Study of the twinned dendrite tip shape I: Phase-field modeling

The growth kinetics advantage of twinned aluminum dendrites over regular ones is still an unsolved problem of solidification. Although it is linked to the tip geometry, the influence of a coherent (1 1 1) twin plane on a 〈1 1 0〉 twinned dendrite tip is unclear, despite several past experimental observations. In the present contribution, a three-dimensional phase field model implemented on a cluster of parallel computers has been used to simulate the growth of a twinned dendrite under various directional solidification conditions. Only half a dendrite was modeled by replacing the coherent twin plane by a boundary with an appropriate condition on the phase parameter that is equivalent to the Young–Laplace equilibrium condition along the triple line between twinned solid, untwinned solid and liquid. It is found that the small liquid cusp present at the tip rapidly evolves into a doublon-type morphology, i.e. a 〈1 1 0〉 dendrite split in its center by a deep and thin liquid pool with the triple line at the root. At high growth rates, the two sides of the doublon tend to coalescence and form small isolated liquid droplets. The positive concentration gradient near the doublon root appears to be rapidly smeared out by back-diffusion in the solid, thus making difficult its quantification through experimental methods. These simulation results are correlated with new experimental evidence presented in a companion paper.