Abstract
In classical crystallization as well as in nanoparticle engineering crystal shape is an important property of crystalline products. The emergent properties of bulk material are closely related to the crystal shape. We present a single crystal model describing shape evolution. The model has a hybrid character since the appearance and disappearance of crystal facets is a discrete event in the continuous process of crystal growth. Tight control of not only the single crystal's shape and size is desirable but with regards to mass production shape and size distribution control is required. A first step in this direction is a model representing the dynamical evolution of the shape distribution of a crystal population. We show that a population balance approach can be used. In the proposed framework the hybrid nature of the single crystal evolution has to be taken care of. We also sketch a numerical scheme with which the proposed model equations can be solved.
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