Coarsening and the mean shape of three-dimensional dendritic crystals.

Abstract

The mean shape of free dendritic crystals of ${\mathrm{NH}}_{4}$Cl growing in three dimensions from solution is determined. The mean width w\ifmmode\bar\else\textasciimacron\fi{} of the dendrites in the plane of the sidebranches is found to scale with the distance z from the tip according to w\ifmmode\bar\else\textasciimacron\fi{}/\ensuremath{\rho}\ensuremath{\sim}(z/\ensuremath{\rho}${)}^{0.74\ifmmode\pm\else\textpm\fi{}0.06}$, where \ensuremath{\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.