Coarsening of Dendritic Solid-Liquid Mixtures: The Low Volume Fraction Limit
Dendrites form during solidification into an undercooled melt. These dendrites possess secondary and sometimes even ternary arms. While the tip radius and tip velocity of the dendrite are set by the growth conditions, the sidebranches behind the tip undergo a coarsening process under nearly isothermal conditions. This coarsening process sets the final arm thicknesses and distances between dendrite arms in the solidified structure – almost independent of the length-scale given by the dendrite tip. Unfortunately, the morphological evolution of these secondary dendrite arms remains poorly understood. Since there is a close relationship between the size scale of the coarsened dendritic structure and the mechanical properties of the material, a greater understanding of this process will have important practical implications.The reduced gravitational accelerations found during processing on the Interna- tional Space Station can allow for unprecedented insights into coarsening processes of solid-liquid mixtures in which the volume fraction of solid dendrites is small. In a microgravity environment it will be possible to follow the evolution of the morphology of the mixtures in the diffusive limit where the concentration field is set by the curvatures of the solid-liquid interfaces. It will also be possible to determine the evolution of the topology of the solid-liquid mixtures. For example, when secondary dendrite arms detach from the primary dendrite stem they will not sediment, and it will thus be possible to determine the rate at which this detachment process occurs and its spatial location. The topology and morphology of these dendritic mixtures will be determined using three-dimensional reconstructions and insights into the mechanisms of coarsening will be provided by phase field simulations that employ these reconstructions as initial conditions. These studies will provide insights into the dynamics of morphological evolution of these systems and will point the way to the formulation of models of this technologically important coarsening process.