Experimental Evidence for a Zigzag Bifurcation in Bulk Lamellar Eutectic Growth

We present real-time observations of the directional-solidification patterns of a transparent nonfaceted eutectic alloy (${\mathrm{C}\mathrm{B}\mathrm{r}}_4\mathrm{\text{−}}{\mathrm{C}}_2{\mathrm{C}\mathrm{l}}_6$) in bulk samples. The growth front of the two-phase solid is observed from the top through the liquid and the glass wall of the container with a long-distance microscope. We show that, in near-eutectic ${\mathrm{C}\mathrm{B}\mathrm{r}}_4\mathrm{\text{−}}{\mathrm{C}}_2{\mathrm{C}\mathrm{l}}_6$ alloys, the upper stability limit of the stationary lamellar patterns is due to a zigzag bifurcation, which occurs at an interlamellar spacing of about $0.85{\lambda }_m$, where ${\lambda }_m$ is the minimum-undercooling spacing. The zigzag patterns undergo a lamella breakup instability leading to the creation of new lamellae at about $1.1{\lambda }_m$. On the other hand, the lower stability limit of the stationary patterns is due to the same instability as in thin samples, namely, a lamella termination instability that occurs at about $0.7{\lambda }_m$.

Figure 1

(a) Sketch of a stationary lamellar eutectic pattern; $\alpha ,\beta$: eutectic crystal phases; $\mathbf{z}$: axis of the thermal gradient, and normal to the growth front. (b) Sketch of the experimental setup; $V$: pulling velocity; ${\theta }_0$: tilt angle of the direction of observation to the horizontal.

Figure 2

Top view of a symmetric lamellar eutectic pattern in a $350\mathrm{\text{−}}\mu \mathrm{m}$-thick sample of a slightly hypereutectic ${\mathrm{C}\mathrm{B}\mathrm{r}}_4\mathrm{\text{−}}{\mathrm{C}}_2{\mathrm{C}\mathrm{l}}_6$ alloy. $V=0.37\mu \mathrm{m}{\mathrm{s}}^{-1}$. The sample was pulled at $V=0.5\mu \mathrm{m}{\mathrm{s}}^{-1}$ for 4.5 h and then at $0.37\mu \mathrm{m}{\mathrm{s}}^{-1}$ for 1.5 h. Bright and dark stripes are $\beta$ and $\alpha$ lamellae, respectively. Horizontal width of the image: $860\mu \mathrm{m}$. Average value of $\lambda$: $0.82{\lambda }_m$. Arrows: lamella terminations.

Figure 3

View of a pattern after 10 min at $V=0.5\mu \mathrm{m}{\mathrm{s}}^{-1}$, and 35 min at $V=1\mu \mathrm{m}{\mathrm{s}}^{-1}$ in a $300\mathrm{\text{−}}\mu \mathrm{m}$-thick sample. Lamellar domains are separated by disordered regions containing topological defects, and rods. Horizontal width $440\mu \mathrm{m}$.

Figure 4

Top views of zigzag patterns (a) $V=0.5\mu \mathrm{m}{\mathrm{s}}^{-1}$. Solidification time: 4 h; (b) $V=0.39\mu \mathrm{m}{\mathrm{s}}^{-1}$. Solidification time: 30 min; (c) $V=0.3\mu \mathrm{m}{\mathrm{s}}^{-1}$; solidification time: 30 min. Sample thickness $300\mu \mathrm{m}$. Horizontal width $440\mu \mathrm{m}$.

Figure 5

(a) Amplitude $A$ and (b) wavelength $L$ of the zigzags vs the reduced spacing $\lambda /{\lambda }_m$. Filled (open) symbols: data obtained by decreasing (increasing) $V$. The error bars represent the experimental dispersion.