Multi-scale needle-network model of complex dendritic microstructure formation

Abstract

We present a novel multi-scale Dendritic Needle Network (DNN) approach in order to model well-developed highly-ramified dendritic microstructures on the coarser scale of several crystal grains while retaining a faithful quantitative description of the transient dynamics of individual dendritic branches. This approach is intended to bridge the scale gap between phase-field and cellular automaton methods. The dynamics of each needle-like branch, characterized by its tip velocity V and radius ρ, is fixed by two conditions: (i) on the inner tip scale, a standard microscopic solvability condition relates ρ2V to the strength of surface tension anisotropy, and (ii) on the outer diffusion length scale, a flux balance condition relates the product ρV2 to a flux intensity factor extracted from a contour integral analogous to the J-integral of fracture mechanics. The method is tested for low supersaturation and reproduces the analytical solutions for both early stage and steady state growth dynamics. The results are directly compared with a quantitative phase-field simulation for an experimentally relevant supersaturation. We present as well an illustrative simulation for highly branched polycrystalline growth. This model should permit to investigate the macroscale grain evolution through the dynamics of individual primary dendrites and higher-order branches, controlled by both the intragrain history-dependent selection and the intergrain dendrite interactions.