Crystal growth rate dispersion

Although evidence exists for both mechanisms of growth rate dispersion, separate mathematical models were developed for incorporating the two mechanisms into descriptions of crystal populations random growth rate fluctuations (36) and growth rate distributions (33,40). Both mechanisms can be included in a population balance to show the relative effects of the two mechanisms on crystal size distributions from batch and continuous crystallizers (41). 

Such cases of curvature can arise due to so-called anomalous growth. A variety of mechanistic causes for this behaviour have been proposed which fall into two broad classes viz. growth rate dispersion and size-dependent crystal growth. Both classes... 

Growth rate fluetuations appear to inerease with an inerease in temperature and supersaturation leading to erystals of the same substanee, in the same solution at identieal supersaturation, exhibiting different growth rates this is thought to be a manifestation of the phenomenon of either size-dependent crystal growth or alternatively, growth rate dispersion. 

Ristic, R.I., Sherwood, J.N. and Shripathi, T., 1991. The role of dislocations and mechanical defonuation in growth rate dispersion in potash alum crystals. In Advances in Industrial Crystallization. Eds. J. Garside, R.J. Davey, and A.G. Jones. Oxford Butterworth-Heinemann, pp. 77-91. 

RI Ristic, JN Sherwood, K Wojciechowski. Assessment of the strain in small sodium chlorate crystals and its relation to growth rate dispersion. J Cryst Growth 91 163— 168, 1988. 

Both experimental and theoretical work has demonstrated that growth rate dispersion exists, and has a measurable effect on the CSD in both batch and continuous crystallization processes. Further understanding of this phenomenon on a fundamental level will be required to develop methods to make use of or control growth rate dispersion and make it a tool in control of particle size and shape. 

Example. Consider an evaporative, isothermal. Class II crystallizer with fines removal. It is assumed that the growth rate is size-independent and that there is no growth rate dispersion. Because we assume fines removal, the method of moments can not be applied. 

The nuclei are produced in a variety of sizes ranging up to about 40 ptmeters. This phenomenon is called the birth size dispersion. Similarly, different crystals grow at different rates, a characteristic called growth rate dispersion ... 

Dislocations can occur within crystals as a result of stresses in crystal growth on seeds and around surface nuclei and inclusions. Spiral and other self-perpetuating growth can promote growth rate dispersion (different growth rates on different crystals of the same material) because each crystal is responding to the structure of its own unique dislocation(s). 

Situations 1 and 2 are referred to as size-dependent growth. Another reason for variation of growth rates in a crystal population is growth rate dispersion. This dispersion occurs because of differences in individual crystals. These differences are based on (a) inherent properties of each nucleus, (b) fluctuations with time of each nucleus, or (c) expected differences between crystals growing from (differently sized) dislocations by the BCF mechanism described in Section 4.3.1.3 or by others. 

Size-dependent growth and growth rate dispersion do affect the ultimate size distribution in industrial crystallizers. To a large extent, measurement of growth rates with large numbers of crystals in suspension adequately compensates for individual variations within the crystal population. 

Agglomeration and/or aggregation are common in reactive crystallization and should not be confused with true growth (see Section 10.3.8.1 below). Secondary growth phenomena can also be expected, such as growth rate dispersion and size-dependent growth (see Section 10.3.8.2 below). 

Other secondary effects, which are not exclusive to reactive crystallization, are size-dependent growth and growth rate dispersion. These effects may not be separable, but both can change the final mean particle size and PSD. Both are discussed in Sohnel and Garside (1992, pp. 103-105) and in Chapter 4 of this book. 

The crystal growth rates of PVDF, PA-6, and POM amount to at least lOpm/min in the temperature range where their crystallization steps occur (6,52,67). A dispersed particle, therefore, once nucleated, crystallizes promptly and the primary rather than the secondary nucleation is the rate-controlling factor of the crystallization kinetics of the dispersed phase. Thus, the crystallization temperatures as observed in the DSC-cooling run agree roughly with the nucleation temperatures. 

Girolami, M. W. Rousseau, R. W. 1985 Size-dependent crystal growth a manifestation of growth rate dispersion in the potassium alum-water system. AIChE Journal 31, 1821-1828. 

Larson, M. A., WraTE, E. T., Ramanarayanan, K. A. Berglund, K. A. 1985 Growth rate dispersion in MSMPR crystallizers. AlChE Journal 31, 90-94. 

Mydlarz, J. Briedis, D. 1992 Growth rate dispersion vs size-dependent growth rate for MSMPR crystallizer data. Computers and Chemical Engineering 16, 917-922. 

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