crystallization Kinetics of K2SO4 from Picromerite-Based MgSO4 and KCl

Crystals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1558
Author(s):  
Abad Albis ◽  
Yecid P. Jiménez ◽  
Teófilo A. Graber ◽  
Heike Lorenz
Keyword(s):  
Crystal Growth ◽  
Nucleation Rate ◽  
Length Distribution ◽  
Analytical Techniques ◽  
Nucleation And Growth ◽  
Solution Temperature ◽  
Secondary Nucleation ◽  
Primary Nucleation ◽  
Reactive Crystallization ◽  
Kinetics Of

In this work, the kinetic parameters, the degrees of initial supersaturation (S0) and the profiles of supersaturation (S) were determined for the reactive crystallization of K2SO4 from picromerite (K2SO4.MgSO4.6H2O) and KCl. Different reaction temperatures between 5 and 45 °C were considered, and several process analytical techniques were applied. Along with the solution temperature, the crystal chord length distribution (CLD) was continuously followed by an FBRM probe, images of nucleation and growth events as well as the crystal morphology were captured, and the absorbance of the solution was measured via ATR-FTIR spectroscopy. In addition, the ion concentrations were analyzed. It was found that S0 is inversely proportional to the reactive crystallization temperature in the K+, Mg2+/Cl−, SO42−//H2O system at 25 °C, where S0 promotes nucleation and crystal growth of K2SO4 leading to a bimodal CLD. The CLD was converted to square-weighted chord lengths for each S0 to determine the secondary nucleation rate (B), crystal growth rate (G), and suspension density (MT). By correlation, from primary nucleation rate (Bb) and G with S0, the empirical parameters b = 3.61 and g = 4.61 were obtained as the order of primary nucleation and growth, respectively. B versus G and MT were correlated to the reaction temperature providing the rate constants of B and respective activation energy, E = 69.83 kJ∙mol−1. Finally, a general Equation was derived that describes B with parameters KR = 13,810.8, i = 0.75 and j = 0.71. The K2SO4 crystals produced were of high purity, containing maximal 0.51 wt% Mg impurity, and were received with ~73% yield at 5 °C.

scholarly journals Monitoramento da cristalização da lactose em soro concentrado

2017 ◽  
Vol 72 (4) ◽  
pp. 215-226
Author(s):  
Ítalo Tuler Perrone ◽  
João Pablo Fortes Pereira ◽  
Isis Rodrigues Toledo Renhe ◽  
Júlia D’Almeida Francisquini ◽  
Rodrigo Stephani ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Soluble Solids ◽  
Nucleation Process ◽  
Secondary Nucleation ◽  
Primary Nucleation ◽  
Industrial Setting ◽  
Mathematical Equations ◽  
Average Size ◽  
Two Stages ◽  
Kinetics Of

The kinetics of lactose crystal growth in concentrated whey were studied in two stages. The first took place in a bench-top crystallizer and the second in an industrial crystallizer using concentrated whey obtained by vacuum evaporation, consisting of 3 treatments: crystallization by primary nucleation, by secondary nucleation with the addition of 0.05% and with the addition of 0.1% microcrystalline lactose. The average size of the crystals remained between 60.7 mm and 63.8 mm. The percentage of crystallization was greater in the secondary nucleation process than in the primary nucleation, where crystallization stabilized first. Mathematical equations which independently related crystallization times of the concentrated whey to the concentrations of soluble solids, crystallization percentage and mass of lactose in water were established, that can be used in the industrial setting to process whey. The kinetics of lactose crystal growth was not well described by models of first or second order reactions.

Studies on nucleation and crystal growth kinetics of plutonium(IV) oxalatex

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chuanbo Li ◽  
Bo Wang ◽  
Xiang Li ◽  
Taihong Yan ◽  
Weifang Zheng
Keyword(s):  
Growth Rate ◽  
Crystal Growth ◽  
Nucleation Rate ◽  
Crystal Growth Rate ◽  
Acid Solutions ◽  
Dilution Ratio ◽  
Secondary Nucleation ◽  
Supersaturation Ratio ◽  
Crystal Growth Kinetics ◽  
Kinetics Of

