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

Abstract 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 Λ and tip radius ρ. While ρ shows a good agreement between experimental measurements and dendrite growth theory, with ρ ∼ V − 1 / 2 , Λ is observed to increase with V ( ∂ Λ / ∂ V > 0 ), in apparent disagreement with classical scaling laws for primary dendritic spacing, which predict that ∂ Λ / ∂ V 0 . We show through simulations that this trend inversion for 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 by a combination of slow transient dynamics of microstructural homogenization and the influence of the sample thickness.