Dendritic solidification of krypton and xenon

Rare gases form simple liquids and thus they can be used as model substances to study the dendritic solidification of metals and the developments of spatial structures at conditions far from equilibrium. Krypton and xenon form an ideal couple to study scaling laws, because the physical properties of heavy rare gases scale according to their simple interaction forces. The growth of rare gas dendrites into a volume of about 100 cm ³ supercooled melt was investigated using the capillary injection technique. The supercooling of the melt, ΔT = T_m - T_∞, was held constant to within ±0.0002 K during an experiment. T_m designates the triple point temperature of the rare gas and T_∞ the temperature of the melt far away from the dendrite. Tip growth velocity v_tip, tipradiusR and secondary side arm spacing S_tip of krypton and xenon dendrites have been measured in the supercooling range 0.005 < ΔT < 0.3 K. The tip regions showed a fourfold symmetry with wings reaching almost to the tip. At low supercooling ( ΔT < 0.02 K) the dendrite tips become rotationally symmetric, suggesting that anisotropy of surface free energy in kinetics is not important in this regime. The dependences of v_tip [ cm/ s], R[ cm] andS_tip[ cm] onΔT [ K] were determined under steady state conditions and could be fitted for krypton by v_tip = 3.12 × 10 ^-2ΔT^1.73, R = 6.70 × 10 ^-4ΔT^-0.68 and S_tip = 1.47 × 10 ^-3ΔT^-0.80, and for xenon by v_tip = 1.89 × 10 ^-2ΔT^1.74, R = 7.48 × 10 ^-4ΔT^-0.68 and S_tip = 1.78 × 10 ^-3ΔT^0.79. Thus the Péclet number, p = v_tipR/(2 α), where α is the thermal diffusivity in the melt, is proportional to Δ T. This is in agreement with the so-called Ivantsov solution. The measured growth velocities of Kr and Xe are indistinguishable if measured in dimensionless units. The data of Kr and Xe do not confirm a crucial result of stability theories and of more recent numerical analyses of the diffusion problem. In these theoretical treatments it is assumed that the kinetics at the solid-liquid interface do not at all influence the solidification process, and it is found that v_tipR ² = constant, i.e. the volume solidification rate does not depend on supercooling. The rare gas data show that the volume solidification rate increases with increasing supercooling.