Crystal growth approach

In general, both nucieation and crystal growth depend on supersaturation and to lesser extent temperature and magma characteristics. Such data must therefore be collected to gain maximum benefit from the population balance approach (Jones and MuIIin, 1974 Jones, 1974). Further simplifications to the describing equations are also possible, however (as follows). 

R. Kobayashi. Modeling and numerical simulations of dendritic crystal growth. Physica D (55 410, 1993 R. Kobayashi. A numerical approach to three-dimensional dendritic solidification. Exp Math 5 59, 1994. 

Substantial evidence in a number of existing experimental studies can be easily reconciled with the models discussed in the present contribution. For example segregation of short chains reported during crystal growth [1] may be thought to arise with chains which are too short to form bundles and are thus unable to provide a sufficient amount of simultaneous attractive interactions with the crystal to yield stable adsorption. We recall in this respect that one of us obtained the correct trend of the minimum chain length of PE for crystal inclusion vs. the crystallization temperature, using the bundle approach [8]. 

Some of the difficulties encountered in establishing the effect of solvent on crystal growth may be circumvented by focusing on polar crystals. This is because the difference in the rates of growth of opposite faces (hid) and (hkl) along a polar direction must arise primarily from differences in their solvent-surface interactions. Thus, one generally does not have to be concerned with faces other than the hemihedral ones in question. We illustrate below an approach to understanding solvent-surface interactions in the polar crystals of resorcinol (102). 

In this paper, three methods to transform the population balance into a set of ordinary differential equations will be discussed. Two of these methods were reported earlier in the crystallizer literature. However, these methods have limitations in their applicabilty to crystallizers with fines removal, product classification and size-dependent crystal growth, limitations in the choice of the elements of the process output vector y, t) that is used by the controller or result in high orders of the state space model which causes severe problems in the control system design. Therefore another approach is suggested. This approach is demonstrated and compared with the other methods in an example. 

Ataka, M. (1993). Protein crystal growth An approach based on phase diagram determination. Phase Transitions 45, 205-219. 

Carter, C. W. J. (1999). Experimental design, quantitative analysis, and the cartography of crystal growth. In Crys-tall ization of Nucleic Acids and Proteins. A practical approach, Ducruix, A. and R. G., eds., pp. 75-120. IRL Press, Oxford. 

Once more, the warning concerning using the commercial raw materials must be uttered. All crystals growth and nucleation phenomena are pronouncedly dependent on small amounts of impurities. Crystal habit, extent of twinning, etc, may be altered by unknown impurities in the commercial materials, it is essential, therefore, that any rate measurements which are to be of use for plant design must use the approach reagents. 

Similarly, for the general problem of crystal growth in silicate melts, it is necessary to use the diffusion matrix approach. 

Carra S, Masi M (1998) Kinetic approach to materials synthesis by gas-phase deposition. Progress in Crystal Growth and Characterization of Materials 37(1), 1-46... 

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