Growth shape of 3He needle crystals.

Abstract

We present experiments on the growth shape of $^{3}\mathrm{He}$ needle crystals. These crystals show a surprisingly weak sidebranching. Growth velocities v and the tip radii \ensuremath{\rho} have been measured, and v${\mathrm{\ensuremath{\rho}}}^{2}$ is found to be roughly constant. We also measured the surface tension anisotropy. We compare our results with the microscopic solvability theory, which needs to be modified due to the existence of a thermal (Kapitza) resistance ${\mathit{R}}_{\mathit{K}}$ at the interface. By studying the linear stability of a spherical seed, we show that ${\mathit{R}}_{\mathit{K}}$ can be taken into account by modifying the ratio of the bulk heat conductivities. The selected values v and \ensuremath{\rho} at the tip are found, in satisfactory agreement with the modified theory. Some qualitative arguments are also presented which may explain the weakness of the sidebranching instability.