Abstract A new method is developed to calculate the dilution ratio N of the two reactant solutions during nucleation rate determination. When the initial apparent supersaturation ratio S N  = f(N) in the dilution tank is controlled between 1.66 and 1.67, the counted nuclei is the most, both nuclei dissolving and secondary nucleation avoided satisfactorily. Based on this methoed, Plutonium(IV) oxalate is precipitated by mixing equal volumes of tetravalent plutonium nitrate and oxalic acid solutions. Experiments are carried out by varying the supersaturation ratio from 8.37 to 22.47 and temperature from 25 to 50 °C. The experimental results show that the nucleation rate of plutonium(IV) oxalate in the supersaturation range cited above can be expressed by the equation R N  = A N exp(−E a /RT)exp[−B/(ln S)2], where A N  = 4.8 × 1023 m−3 s−1 , and E a  = 36.2 kJ mol−1, and B = 20.2. The crystal growth rate of plutonium(IV) oxalate is determined by adding seed crystals into a batch crystallizer. The crystal growth rate can be expressed by equation G(t) = k g exp(−E’ a /RT) (c − c eq) g , where k g  = 7.3 × 10−7 (mol/L)−1.1(m/s), E’ a  = 25.7 kJ mol−1, and g = 1.1.

Crystallization of Pentaerythritol I. Solubility, Density and Metastable Zone Width

1994 ◽  
Vol 59 (6) ◽  
pp. 1261-1269 ◽  
Author(s):  
Miloslav Karel ◽  
Jaroslav Nývlt ◽  
Angelo Chianese
Keyword(s):  
Aqueous Solutions ◽  
Nucleation Rate ◽  
Laboratory Experiments ◽  
Metastable Zone Width ◽  
Zone Width ◽  
Kinetics Of Crystallization ◽  
Primary Nucleation ◽  
Metastable Zone ◽  
Width Measurements ◽  
Kinetics Of

Solubility of pentaerythritol in water has been determined using literature data, the polythermal method and the dry residue method. Densities of its aqueous solutions have been measured using a pycnometer. Kinetics of crystallization of the pentaerythritol has been determined in laboratory experiments. In this paper, metastable zone width measurements have been employed for the assessment of the primary nucleation rate.

The initiation of crystal growth in glasses

1970 ◽  
Vol 37 (291) ◽  
pp. 741-758 ◽  
Author(s):  
P. S. Rogers
Keyword(s):  
Phase Separation ◽  
Crystal Growth ◽  
Nucleation And Growth ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Nucleating Agents ◽  
Metastable Liquid ◽  
The Third ◽  
Kinetics Of ◽  
Liquid Liquid Phase Separation

SummaryThe application of classical nucleation theory to the initiation of crystal growth in glasses is discussed. Its application to experimental results obtained for the rate of nucleation in three types of glass, one showing nucleation separately from crystal growth, another showing simultaneous nucleation and growth, and the third showing crystal growth after metastable liquid/liquid phase separation, is then described. Recent work on the kinetics of unmixing in glasses is outlined. The influence of so-called ‘nucleating agents’ in the glasses described appears to be exerted through changes in the anionic structure.

Crystallization Kinetics for Synthesis Hyper-Structure in P2O5-ZnO-B2O3-BaO-Al2O3-TiO2 Glass Ceramic Composite

2008 ◽  
Vol 569 ◽  
pp. 153-156 ◽  
Author(s):  
Young Seok Kim ◽  
Kyu Ho Lee ◽  
Tae Ho Kim ◽  
Young Joon Jung ◽  
S. H. Yim ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Crystallization Kinetics ◽  
Nucleation Rate ◽  
Kinetic Equations ◽  
Fixed Number ◽  
Heating Process ◽  
Crystallization Peak ◽  
Heat Treated ◽  
Kinetics Of ◽  
Isothermal Measurements

The nucleation and crystallization kinetics of P2O5-B2O3-ZnO-BaO-Al2O3-TiO2 crystals in bulk glass in which this crystals were found to crystallize in the heating process of the glass, were studied by non-isothermal measurements using differential thermal analysis (DTA). A nucleation rate-temperature was determined by plotting either the reciprocal of the temperature corresponding to the crystallization peak maximum, 1/Tp, or the height of the crystallization peak, (*T)p, as a function of nucleation temperature, Tn. The temperature where nucleation can occur for this glass ranges from 700°C to 890°C and the temperature for maximum nucleation is 760±5°C. The correct activation energy for crystallization, Ec, for this glass is the same for surface and/or bulk crystallization, and is 533±15°CkJ/mol. The analysis of the crystallization data with the Kissinger equation and the Marotta equation yields the correct value for Ec only crystal growth occurs on a fixed number of nuclei. The crystallization process of a sample heat treated at the temperature of the maximum nucleation rate was fitted to kinetic equations with an Avrami constant, n ≈2 and a dimensionality of crystal growth, m ≈2.

