Modeling of Diffusion for Crystal Growth

Abstract

Computer simulations have a wide range of applications in crystallization of which crystal habit prediction is one of the most important. In the absence of routine experimental methods, computer simulations can provide a detailed picture of the kinetics of crystallization. The mechanism of crystal growth from solutions is subject to different processes. Present computational methods available as part of commercially available modeling software are based upon either the Bravais–Friedel–Donnay–Harker (BFDH), the attachment energy (AE) or the surface energy models and do not account for the influence of the growth environment of the crystal upon its growth. In order to control the growth of crystals and therefore their habit, it is necessary to understand the factors that govern individual face growth rates. Since crystal growth depends upon mass transport to the surface of the crystal whenever crystal growth occurs in solution, it is reasonable to assume that a quantitative description of the mass transport at the solid liquid interface can give useful insight concerning the calculation of face growth rates. If crystallization takes place in the melt, consideration should be focused on heat transfer. Here, the determination of molecular scale features of crystal growth and a road map how to simulate face growth rates under consideration of the growth environment is presented. Molecular dynamics simulations are employed to study diffusion coefficients. The two examples presented here are benzophenone and hydroquinone. The one component system is considered a melt and computer experiments are performed on the system and characteristic changes of the transport parameters depending upon variations in the external factors, such as temperature level, simulation time, number of molecules in the amorphous cell, and force fields used in the simulations. After acquiring enough simulation experience and eliminating unsuitable system conditions a solution (solute-solvent) was simulated and effects of changes of other system parameters such as supersaturation level were investigated. The data obtained from these simulations are used to calculate the transport properties of the molecules under the given conditions and are compared to the results of the empirical equations which are available in the literature. Data obtained from these simulations producing diffusion coefficient values are used to correlate to the calculations of face growth rates by considering the ambient system conditions. Finally, depending upon the value of the mass transfer coefficients, the process controlling solution growth is defined and face growth rates are calculated depending upon the process which limits the face growth.

Keywords:

• Benzophenone
• Crystal growth
• Diffusion
• Hydroquinone
• Molecular modeling

ACKNOWLEDGMENTS

Authors wish to thank the Deutsche Forschungsgemeinschaft DFG (SPP-1155) for financial support and prolific discussions about the project.