More sophisticated techniques for the estimation of growth kinetics involve the use of the entire desupersaturation curve with parameter estimation techniques (Qiu and Rasmussen 1990). The combination of the desupersaturation curve and the crystal size distribution can be used to estimate both growth and nucleation [Pg.61]

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. [Pg.790]

Several investigators have offered various techniques for estimating crystallization growth and nucleation parameters. Parameters such as kg, 6, and ki are the ones usually estimated. Often different results are presented for identical systems. These discrepancies are discussed by several authors (13,14). One weakness of most of these schemes is that the validity of the parameter estimates, i.e., the confidence in the estimates, is not assessed. This section discusses two of the more popular routines to evaluate kinetic parameters and introduces a method that attempts to improve the parameter inference and provide a measure of the reliability of the estimates. [Pg.104]

Furthermore, the model has been used to analyze data found in the Hterature [62] for C distribution in LEC-grown GaAs single crystals due to a step-wise increase of the CO partial pressure in the gas atmosphere (Fig. 9.30). The same set of parameters was used with the exception of crucible, crystal diameter and growth rate. Estimates of initial carbon and oxygen concentrations were made additionally. There is a satisfactory correspondence between the calculated and the experimentally determined C distribution. [Pg.259]

The observed transients of the crystal size distribution (CSD) of industrial crystallizers are either caused by process disturbances or by instabilities in the crystallization process itself (1 ). Due to the introduction of an on-line CSD measurement technique (2), the control of CSD s in crystallization processes comes into sight. Another requirement to reach this goal is a dynamic model for the CSD in Industrial crystallizers. The dynamic model for a continuous crystallization process consists of a nonlinear partial difference equation coupled to one or two ordinary differential equations (2..iU and is completed by a set of algebraic relations for the growth and nucleatlon kinetics. The kinetic relations are empirical and contain a number of parameters which have to be estimated from the experimental data. Simulation of the experimental data in combination with a nonlinear parameter estimation is a powerful 1 technique to determine the kinetic parameters from the experimental [Pg.159]

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