Noriaki Kubota

A kinetic model for crystal growth from aqueous solution in the presence of impurity

A mathematical model describing crystal growth rates from aqueous solution as a function of impurity concentration is presented. The model assumes that the step velocity decreases linearly with increasing surface coverage (θeq) by impurities adsorbed on the growing crystal, and a proportionality constant α is introduced to take into account the effectiveness of the impurity. When α > 1, the step velocity is stopped at θeq < 1 (incomplete coverage of the active sites for adsorption). In the case of α = 1, the velocity reaches zero just at θeq = 1, and for α < 1, it never becomes zero even at θeq = 1 (complete coverage) but approaches a limiting value. The Langmuir adsorption isotherm is used to relate the relative step velocity with the impurity concentration in solution. Three typical cases reported in the literature, each previously explained with a different model, are shown to be described satisfactorily with this new single model. The value of α is changed by stereochemical factors and decreases as the supersaturation is increased. The supersaturation effect is explained with the aid of the Cabrera-Vermilyea model.

Supersaturation dependence of crystal growth in solutions in the presence of impurity

Abstract It is proposed to describe the rate of crystal growth in solution in the presence of impurity as a function of supersaturation. The theoretical equations are based on the pinning mechanism of Cabrera and Vermilyea for the inhibition of step advancement, assuming that impurity species are adsorbed one-dimensionally on the step lines. The Langumir adsorption isotherm is assumed to hold for impurity adsorption. Experimental growth rate data from the literature are used to assess the model. The supersaturation dependence of crystal growth rate in the presence of impurity is also well described with the model. The critical supersaturation below which a crystal does not grow is correlated with the impurity concentration. For the case where an impurity has no effect at high supersaturation, two possible mechanisms are discussed: one related to a change of rate-determining process and the other related to competition between impurity adsorption and growth unit deposition processes.

Seeding policy in batch cooling crystallization

Abstract The effect of seeding in batch cooling crystallization is discussed on the basis of original experimental data on potassium alum–water system obtained for both controlled and natural cooling modes. Regardless of the cooling mode, unimodal product crystal size distributions of grown seeds were obtained, provided that enough seed loadings are above a critical concentration. Slow cooling was not a necessary condition to avoid secondary nucleation. The critical seed concentration can be determined easily from several batch trials with the help of a seed chart, in which mean mass size of product crystals normalized with the seed size is plotted as a function of seed concentration, with seed size as a parameter. This type of seeding effect could be observed for cooling crystallization of other systems and for crystallization employing other supersaturation-generating methods.

The combined influence of supersaturation and impurity concentration on crystal growth

Supersaturation dependence of crystal growth in the presence of impurity is discussed. The supersaturation dependence was divided conveniently into two types: the case where growth rate is suppressed over a wide range of supersaturation and the case where it is suppressed only in the low range of supersaturation while at the higher supersaturation range the impurity effect disappears completely. The latter case is explained theoretically by assuming slow unsteady state adsorption of impurity species at higher supersaturations. Literature data of the growth rate of an ammonium sulfate crystal are successfully explained. It is pointed out that classification of impurity action into the two types is not essential. The former type is a special case of the second one where the time constant of adsorption process becomes very small even at higher supersaturations.

Effect of Cooling Mode on Product Crystal Size in Seeded Batch Crystallization of Potassium Alum

Potassium alum was crystallized by seeding in a batch crystallizer under controlled and natural cooling modes. Regardless of the cooling mode, the product crystal size distribution (CSD) became bi-modal at low seed concentrations because of enormous secondary nucleation. The mean mass size of the product was smaller for the natural cooling mode compared to that for the controlled cooling mode with more intensive secondary nucleation. On the other hand, at high seed concentrations, the product CSD became uni-modal with the same mean mass size for both cooling modes, where the crystallization was dominated by seed growth. The low supersaturation caused by the growth of enough seeds plays a key role to produce uni-modal size distribution with suppressed nucleation. Adhering of small crystals (secondary nuclei) to growing seed crystals is also considered to be another mechanism for generating uni-modal CSD.

Unsteady-state impurity effect of chromium (III) on the growth rate of potassium sulfate crystal in aqueous solution

Abstract Growth length of a single potassium sulfate crystal was measured at a constant supercooling of 7°C in a flow cell in the presence of a trace of chromium (III) (up to 5 ppm) under natural and controlled pH conditions. The impurity action of chromium (III) exhibited unsteady-state behavior. The growth rate decreased gradually, reaching zero in about 100 min at an impurity concentration of 2 ppm under the condition of pH = 5.8. At higher impurity concentrations (3 and 5 ppm), the growth was completely stopped at an early stage of the run nearly at the same pH level. No impurity effect was observed at higher pHs (= 7 and 10), while, at lower pHs (= 3 and 5), the effect was very strong even at an impurity concentration of 2 ppm. The unsteady-state growth behavior is reasonably explained by a model assuming that the impurity species, which acts as a stopper for the step advancement, adsorbs very slowly on the step lines. The effect of pH on the impurity action is explained by assuming that the first hydrolysis product, [Cr(H2O)5(OH)]2+, of the aqua complex compound of chromium (III) acts as the active species for growth inhibition.

