Nucleation and growth probabilistic models for powders transformation
This work focuses on powder transformations using the Mampel model, i.e. proceeding by surfacic nucleation and isotropic growth. In the first part, using a probabilistic approach, a new expression of the fractional conversion is established. This expression is more general than the existing ones because it is free of any geometrical dependence and is available in non isothermal/non isobaric conditions. The fractional conversion is then numerically evaluated by a Monte Carlo method. Different variance reduction methods are implemented, allowing to improve time calculation. In the following part it is shown how the probabilistic structure of the measured fractional conversion influences the choice of the fitting method and leads to the quantification of the parameters uncertainties. Finaly, a new nucleation model is introduced. It describes the phenomenon from a microscopic point of view where a nucleus is a group of defects which appear and move randomly in the cristalline structure.