Kinetics, crystal growth

Garside, J., Gibilaro, L.G. and Tavare, N.S., 1982. Evaluation of crystal growth kinetics from a desupersaturation curve using initial derivatives. Chemical Engineering Science, 37, 1625-1628. 

Nielsen, A.E. and Toft, J.M., 1984. Electrolyte crystal growth kinetics. Journal of Crystal Growth, 67, 278-288. 

A comparative study [10] is made for crystal-growth kinetics of Na2HP04 in SCISR and a fluidized bed crystallizer (FBC). The details of the latter cem be found in [11]. Experiments are carried out at rigorously controlled super-saturations without nucleation. The overall growth rate coefficient, K, are determined from the measured values for the initial mean diameter, t/po, masses of seed crystals before and after growth. The results show that the values for K measured in ISC are systematically greater than those in FBC by 15 to 20%, as can be seen in Table 2. On the other hand, the values for the overall active energy measured in ISC and FBC are essentially the same. 

Busenberg, E. Plummer, L.N. 1986. A comparative study of the dissolution and crystal growth kinetics of calcite and aragonite. U S. Geological Survey Bulletin, 1578, 139-168. 

Busenberg, E., and L. N. Plummer (1986b), "A Comparative Study of the Dissolution and Crystal Growth Kinetics of Calcite and Aragonite", in F. A. Mumpton, Ed., Studies in Diagenesis, U.S. Geol. Surv. Bull. 1578, pp. 139-168. 

Nancollas, G. H., and M. M. Reddy (1974), "Crystal Growth Kinetics of Minerals Encountered in Water Treatment Processes", Aqueous-Environ. Chem. Met., 219-253. 

Nancollas, G. H., Reddy, M. M. and Tsai, F. J. Cryst. Growth 20 (1973) 125-134. Crystal growth kinetics of minerals encountered in water treatment processes. 

Clearly this is a very interesting problem and of great practical relevance, very well suited to Monte Carlo simulation. At the same time, simulations of such problems have just only begun. In the context of crystal growth kinetics, models where evaporation-condensation processes compete with surface diffusion processes have occasionally been considered before . But many related processes can be envisaged which have not yet been studied at all. 

Muncill G.E. and Lasaga A.C. (1987) Crystal-growth kinetics of plagioclase in igneous systems one-atmosphere experiments and application of a simplified growth model. Am. Mineral. 72, 299-311. 

If all possible combinations were equally probably, we would observe stochastic behavior like primary nucleation, so that crystal growth kinetics would be virtually unpredictable. However, a few molecular paths for crystal growth are highly preferred over others, these paths combine in an ensemble to provide the macroscopic observations of crystal growth described in the next section. 

All seven steps require time, resulting in a rate of incorporating clusters into the growing crystal surface, which is called crystal growth kinetics. The following two sections consider translation of such a rate into a macroscopic equation for correlation and prediction. It is difficult to say which of the steps control the process, or even if the conceptual picture is valid. However, the first step—species transport to the solid surface—is well established and a brief description is given in Section 3.2.1.2. 

By use of the proper experimental conditions and Ltting the four models described above, it may be possible to arrive at a reasonable mechanistic interpretation of the experimental data. As an example, the crystal growth kinetics of theophylline monohydrate was studied by Rodriguez-Hornedo and Wu (1991). Their conclusion was that the crystal growth of theophylline monohydrate is controlled by a surface reaction mechanism rather than by solute diffusion in the bulk. Further, they found that the data was described by the screw-dislocation model and by the parabolic law, and they concluded that a defect-mediated growth mechanism occurred rather than a surface nucleation mechanism. 

Rodriguez-Hornedo, N. and Wu, H.-J. (1991) Crystal growth kinetics of theophylline monohy hstB7i. 

Zipp, G. L. and Rodriguez-Hornedo, N. (1989) Determination of crystal growth kinetics from desupersaturation measurement. J. Pharm., 51 147-156. 

The results reflected by the data in Table 12.5 are similar to those on the crystal-growth kinetics of Na2HP04, />., the values for the reaction rate constant measured in the SCISR, Ais, are systematically higher than those measured in the STR, kSJ, by about 20%. 

Illustrating the formulation of mass and energy balances is simplified by restricting the analysis to systems whose crystal growth kinetics are sufficiently fast to utilize essentially all of the supersaturation provided by the crystallizer in other words, the product solution... 

A variety of techniques have been used to study crystal growth kinetics in aqueous systems. The most popular are briefly described below. 

Huang F, Zhang H, Banfield IF (in prep.) Two-step crystal-growth kinetics observed in hydrothermal coarsening of nanocrystalline ZnS. 

Understanding of the possible nucleation and crystal growth kinetics for desired (and undesired) compounds can place the process development effort on a considerably shorter path to success. Reference will be made to examples in the other chapters in this book. 

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