Crystal growth prediction

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. 

The data plotted in the figure clearly support the predicted positive dependence of crystal size on agitation rate. Precipitation in the crystal film both enhances mass transfer and depletes bulk solute concentration. Thus, in the clear film model plotted by broken lines, bulk crystal sizes are initially slightly smaller than those predicted by the crystal film model but quickly become much larger due to increased yield. Taken together, these data imply that while the initial mean crystal growth rate and mixing rate dependence of size are... 

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... 

Although specific calculations for i and g are not made until Sect. 3.5 onwards, the mere postulate of nucleation controlled growth predicts certain qualitative features of behaviour, which we now investigate further. First the effect of the concentration of the polymer in solution is addressed - apparently the theory above fails to predict the observed concentration dependence. Several modifications of the model allow agreement to be reached. There should also be some effect of the crystal size on the observed growth rates because of the factor L in Eq. (3.17). This size dependence is not seen and we discuss the validity of the explanations to account for this defect. Next we look at twin crystals and any implications that their behaviour contain for the applicability of nucleation theories. Finally we briefly discuss the role of fluctuations in the spreading process which, as mentioned above, are neglected by the present treatment. 

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. 

As discussed in section 2.4.4 the coordinating ability of a solvent will often affect the rate of nucleation and crystal growth differently between two polymorphs. This can be used as an effective means of process control and information on solvent effects can often be obtained from polymorph screening experiments. There are no theoretical methods available at the present time which accurately predict the effect of solvents on nucleation rates in the industrial environment. 

Ouvrard, C., Price, S.L., 2004, Toward Crystal Structure Prediction for Conformationally Flexible Molecules The Headaches Illustrated by Asprin, Crystal Growth and Design, Vol.4, No. 6, 1119-1127. 

A better insight into the mechanisms of the individual steps in the formation of crystals would be of great help in explaining the creation and transformation of sedimentary deposits and biological precipitates. Valuable reviews are available on the principles of nucleation of crystals and the kinetics of precipitation and crystal growth (Zhang and Nancollas, 1990 Steefel and Van Cappellen, 1990 Van Cappellen, 1991). Only a few important considerations are summarized here to illustrate the wide scope of questions to be answered in order to predict rates and mechanisms of precipitation in natural systems. 

Table I. Prediction of Electrolyte Crystal Growth Rates... 

In their pioneering work on crystal growth Burton, Cabrera and Frank predicted that on an atomic length scale the equilibrium structure of a crystal surface should exhibit a transition from a smooth state at low temperatures to... 

The development and refinement of population balance techniques for the description of the behavior of laboratory and industrial crystallizers led to the belief that with accurate values for the crystal growth and nucleation kinetics, a simple MSMPR type crystallizer could be accurately modelled in terms of its CSD. Unfortunately, accurate measurement of the CSD with laser light scattering particle size analyzers (especially of the small particles) has revealed that this is not true. In mar cases the CSD data obtained from steady state operation of a MSMPR crystallizer is not a straight line as expected but curves upward (1. 32. 33V This indicates more small particles than predicted... 

The use of tailor made additives holds great promise in the area of crystal growth and morphology control. The routine selection and use of these type of additives will require a fundamental understanding of the mechanism which the additives work on a molecular basis. At the same time, the effect of solvent molecules on the crystal growth process is another related and important problem. In both instances, the relationship between internal aystal structure, aystal growth rate, solvent and impurities are needed to predict the habit of a crystal and thus allow seleaion of the proper conditions and components required to obtain a desired habit... 

The structural and equilibrium forms of crystals are predicted assuming that the crystal is perfect and that the ambient phase is isotropic. Growth forms, however, describe real crystals containing lattice defects growing in a real ambient phase. We should therefore consider the following factors, which may affect the growth forms. 

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