Atomistic and continuum modeling of dendritic solidification

Due to its technological importance, modeling of dendrite growth in pure metals and alloys remains a significant challenge in the field of materials science. In this review recent achievements in the dendrite modeling problem, using two distinct length scale approaches, are summarized. At the nanometer scale, molecular dynamics and Monte Carlo techniques have been developed to extract two important properties of the solid–liquid interface: the kinetic coefficient and the solid–liquid interfacial free energy. Perhaps more importantly the atomistic simulation methods are capable of accurately determining the small, yet crucially important, anisotropies of these parameters. At the mesoscopic scale, advances in phase field modeling have largely overcome the numerical problem associated with the large disparity in length scales typically found in dendrite growth. It is demonstrated that, when the atomistic and continuum level approaches are combined, accurate and parameter free predictions of dendrite growth velocities are possible. In addition, extensions of atomistic and phase field modeling to the case of binary alloys are described.