Equilibrium shape of (4)He crystal under zero gravity below 200 mK.

Abstract

Equilibrium crystal shape is the lowest energy crystal shape that is hardly realized in ordinary crystals because of their slow relaxation. (4)He quantum crystals in a superfluid have been expected as unique exceptions that grow extremely fast at very low temperatures. However, on the ground, gravity considerably deforms the crystals and conceals the equilibrium crystal shape, and thus, gravity-free environment is needed to observe the equilibrium shape of (4)He. We report the relaxation processes of macroscopic (4)He crystals in a superfluid below 200 mK under zero gravity using a parabolic flight of a jet plane. When gravity was removed from a gravity-flattened (4)He crystal, the crystal rapidly transformed into a shape with flat surfaces. Although the relaxation processes were highly dependent on the initial condition, the crystals relaxed to a nearly homothetic shape in the end, indicating that they were truly in an equilibrium shape minimizing the interfacial free energy. Thanks to the equilibrium shape, we were able to determine the Wulff's origin and the size of the c-facet together with the vicinal surface profile next to the c-facet. The c-facet size was extremely small in the quantum crystals, and the facet-like flat surfaces were found to be the vicinal surfaces. At the same time, the interfacial free energy of the a-facet and s-facet was also obtained.