Crystal growth determination

Along with operating variables of the crystallizer, nucleation and growth determine such crystal characteristics as size distribution, purity, and shape or habit. 

The dominant crystal size, is most often used as a representation of the product size, because it represents the size about which most of the mass in the distribution is clustered. If the mass density function defined in equation 33 is plotted for a set of hypothetical data as shown in Figure 10, it would typically be observed to have a maximum at the dominant crystal size. In other words, the dominant crystal size is that characteristic crystal dimension at which drajdL = 0. Also shown in Figure 10 is the theoretical result obtained when the mass density is determined for a perfectiy mixed, continuous crystallizer within which invariant crystal growth occurs. That is, mass density is found for such systems to foUow a relationship of the form m = aL exp —bL where a and b are system-dependent parameters. 

It has often been observed that the plot of ln(L) versus L results in curvature rendering the method of determining the growth rate from the slope strictly inappropriate, but ways to accommodate such deviations have also been proposed. Thus, if G = G(L) integration of equation 3.15 leads to the following expression for determining crystal growth rates (Sikdar, 1977)... 

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. 

The crystal growth rates can be directly determined from the second and third moment as described above. The calculated rates for calcium oxalate here are in the range 0.75 x 10 to 4.7 x 10 m/s. Literature values for the growth rate of calcium oxalate monohydrate vary considerably 1.08 x 10 m/s (Kavanagh, 1992), 3.4 X 10 to 5.0 x 10 m/s (Garside etal., 1982) and 2.8 x lO to 1.11 X 10 m/s (Nielsen and Toft, 1984). The values obtained from the experiments are therefore within the range of the literature data. It should be borne in... 

Rates of nucleation, B , and crystal growth, G, are respectively evaluated as the functions of supersaturation. The level of supersaturation, AC, is determined... 

It was shown in Chapter 7 that the performance of continuous crystallizers is determined by the characteristics of a feedback loop relating the output performance expressed as crystal size distribution and to the feed concentration and residence time. Thus, an increase in crystallizer residence time, or decrease in feed concentration, reduces the working level of supersaturation. This decrease in supersaturation results in a decrease in both nucleation and crystal growth. This in turn leads to a decrease in crystal surface area. By mass balance, this then causes an increase in the working solute concentration and hence an increase in the working level of supersaturation and so on. There is thus a complex feedback loop within a continuous crystallizer, as considered in Chapter 7 and illustrated in Figure 8.11. 

Sohnel, O. and Mullin, J.W., 1978. A method for the determination of crystallization induction periods. Journal of Crystal Growth, 44, 377-382. 

The nucleation rate onto a crystal is determined by the flux onto an ensemble of substrates. As the nuclei should be widely separated for the nucleation approach to be valid, this does not appear to be unreasonable. However, the subsequent way in which this flux is used to determine the thickness and growth rate seems somewhat inconsistent as explained below. However, a modification of the derivations would satisfy this query, and it is not likely that this will greatly affect the results. 

Thirdly, the multicomponent model was applied to the case of crystallization of a random A-B copolymer by Helfand and Lauritzen [127]. Their main result is that the composition of, 4 s and B s in the crystal is determined by kinetic, rather than equilibrium considerations the inclusion of excess B increases with growth rate. 

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. 

If these are not within the correct range, one does not obtain single crystal growth. This method has been used in the past only because of its relative simplicity of apparatus and materials. However, the quality of crystals so-produced has been rather poor. Ciystels produced by this method are suitable for structure determinations, but are poor in optiCcd quality and are notat all suited for electronic applications. 

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