COARSENING AND THE MEAN SHAPE OF 3-DIMENSIONAL DENDRITIC CRYSTALS

The mean shape of free dendritic crystals of NH4Cl growing in three dimensions from solution is determined. The mean width wBAR of the dendrites in the plane of the sidebranches is found to scale with the distance z from the tip according to wBAR/rho is similar to (z/rho)0.74+/-0.06, where rho is the tip radius. This is significantly different from the exponent of 1/2 that would be expected if the mean shape corresponded to a parabolic steady-state solution, as was found in two-dimensional growth [Y. Couder et al., Phys. Rev. A 42, 3499 (1990)]. Estimates of the axially averaged three-dimensional shape and possible implications for steady-state theories of dendritic growth are also discussed.