## Prof. dr Helena Zapolsky

Université de Rouen, Saint-Etienne du Rouvray, France

"Multiscale modelling of phase transitions"

The phase field method has recently emerged as a powerful computational approach to modelling and predicting mesoscale morphological and microstructure evolution in materials. It describes a microstructure using two field variables: concentration (a conserved variable) and order parameter (nonconserved variable). The temporal and spatial evolution of these field variables is governed by the Cahn-Hilliard non-linear diffusion equation and the Allen-Cahn relaxation equation. At present stage the phase field method is able to predict the evolution of arbitrary morphologies and complex microstructures. However, some important phenomena like defects formation, grain boundaries motion or reconstructive phase transitions require atomic scale study. Recently an approach coined atomic density function (ADF) modelling has been developed to incorporate atomic-level crystalline structures into standard continuum theory for pure and binary systems. The ADF model describes the diffusive, large-time-scale dynamics of the atomic density field ?, which is spatially periodic on atomic length scales. In this talk the application of phase field and ADF models for various material processes including solidification, solid-state structural phase transformations, coarsening and microstructure evolution will discussed.