The Modeling of growth process on the surface of crystal (original) (raw)
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A system of rate equations previously proposed in the literature [Phys. Rev. B 54 (1996) 9828] has been numerically solved. At variance with the other rate equation schemes adopted until now, as well as describing the nucleation stage, the new scheme allows one to follow the film growth to its completion. This result has been achieved thanks to the right treatment of the impingement process among the growing clusters. Moreover, the new approach also allows one to predict whether or not the nucleation can be considered as simultaneous for given growth conditions.
A macroscopic model for the habit of crystals grown from solutions
Journal of Crystal Growth, 1969
A macroscopic model for the habit of growth of a crystal of an arbitrary shape is presented. The normal habit is defined as a first approximation of the real one. The model predicts the reappearance and disappearance of a given crystallographic face or edge of the grown crystal. The growth velocity is expressed in
Growth kinematics of the regeneration surfaces of crystals
Crystallography Reports, 2009
A formula for the propagation velocity of the regeneration surface front is derived under the assumption of equal growth rates of the polyhedral crystal faces and the corresponding faces forming subindividuals of the regeneration surface. It is shown that both sharp minima (increase of the face) and sharp maxima (decrease of the face) can correspond to faces in the growth
physica status solidi (b), 2007
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Computer modeling of atomic scale crystal growth processes
Journal of Crystal Growth, 1999
The wide availability of extremely powerful computers has ushered in a new era in which simulation is the preferred method for the modeling of physical processes. The development of our understanding of the atomic scale processes involved in crystal growth, where computer simulations have played a central role, is an example of the power of these methods. It has now become apparent that computer simulations have not only been useful, but were essential for this development. Crystallization processes will be discussed in the context of the role of computer modeling in the development of our current understanding, and to illustrate how it is continuing to play a central role.
Modeling of Diffusion for Crystal Growth
Soft Materials, 2012
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.
Crystal growth mechanisms: Interface kinetics
Materials Chemistry, 1979
A survey is given of the main theories on the interfacial kinetics of the growth from vapour and solution. Apart from the classical theory of the growth of singular faces by the 2D nucleation mechanism (mononuclear and polynuclear), special stress is laid on the fundamental of the theory of Burton, Cabrera and Frank for both the surface and volume diffusion; its more significant developments are considered as well (Chernov model on the volume diffusion, Gilmer, Ghez and Cabrera analysis of combined surface and volume diffusion processes). Furthermore the analysis of the implications of the Miiller-Krumbhaar generalized equation for crystal growth is carried out, when applied to the growth of spirals under an anisotropic chemical potential
Morphology evolution of crystal populations: Modeling and observation analysis
Chemical Engineering Science, 2012
The joint analysis of modeling and observation of crystallization systems with regard to shape is taken out. We start with the modeling and numerical solution of the balance equations for a seeded batch crystallizer accounting for crystal shape distributions. For this, a meshing algorithm is used to establish appropriate origins for characteristic curves of the population balance. The calculated number density evolution is sampled and the resulting representative crystal shapes are photographed. The orientation of the crystal relative to the photoplane is modeled as a stochastic process. Therefore, the projection cannot be related to the actual 3D shape in a trivial way. We design an estimation scheme and evaluate its reliability for some test populations. Finally, the number density evolution of a whole simulated experiment is observed at different sampling rates. We show that the underlying growth parameters can be reestimated from the observed data in a reliable way for which a relatively small number of samples is required.