Crystal growth measurement

Wang, X. Z., Roberts, K. J. Ma, C. 2008 Crystal growth measurement using 2D and 3D imaging and the perspectives for shape control. Chemical Engineering Science 63, 1173-1184. 

Estimation of Crystal Growth Kinetics. The techniques for crystal growth measurement discussed in the last section all involved direct measurement of the change in mass or size of a crystal (or crystals) at a fixed temperature and supersaturation. To obtain kinetic parameters, these experiments are repeated at a several different supersaturations at each temperature of interest and then fit to a power law model given by Eqs. (2.55) or (2.56). In the MSMPR method, which will be described in detail in Chapter 4... 

At the present study the diffusion-controlled growth process from the ternary system was modelled by the Maxwell-Stefan equations. The estimation methods of the required parameters in the model were shown. The model was evaluated from single crystal growth measurements in the ternary system. The results showed that experimental and predicted growth rates were within acceptable agreements. 

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. 

Crystal growth. As we saw in the preceding section, before World War II the dislocation pioneers came to the concept through the enormous disparity between calculated and measured elastic limiting stresses that led to plastic deformation. The same kind of disparity again led to another remarkable leap of imagination in postwar materials science. 

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... 

Brown, C.M., Ackemiann, D.K., Puricli, D.L. and Finlayson, B., 1991. Nucleation of calcium oxalate monoliydrate use of turbidity measurements and computer-assisted simulations in characterising early events in crystal formation. Journal of Crystal Growth, 108, 455 64. 

Bujac, P.B. and Mullin, J.W., 1969. A rapid method for the measurement of crystal growth rates in a fluidised bed crystallizer. Symposium on Industrial Crystallization. London, 1969. Rugby Institution of Chemical Engineers, pp. 121-129. 

Dunuwila, D. and Berglund, K.A. 1997. ATR FTIR spectroscopy for in situ measurement of supersaturation. Journal of Crystal Growth, 179, 185-193. 

One of the more important uses of OM is the study of crystallization growth rates. K. Cermak constructed an interference microscope with which measurements can be taken to 50° (Ref 31). This app allows for study of the decompn of the solution concentrated in close proximity to the growing crystal of material such as Amm nitrate or K chlorate. In connection with this technique, Stein and Powers (Ref 30) derived equations for growth rate data which allow for correct prediction of the effects of surface nucleation, surface truncation in thin films, and truncation by neighboring spherulites... 

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. 

Comparison of crystal growth rate coefficients measured in ISC and FBC... 

The overall rate of crystallization is determined by both the rate of nuclei formation and by the crystal growth rate. The maximum crystal growth rate lies at temperatures of between 170 and 190 °C [71, 72], as does the overall crystallization rate [51, 61, 75], The former is measured using hot stage optical microscopy while the latter is quantified by the half-time of crystallization. Both are influenced by the rate of nucleation on the crystal surface and the rate of diffusion of polymer chains to this surface. It has been shown that the spherulite growth rate decreases with increasing molecular weight due to the decrease in the rate of diffusion of molecules to this surface [46, 50, 55, 71, 74],... 

As with nucleation, classical theories of crystal growth 3 20 2135 40-421 have not led to working relationships, and rates of crystallisation are usually expressed in terms of the supersaturation by empirical relationships. In essence, overall mass deposition rates, which can be measured in laboratory fluidised beds or agitated vessels, are needed for crystalliser design, and growth rates of individual crystal faces under different conditions are required for the specification of operating conditions. 

Methods used for the measurement of crystal growth rates are either a) direct measurement of the linear growth rate of a chosen crystal face or b) indirect estimation of an overall linear growth rate from mass deposition rates measured on individual crystals or on groups of freely suspended crystals 35,41,47,48). 

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