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

Abstract

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 h1 1 0i 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 h1 1 0i 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.

Study of the twinned dendrite tip shape II: Experimental assessment

“…This last profile shows no sign of positive segregation near the dendrite trunk center, in agreement with our previous observations [6]. Indeed, considering a diffusion coefficient in the solid of about 3 Â 10 À12 m 2 s À1 and a doublon inner pool a few microns wide (see [10]), back-diffusion at high temperature occurs only within a few seconds and can therefore smear out any slight positive segregation within this region. On the other hand, the composition profile (A) measured along the twin plane reveals a slight solute increase as one moves closer to the tip.…”

“…As presented in the companion paper [4], three conjectures have been put forward for the tip shape of h1 1 0i twinned dendrites in order to explain their growth advantage over regular h1 0 0i dendrites in Al alloys: (i) a dendrite tip with a groove that is required to satisfy the Smith equation at the triple line between the twinned solid, the untwinned solid and the liquid [1]; (ii) a dendrite tip split in its center by a thin liquid pool, also called a doublon, due to solute pile-up ahead of a grooved tip [2]; and (iii) an edgy tip with consideration of torque terms induced by the anisotropy of the solid-liquid interfacial energy c s' [3]. An edgy tip would definitely give a growth advantage to twinned dendrites over regular ones, but this shape is incompatible with the very weak anisotropy measured recently for c s' in Al-Cu alloys [5].…”

“…The peaks of this profile are higher than the solid composition C s calculated with the regular dendrite tip model of Kurz et al [9] (the so-called KGT model for columnar dendrite growth) and indicated with a dashed horizontal line. These oscillations intensify as the end of the twin plane is reached and their spacing (about %3 lm) can be correlated with the periodic formation of small liquid droplets at the root of the doublon predicted by the phase field model in the first part of this study [10].…”

“…Indeed, the positive segregation measured in the twin plane can be related to the solute gradient observed within the solid phase below the doublon root in the simulations (see Fig. 9 of [10]), and could also account for the eventual formation of small particles in the Al-Zn alloy.…”

Influence of Cr on the nucleation of primary Al and formation of twinned dendrites in Al–Zn–Cr alloys: Can icosahedral solid clusters play a role?

“…More confusion has been brought recently by Li et al [13], who observed that the application of a static magnetic field of only 0.2 T, which is supposed to weaken convection, induces the formation of twinned dendrites in Al-Fe and Al-Zn alloys in small DC cast ingots. Finally, although twinned dendrites have a growth advantage over regular dendrites under the above-mentioned conditions, there is still some uncertainty about their tip morphology [3,12,[14][15][16][17][18]. More important, nothing is known about twin nucleation.…”