Anisotropy-driven dynamics of cellular fronts in directional solidification in thin samples

We present an experimental investigation of the influence of interfacial anisotropy on the cellular growth patterns observed in directional solidification of the CBr₄-8mol% C₂Cl₆ alloy at pulling velocities less than twice the cellular-threshold velocity. The experiments are performed with single-crystal samples about 8 mm wide and 12 {μ}m thick. In such samples, the solidification dynamics is essentially two dimensional, and the effective anisotropy of the system can be varied by changing the orientation of the (face centered cubic) crystal with respect to the solidification setup, as was previously established by S. Akamatsu, G. Faivre, and T. Ihle [Phys. Rev. E, 51, 4751 (1995)]. We find that the cellular pattern is unstable at all values of the spacing {λ} for crystal orientations corresponding to a vanishing effective interfacial anisotropy. For the other crystal orientations, i.e., for a nonvanishing effective interfacial anisotropy, stable cellular patterns are found over a finite-width {λ} range. The various modes of instability limiting this range are described. In particular, we show that a homogeneous tilt bifurcation exists for some orientations of the ``degenerate'' type (i.e., such that a {110} plane of the crystal is parallel to the growth direction and perpendicular to the sample plane). This bifurcation is not spontaneous, however, but a consequence of the particular symmetry of the effective interfacial anisotropy of the system for this crystal orientation.