Shape of the tip and the formation of sidebranches of xenon dendrites.

Abstract

Experimental studies of the growth of three-dimensional xenon dendrites into a supercooled pure melt are presented. The shape of the dendrite tip and the origin of sidebranching are investigated. It is found that the shape in the tip region is not axisymmetric showing a fourfold symmetry. Four fins grow along the dendrite starting immediately behind the tip. Sidebranches develop at the ridges of these fins. The contour of the fins is not parabolic and can be described in dimensionless units, i.e., measured in units of the tip radius R, by a power law z=a|x${\mathrm{|}}^{\mathrm{\ensuremath{\beta}}}$, with a=0.58\ifmmode\pm\else\textpm\fi{}0.04 and \ensuremath{\beta}=1.67\ifmmode\pm\else\textpm\fi{}0.05, where z is oriented along the growth direction of the dendrite and x is the width of the fins. Selective amplification of thermal noise as well as tip splitting has been discussed in the literature as possible origins of sidebranching. It is found that xenon dendrites grow in a stable mode and do not show any temporal oscillations in either the tip velocity or the curvature of the dendrite tip. Therefore, tip splitting can be excluded as an origin of sidebranching. The distance between the tip and the first sidebranch ${\mathit{z}}_{\mathrm{SB}}$ of a dendrite has been determined. ${\mathit{z}}_{\mathrm{SB}}$ is used to estimate the noise strength needed to form sidebranches as observed in experiments with xenon dendrites. The experimental results, i.e., \ensuremath{\beta}, a, and ${\mathit{z}}_{\mathrm{SB}}$, have been compared with analytical studies [E. Brener and D. Temkin, Phys. Rev. E 51, 351 (1995)]. Quantitative agreement between experiment and theory is found. It is concluded that the formation of sidebranches is initiated by thermal fluctuations. Dendritic structures may be characterized by parameters that describe the ``integral'' dendrite. The fractal dimension is an example of such an integral parameter. The averaged fractal dimension ${\mathit{d}\mathit{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{f}}$ of the contour of a dendrite was determined for various supercoolings in the range of 20 mK\ensuremath{\le}\ensuremath{\Delta}T\ensuremath{\le}150 mK. The contour is fractal over a range of more than two orders of magnitude in length scale. The fractal dimension is ${\mathit{d}\mathit{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{f}}$=1.42\ifmmode\pm\else\textpm\fi{}0.05 and does not depend on supercooling. \textcopyright{} 1996 The American Physical Society.