Scale-invariant competitive growth of side branches in a dendritic crystal

We experimentally investigated statistical properties of side branches of quasi-two-dimensional $\mathrm{N}{\mathrm{H}}_4\mathrm{Cl}$ dendritic crystals. The height distributions of the side branches and their number density exhibit scale-invariant power laws. The results are in good agreement with the results of numerical simulations and theories of diffusion-limited needle growth. Our scaling exponents are independent of supersaturation and the statistical properties are universal in dendrites.

Figure 1

Cell structure.

Figure 2

Experimental setup.

Figure 3

Time sequences of a typical dendrite $(V=34\mu \mathrm{m}∕\sec )$ for different microscope magnifications. From top to bottom, (a) the images are captured every $14\sec$ and $L=264\mu \mathrm{m}$, and (b) the images are captured every $60\sec$ and $L=2635\mu \mathrm{m}$.

Figure 4

(a) Height distributions and (b) number density profiles of the branches of dendrites with $V=34\mu \mathrm{m}∕\sec$ and $L=264$ and $2635\mu \mathrm{m}$ shown in Figs. 3a, 3b.

Figure 5

Three different dendrites at higher supersaturation. The tip velocities are (a) $49\mu \mathrm{m}∕\sec$, (b) $58\mu \mathrm{m}∕\sec$, and (c) $72\mu \mathrm{m}∕\sec$, and $L=2635\mu \mathrm{m}$.

Figure 6

Height distributions of the branches of dendrites with tip velocities of 49, 58, and $72\mu \mathrm{m}∕\sec$, and $L=2635\mu \mathrm{m}$ shown in Figs. 5.

Figure 7

Number density distributions of branches of the dendrites with tip velocities of 49, 58, and $72\mu \mathrm{m}∕\sec$, and $L=2635\mu \mathrm{m}$ shown in Figs. 5.