Nucleated crystal, ratio

Several crystallization objectives have been recommended to favor downstream operations or product quality. One can maximize the number-mean or weight-mean crystal size, maximize the final size of crystals grown from seed crystals, or minimize the ratio of nucleated crystal mass to seed crystal mass.f ° Other particle size-related characteristics of product crystals that have been optimized during crystallization include the coefficient of variation and the crystal shape. Although the weight-mean crystal size is the most commonly used objective in optimal control studies, the weight-mean crystal size is too insensitive to the number of small crystals that can cause filtration problems when used as an objective to optimize the crystallization operations. 

Calcium sulfite and calcium sulfate scaling in the system can be a problem for the lime/limestone wet scrubber systems. Scaling occurs when the solutions are supersaturated to a point where heterogeneous crystallization (crystallization on foreign surfaces such as the scrubber walls, overfiow pots, marbles) takes place, resulting from nucleation. The ratios of the products of the activities (A) of Ca and S04 " or to their solubility product constants Kgp) as a measure of the degree of supersaturation are ... 

Fig. 7-24. Nucleation rate, crystal growth rate, and crystal growth rate/nucleation rate ratio as functions of supersaturation.

Nucleation is defined as the point where the protonucleus is sufficiently large that its surface area to volume ratio exceeds a critical point, and further growth results in a reduction in global free energy surface effects are now small compared to the inside of the crystal. This is the point where enthalpy dominates over entropy. Subsequent crystal growth and further nucleation events will occur until thermodynamic equilibria is reached, as defined by Eq. 3. The rate of nucleation is defined as the rate at which clusters grow through this critical point. 

Heterogeneous nucleation, however, is in many cases the predominant formation process for crystals in natural waters. In a similar way as catalysts reduces the activation energy of chemical reaction, foreign solids may catalyze the nucleation process by reducing the energy barrier. Qualitatively, if the surface of the solid substrate matches well with the crystal, the interfacial energy between the two solids is smaller than the interfacial energy between the crystal and the solution, and nucleation may take place at a lower saturation ratio on a solid substrate surface than in solution. 

This method has also been successfully applied in the synthesis of Cu(II)-containing LDHs, although well crystallized materials are difficult to prepare as a consequence of the Jahn-Teller distortion found in the coordination shell of Cu(II) [70,71]. Incorporation of Ni(II) in the layers was found to improve the crystallinity and structural stability of such LDHs. For the synthesis of Cu/Ni/Al - CO3 and Cu/Ni/Mg/Al - CO3 LDHs [70] by the method with separate nucleation and aging steps, LDHs with both smaller particle size and narrower distribution of particle size were obtained compared with those prepared using a conventional coprecipitation method, similar to the case for Mg/Al-C03 LDHs [20]. Well crystallized Cu/Ni/Cr-COs LDHs [71] were obtained when the Cu/Ni/Cr atom ratio ranged from 1 2 1 to 1 3 1 in the reaction mixture with hydrothermal aging conditions at 180 °C for 4 h. 

The ratio of the instantaneous solute concentration c to the solute s solubility s, where the latter is the solute concentration in equihbrium with its crystalline or precipitated phase. Hence, RS = c/s, and a supersaturated solution experiences a thermodynamic driving force (AG = RT ln[RS]). A supersaturated solution will remain as a metastable state, because crystallization or precipitation requires a mechanism for relieving the supersaturated condition (eg., nucleation or addition of crystallite/precipitate). See Biomineralization... 

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