Calculation of supercooling temperature for primary nucleation of potassium nitrate from aqueous solution by the two-kind active site model

This paper describes the calculation of the supercooling temperature, i.e., the degree of supercooling at which the first nucleation occurs during cooling at a constant rate. The calculation uses the two-kind active site model, a stochastic model in which primary nucleation is assumed to be induced heterogeneously by the active sites in a stochastic manner. The nucleation probability W per unit time cannot be expressed as a function of the degree of supercooling, since the variable p1, which is the number of the first kind active site, satisfies a Poisson distribution. Therefore, a Monte Carlo simulation has been used for its calculation. Analytical solutions, however, are also given for the two limiting cases in which W is given as a function of the degree of supercooling. The calculated average supercooling temperature is in good agreement with the experimental values. The parameter values used for the theoretical calculation were determined experimentally from the time distribution of the first nucleation which occurs at a constant degree of supercooling. The good agreement between theory and experiment proves that nucleation at constant temperature and at constant cooling rate is well understood. The effect of filtering the solution on the supercooling temperature is explained by the reduction of the number of the active sites.

Impurity effect of chromium(III) on the growth and dissolution rates of potassium sulfate cyrstals

Abstract Growth and dissolution rates of a potassium sulfate crystal were measured under controlled pHs in potassium sulfate solutions contaminated by traces of chromium(III): up to 5 ppm for growth and 15 ppm for dissolution. Four kinds of chromium(III) salts, Cr 2 (SO 4 ) 3 · 4H 2 O, CrCl 3 · 6H 2 O, CrF 3 · 3H 2 O and Cr(CH 3 COO) 3 · H 2 O, were examined as the chromium(III) impurity source. The former two suppressed both rate processes, while the latter two were inactive. The suppression effect on growth rate was increased with increasing the solution pH when CrCl 3 · 6H 2 O was added, but the effect was unchanged with the pH for the case of Cr 2 (SO 4 ) 3 · 4H 2 O. However, on the dissolution rate, the suppression effect was increased with increasing the solution pH for both impurities. With increasing the impurity concentration, the effects on the growth and dissolution rates were increased. These results are explained by a mechanism in which the adsorbed hydrolysis product (an assumed active species) of a hydrated chromium(III) retards the rate processes. The hydrolysis product (hydroxo complex), which is in equilibrium with the inactive hydrated complex in the solution, is assumed to adsorb on the surface of the potassium sulfate crystal according to the Langmuir adsorption mechanism.

Liquid inclusions in crystals produced in suspension crystallization

Abstract Sodium chloride, potassium chloride, succinic acid and potassium hydrogen phthalate crystals were crystallized batchwise in an agitation vessel and the total volume of liquid inclusions per crystal, V (μm 3 ), was measured as a function of crystal size, d (μm). The found data of the total volume, including literature data from a continuous crystallizer, was correlated with a simple equation, V =4.0×10 −6 d 4 . Most of the inclusions observed in sodium chloride and potassium chloride crystals were layer inclusions, which were aligned two-dimensionally in parallel with crystal faces. This type of inclusion pattern was suggested, with the help of the results of additional in situ experiments under a microscope, to be caused by the adhesions of small crystals to growing crystals and mechanical contacts imposed to these crystals during growth. Although the layer pattern was not found in the other crystals examined, the same mechanism was considered to work for the inclusion formation.

Precipitation of BaCO3 in a semi-batch reactor with double-tube gas injection nozzle

Abstract BaCO3 crystals were produced in a semi-batch reactor by adding CO2 gas continuously to the agitated BaS aqueous solution through a double-tube gas injection nozzle. Larger crystals were obtained in comparison with the case where the gas directly dispersed in the whole reactor as usually done. The gas bubbles, around which the higher supersaturation regions are thought to be localized, were made to contact only with the solution inside the outer tube of the nozzle. The gas was absorbed there and the adsorbed gas was transferred into the agitated bulk solution through the lower opening of the nozzle and then it reacted with Ba2+ ion in the bulk solution. The larger crystals were thought to be obtained because of lower nucleation rate caused by the limited bubbling region. In addition, the lower pH of the solution in the nozzle was thought to help in lowering the nucleation rate, since CO2 gas was dissolved as HCO-3 ion rather than as CO2-3 ion at such lower pH values.