Control of Crystallization Process

A local view of the computation grid in the melt-crystal domain when the interface is moving upward as a function of time is shown in Fig. 4.2. In order to fit to the moving interface as a function of time, the grid cells in the melt and solidified ingot are stretched, and the grid points are moved upward as well. 

Conductive heat transfer in all solid components, radiative heat exchange between all diffusive surfaces in the unidirectional solidification furnace, and the Navier-Stokes equations for the melt flow in the crucible are coupled. 

they are solved iteratively in a transient way. Time histories of heater power, fraction solidified, and growth velocity during a unidirectional solidification process are shown in Fig. 4.3 [16]. Variation of heater power as a function of time was imposed as a process parameter. 

The impurity distribution in the silicon melts and solidified silicon ingot was solved on the basis of solutions of the thermal field and melt flow in a 

Concentration taking into account on segregation of impurity was expressed by (4.1) at the m-c interface  

---

Rawlings, J.B., Sink, C.W. and Miller, S.M., 2001. Control of crystallization processes. In Handbook of Industrial Crystallization. Ed. A.S. Myerson, 2nd edition. Oxford Butterworth-Heinemann. 

The design and operation of industrial crystallizers is where developments in the laboratory are confirmed and their practical significance determined. In recent years, crystallization processes involving specialty chemicals and pharmaceuticals have increased. This has led increased interest in batch crystallization operation, optimization and desigrt At the same time, the advent of powerful computers and their routine avaUabilily has stimulated interest in the area of on-line control of crystallization process (both batch and continuous). Progress in batch crystallization is surrunarized in a number of recent papers and reviews 173-801. In this section I will discuss two areas which I think will have an impact in the next decade. 

Control of crystallization processes requires modulation of either nucleation or growth or, as is most often the case, both modes of crystal development simultaneously. Each operation must be evaluated to determine which of these process objectives is most critical, from the point of view of overall outcome, to determine whether nucleation or growth should be the dominant phase. Much of the literature is focused on nucleation for the obvious reason that the number and size of nuclei initially formed can dominate the remainder of the operation. However, it is generaUy agreed that nucleation can be difficult to control, since there are several factors that can play a role in the conditions for nucleation onset, nucleation rate, and number of crystals generated before growth predominates. 

Aamir, E., Nagy, Z. K., Rielly, C. D., Kleinert, T. Judat, B. 2009 Combined quadrature method of moments and method of characteristics approach for efficient solution of population balance models for dynamic modeling and crystal size distribution control of crystallization processes. Industrial Engineering Chemistry Research 48, 8575-8584. 

Mohan, R. Boateng, K. A. Myerson, A. S. Estimation of crystal growth kinetics using differential scanning calorimetry, J. Cryst. Growth 2000, 212,489-499. See in this paper a brief review of some key references to analysis and control of crystallization processes in industrial applications. 

---