Atomistic and continuum models for phase change dynamics
Anders SzepessyKungl. Tekniska Högskolan, Stockholm, Sweden
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The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and capillary forces acting on length scales compared to the nanometer width of the solid-liquid interface. Its modeling is useful for instance in processing techniques based on casting. The phase ﬁeld method is widely used to study evolution of such microstructures of phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen–Cahn/Ginzburg–Landau equation modeling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic ﬂuctuations to obtain the qualitative correct result of dendritic side branching. This lecture presents some ideas to derive stochastic phase ﬁeld models from atomistic formulations by coarse-graining molecular dynamics and kinetic Monte Carlo methods.