INTEGRAL PARAMETERS OF XENON DENDRITES

The shape of xenon dendrites has been studied in situ during growth into a three-dimensional "infinite" volume of supercooled melt. The contours of dendrite projections have been extracted from digitized video pictures by an image processing system. In difference to earlier studies of the properties of the dendrite tip, the whole dendrite has been investigated now. Special emphasis was given on the development of sidebranches and the coarsening process in dendrite regions far away from the dendrite tip. No reproducible parameters have been found to characterize individual sidebranches far from the tip. The following geometry parameters of the dendrite have been determined: the radius of curvature R of the dendrite tip, the distance Z(SB) between the tip and the position of the first sidebranch with an amplitude of about 1 R and the amplitude w(p) of the sidebranches as a function of the position l(p) at the fins along the dendrite. These measurements have been performed in the supercooling range 0.025 K less-than-or-equal-to DELTAT less-than-or-equal-to 0.150 K. Parameters which characterize individual sidebranches do not take into account the interaction of the sidebranches through the diffusion field. An alternative set of integral parameters is proposed: the contour length U, the projection area F, and the volume V of a dendrite. These parameters characterize the integral dendrite. They have been measured in the supercooling range 0.025 K less-than-or-equal-to DELTAT less-than-or-equal-to 0.170 K. The measurements show that parameters characterizing a dendrite are scaled by the tip radius R: (1) The position of the first sidebranch, i.e., the distance z(SB) from the tip where a sidebranch has the amplitude 1 R is about 18 R for any supercooling. (2) The sidebranch spacing S near the tip scales with R, i.e., S/R is independent of supercooling. S/R = 3.2 +/- 0.4. (3) The amplitude w(p) of the sidebranches which build the envelope increases with l(p) as (w(p)/R) is-proportional-to (l(p)/R)1.78. (4)The projection area F of the dendrite is proportional to the contour length U. The proportionality is 4 R. (5) The filling factor V/[(4pi/3)L3] of a sphere with a volume (4pi/3)L3, which contains a dendrite of overall dimension L, is proportional to R.