Microstructure selection in thin-sample directional solidification of an Al-Cu alloy: In situ X-ray imaging and phase-field simulations

We study microstructure selection during directional solidification of a thin metallic sample. We combine in situ X-ray radiography of a dilute Al-Cu alloy solidification experiments with three-dimensional phase-field simulations. We explore a range of temperature gradient G and growth velocity V   and build a microstructure selection map for this alloy. We investigate the selection of the primary dendritic spacing ΛΛ and tip radius ρ. While ρ shows a good agreement between experimental measurements and dendrite growth theory, with ρ∼V−1/2ρ∼V−1/2, ΛΛ is observed to increase with V   (∂Λ/∂V>0∂Λ/∂V>0), in apparent disagreement with classical scaling laws for primary dendritic spacing, which predict that ∂Λ/∂V<0∂Λ/∂V<0. We show through simulations that this trend inversion for Λ(V)Λ(V) is due to liquid convection in our experiments, despite the thin sample configuration. We use a classical diffusion boundary-layer approximation to semi-quantitatively incorporate the effect of liquid convection into phase-field simulations. This approximation is implemented by assuming complete solute mixing outside a purely diffusive zone of constant thickness that surrounds the solid-liquid interface. This simple method enables us to quantitatively match experimental measurements of the planar morphological instability threshold and primary spacings over an order of magnitude in V  . We explain the observed inversion of ∂Λ/∂V∂Λ/∂V by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.

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