a Quantitative Study of Pattern Formation in Dendritic Crystal Growth from Supersaturated Solution.

The patterns formed in dendritic crystal growth can have characteristic length scales considerably larger than any intrinsic scales of the underlying system. These macroscopic scales result from a complex interaction of microscopic and macroscopic dynamics. Recent theoretical work has focused on the relationship between the macroscopic properties of steady state dendritic tips and the underlying microscopic material properties. In particular, the tip speed v, radius of curvature, rho, and mean initial sidebranch spacing, lambda , are predicted to be determined by a solvability condition involving the anisotropy varepsilon in the surface tension at the solid-liquid interface. The stability constant sigma* is defined to be 2d_0D/(vrho ^2), where D is the diffusion constant and d_0 is a capillary length proportional to the surface tension. The values for sigma * and the ratio lambda/rho are predicted to be constants that depend only on varepsilon. These predictions had not been tested for any materials prior to this work. The complex structure of the time-dependent sidebranches is also not well understood, and is an important area for research. In this work, I report experiments on the dendritic growth of NH_4Br from supersaturated aqueous solution. Digital image processing is used to perform precise measurements of interfacial contours and to provide a quantitative characterization of the growing patterns. For the steady state properties, I find that sigma* is 0.081 +/- 0.02 for NH_4Br, in approximate agreement with the theoretical prediction of 0.065 +/- 0.02 for this material. The ratio lambda/rho is also approximately constant, with an experimental value of 5.2 +/- 0.8, compared to the theoretical prediction of 3.7. I have also characterized the time-dependence of the sidebranch structure near the tip. Even before coarsening becomes significant, sidebranching is a surprisingly irregular process. The branches have a range of spacings and amplitudes, and are imperfectly correlated. The rms sidebranch amplitude grows approximately exponentially with distance from the tip. These findings are consistent with the hypothesis that sidebranches result from the amplification of finite amplitude noise near the tip, but the origin of the noise is not known.