Studies on nucleation and crystal growth kinetics of uranium(IV) oxalate

2020 ◽  
Vol 108 (3) ◽  
pp. 185-193
Author(s):  
Chuanbo Li ◽  
Yongzhi Ning ◽  
Taihong Yan ◽  
Weifang Zheng
Keyword(s):  
Crystal Growth ◽  
Nucleation Rate ◽  
Oxalic Acid Solution ◽  
Supersaturation Ratio ◽  
Tetravalent Uranium ◽  
Reaction Solution ◽  
Crystal Growth Kinetics ◽  
Uranium Nitrate ◽  
Kinetics Of ◽  
Homogeneous Mechanism

AbstractAn improved apparatus is used for nucleation measurements according to Nielsen’s method. A new method is proposed to calculate the dilution ratio N of the reaction solution during nucleation rate determination. With the rule, when the initial apparent supersaturation ratio S′ = f(N) in the dilution tank is controlled from 1.2 to 2.7, crystal nucleus dissolving and secondary nucleation can be avoided satisfactorily. Experiments are realized by varying the supersaturation ratio from 26.0 to 297.5 and temperature from 30 °C to 50 °C. Uranium(IV) oxalate is precipitated by mixing equal volumes of tetravalent uranium nitrate and oxalic acid solution. The experimental results show that the nucleation rate of uranium(IV) oxalate in the supersaturation range as show above is characterized by the primary homogeneous mechanism and can be expressed by the equation ${R_N} = {A_N}{\rm{exp}}( - {E_a}/RT){\rm{exp}}[ - B/{({\rm{ln }}S)^2}],$ where AN = 1.9 × 1027 m−3s−1, Ea = 71.2 kJ mol−1, and B = 34.3. The crystal growth rate can be expressed by the equation $G(t) = {k_g}{\rm{exp(}} - {E^{\prime}_a}/RT{\rm{)(}}c - {c_{{\rm{eq}}}}{{\rm{)}}^g},$ where kg = 7.1 × 105 (mol/L)−0.98 (m/s), ${E^{\prime}_a} = 33.1 \ {\rm{ kJ \ mo}}{{\rm{l}}^{ - 1}},$ and g = 0.98. The results indicate that the crystal growth of tetravalent uranium(IV) oxalate is controlled by the BCF model.

Effects of Impurities on the Kinetics of Nucleation and Growth in Amorphous Silicon

1986 ◽  
Vol 74 ◽  
Author(s):  
J. A. Roth ◽  
G. L. Olson
Keyword(s):  
Nucleation Rate ◽  
Solid Phase ◽  
Nucleation And Growth ◽  
Crystallization Time ◽  
Crystallite Growth ◽  
Impurity Effects ◽  
Time Resolved ◽  
Uniform Distributions ◽  
Amorphous Si ◽  
Kinetics Of

AbstractThe effects of intentionally introduced impurities on the crystallization time, nucleation rate and crystallite growth velocity during solid phase random crystallization of amorphous Si thin films have been determined. Films deposited in UHV onto oxidized Si wafers were subjected to multiple energy ion implantation to introduce uniform distributions of P, B, As, O or F at 0.1–1.0 at.%. Crystallization times and growth velocities were determined over the temperature range 650 to 850°C from time-resolved reflectivity measurements, and nucleation rates were determined from these data using a classical, steady state nucleation and growth model. Strong impurity effects are observed: P, B and As all decrease the nucleation rate but accelerate the growth of crystallites, whereas both 0 and F retard growth while enhancing nucleation. The largest effects are for P, which reduces the nucleation rate more than 100 times at 1% concentration, and F, which increases the rate by roughly the same amount.

Secondary nucleation and growth kinetics of aluminum hydroxide crystallization from potassium aluminate solution

2019 ◽  
Vol 507 ◽  
pp. 232-240 ◽  
Author(s):  
Jin Xue ◽  
Chenglin Liu ◽  
Mengjie Luo ◽  
Mengxing Lin ◽  
Youfa Jiang ◽  
...  
Keyword(s):  
Aluminum Hydroxide ◽  
Growth Kinetics ◽  
Nucleation And Growth ◽  
Secondary Nucleation ◽  
Aluminate Solution ◽  
Kinetics Of

Crystallization of Pentaerythritol II. Model Experiments

1994 ◽  
Vol 59 (6) ◽  
pp. 1270-1278 ◽  
Author(s):  
Miloslav Karel ◽  
Jaroslav Nývlt ◽  
Angelo Chianese
Keyword(s):  
Crystal Growth ◽  
Laboratory Experiments ◽  
Secondary Nucleation ◽  
Mixed Product ◽  
Model Experiments ◽  
Product Removal ◽  
Mixed Suspension ◽  
Kinetics Of ◽  
Kinetics Of Crystal Growth

Kinetics of crystallization of the pentaerythritol has been determined in laboratory experiments: MSMPR (Mixed Suspension Mixed Product Removal) crystallizer experiments served for determination of the kinetics of secondary nucleation and of the kinetics of crystal growth.

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