CSD (Crystal Size Distribution)

In this chapter, the basis for the tool to interpret crystal size distribution (CSD) will be explained. First, we will address the background of CSD introduction, the physical interpretation of the exponential CSD often observed in nature, and the examples of studies on CSD in nature. Then, we will introduce two theoretical methods of describing CSD’s temporal development; the Eulerian and Lagrangian descriptions, which were introduced in the chapters on vesiculation and crystallization. In this chapter on CSD, we will obtain general solutions of CSD under various conditions in closed and open systems. The closed system is a system in which CSD is only determined by the dynamics of nucleation and growth of crystals, and liquid and crystals do not move. An open system is that in which exchange with the external system of crystals essentially influences CSD. An advantage of the mathematical disscussion of CSD is that when CSD obtained by models is compared with that obtained by experiments, the relationship between observable CSD and model parameters can be clearly undrestood than when we use an empirical rule obatained using numerical calculations. Finally, we will derive the CSD corresponding to the Avrami plot, which is often conducted in phade change experiments.