(20c) Modeling of Morphology Transformations In Crystalline Materials: A Generalized Framework

This talk will present a generalized population balance model (PBM) to predict dynamic behavior of morphology (shape) transformations in populations of crystals. The model utilizes symmetry of crystal to reduce the degree of freedom in shape representations. The main crux of the model lies in its ability to describe the evolution of morphology distributions for any type of crystals in least possible dimensions (or dynamic variables). It will be shown subsequently that the dynamic behavior of morphology transformations for any crystalline material can be described by f-dimensional PBM, where f is the number of energetically favorable families of crystal planes.

            The current problem carries immense opportunities for semiconductor, catalyst and pharmaceutical-based industries to produce crystals of desired shapes and shape-related properties. Many efforts have been made in past to understand the dynamics of crystal morphology at molecular level via various approaches like Phase-Field Modeling, Molecular Dynamics simulations, Monte Carlo simulations etc. However, their applications in determining the dynamics of morphology distributions are non-trivial due to the requirement of tremendous computational efforts. Conversely, the mechanistic models like PBMs are efficient in large scale applications as they require relatively less computational efforts and can give reasonably accurate results in no time. The talk will provide the recipe to formulate PBM for any type of crystalline material, which can be solved to predict the evolution of morphology distributions.

            The generalized framework has the following few basic elements, which will be discussed thoroughly in the talk:

1. Identification of Maximum Degenerate State of a Crystal Shape.
2. Identification of Boundaries of Crystal State Space.
3. Developing Morphology Net.
4. Writing Multi-dimensional PBM.
5. Reduction to f-dimensional PBM.

            This model provides the most efficient description for the morphology transformations in population of crystals, whose usefulness is quite apparent in different applications.