From the atomistic to the mesoscopic scale modeling of phase transition in solids

The phase-field method is a very powerful tool to model the phase transformation and microstructural evolution of solids at mesoscopic scale. However, several important phenomena, like defect formation, grain boundary motion, or reconstructive phase transitions require an atomic scale study. Recently an approach called the quasi-particle approach, based on the Atomic Density Function theory was developed to incorporate the atomic-level crystalline structures into standard continuum theory for pure and multicomponent systems. This review focuses on the description of different computational methods used to model microstructural evolution and self-assembly phenomena at mesoscopic and atomistic scales. Various application examples of these methods are also presented.