Kinetic crystallization growth

The presence of other chemical species can also influence the nucleation kinetics, crystal growth and aggregation characteristics, resulting in a modified crystal morphology due to complexation of some precipitant species and/or obstruction of some active growth sites [57,60]. 

The statement is frequently made that one zeolite synthesis is faster than another but the measurement criteria may be extremely loosely defined. Often, there is no distinction between the induction time and the growth period (section 6), so that it is impossible to tell whether a reaction is slow because it takes a long time to nucleate or because the crystals grow slowly in the given circumstances. A comparison of some hypothetical synthesis reactions is shown in Table 2. The data are derived from a computer simulation of zeolite growth based on a very simple kinetic crystal growth model [50,73], i.e. 

However, in crystallizers that are used in everyday situations exactly the opposite may occur [3,4], as illustrated in Figure 11.6. The reason for this is the so-called attrition rate Ga, which counteracts the kinetic crystal growth rate G. While G depends exclusively on the supersaturation Ac, Ga is a function of the crystal size L. From this follows an effective crystal growth rate Gefr, resulting from the difference between G and Ga7 for example, for the crystal size L the attrition rate Ga becomes equal to Gk and Get becomes zero, instead of the ideal kinetic crystal growth rate G. Longer retention times can therefore certainly result in smaller crystals - other than expected. 

The difficulty with each of the theoretical approaches to date, however, is that they cannot yet predict crystal growth rate coefficients and exponents for a particular substance a priori. Thus as with nucleation kinetics, crystal growth rate data from industrial crystallizers are usually correlated empirically with environmental conditions, such as concentration and temperature using a power law model of the form... 

The kinetics of crystal growth has been much studied Refs. 98-102 are representative. Often there is a time lag before crystallization starts, whose parametric dependence may be indicative of the nucleation mechanism. The crystal growth that follows may be controlled by diffusion or by surface or solution chemistry (see also Section XVI-2C). 

At equilibrium, crystal growth and dissolving rates become equal, and the process of Ostwald ripening may now appear, in which the larger crystals grow at the expense of the smaller ones. The kinetics of the process has been studied (see Ref. 103). 

Although magma density is a function of the kinetic parameters fP and G, it often can be measured iadependentiy. In such cases, it should be used as a constraint ia evaluating nucleation and growth rates from measured crystal size distributions (62), especially if the system of iaterest exhibits the characteristics of anomalous crystal growth. 

The population balance analysis of the idealized MSMPR crystallizer is a particularly elegant method for analysing crystal size distributions at steady state in order to determine crystal growth and nucleation kinetics. Unfortunately, the latter cannot currently be predicted a priori and must be measured, as considered in Chapter 5. Anomalies can occur in the data and their subsequent analysis, however, if the assumptions of the MSMPR crystallizer are not strictly met. 

In addition to induction time measurements, several other methods have been proposed for determination of bulk crystallization kinetics since they are often considered appropriate for design purposes, either growth and nucleation separately or simultaneously, from both batch and continuous crystallization. Additionally, Mullin (2001) also describes methods for single crystal growth rate determination. 

Several authors have presented methods for the simultaneous estimation of crystal growth and nucleation kinetics from batch crystallizations. In an early study, Bransom and Dunning (1949) derived a crystal population balance to analyse batch CSD for growth and nucleation kinetics. Misra and White (1971), Ness and White (1976) and McNeil etal. (1978) applied the population balance to obtain both nucleation and crystal growth rates from the measurement of crystal size distributions during a batch experiment. In a refinement, Tavare and... 

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. 

Nancollas, G.H. and Gardner, G.L., 1974. Kinetics of crystal growth of calcium oxalate monohydrate. Journal of Crystal Growth, 21, 267-276. 

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

Tomazic, B. and Nancollas, G.H., 1979. The kinetics of dissolution of calcium oxalate hydrates. Journal of Crystal Growth, 46, 355-361. 

T. Burkhardt, H. Muller-Krumbhaar, D. Kroll. A generalized kinetic equation of crystal growth. J Cryst Growth 5S 13, 1973. 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

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. 

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