Symmetry-broken double fingers and seaweed patterns in thin-film directional solidification of a nonfaceted cubic crystal.

Abstract

We present a detailed experimental and numerical investigation of the directional-solidification growth patterns in thin films of the ${\mathrm{CBr}}_{4}$--8 mol % ${\mathrm{C}}_{2}$${\mathrm{Cl}}_{6}$ alloy, as a function of the orientation of the (fcc) crystal with respect to the solidification setup. Most experiments are performed with single-crystal samples about 10 mm wide and 15 \ensuremath{\mu}m thick. The crystal sometimes contains small faceted gas inclusions, the shape of which gives us direct information about the orientation of the crystal. Numerical simulations by a fully dynamical method are carried out with parameters corresponding to the experimental system. We find experimentally that, in crystals with a {111} plane (nearly) parallel to the plane of the thin film, the growth pattern is nondendritic and unsteady over the explored velocity range (5${\mathit{V}}_{\mathit{c}}$--50${\mathit{V}}_{\mathit{c}}$; ${\mathit{V}}_{\mathit{c}}$\ensuremath{\approxeq}1.9 \ensuremath{\mu}m ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ is the cellular threshold velocity). By studying the time evolution of this pattern, we establish that it is essentially similar to the ``seaweed pattern'' characteristic of vanishingly small capillary and kinetic anisotropies of the solid-liquid interface, recently studied numerically [T. Ihle and H. M\uller-Krumbhaar, Phys. Rev. E 49, 2972 (1994)]. The building blocks of this pattern are local structures---pairs of symmetry-broken (SB) fingers called ``SB double fingers'' or ``doublons,'' and more complex structures called ``multiplets''---whose lifetime is long but finite.We show experimentally that, in agreement with numerical findings, doublons obey selection rules, but do not have a preferential growth direction. We furthermore find that ``dendritic'' doublons also appear in crystals with a 〈100〉 axis close to the pulling direction (thus having a strong two-dimensional anisotropy) above a critical velocity (\ensuremath{\approxeq}20${\mathit{V}}_{\mathit{c}}$). The existence and stability of dendritic doublons in directional solidification at high velocity are confirmed by the simulations. Another crystal orientation of interest is that in which two 〈100〉 axes are symmetrically tilted at \ifmmode\pm\else\textpm\fi{}45\ifmmode^\circ\else\textdegree\fi{} with respect to the pulling axis. We show experimentally and numerically that the nondendritic unsteady ``degenerate'' pattern observed in this case, and previously noticed by F. Heslot and A. Libchaber [Phys. Scr. T9, 126 (1985)], is qualitatively different from the seaweed pattern. In crystals close to this orientation, we find experimentally transitions between the degenerate and the two possible tilted dendritic states. The small amplitude of the sidebranches of dendrites in our system and the fact that the simulations with a purely capillary anisotropy do not reproduce these transitions lead us to attribute them to the increasing effect of kinetic anisotropy as the pulling velocity increases.