Instability of a Crystal 4He Facet in the Field of Gravity

Abstract

We analyze here the analog of the Rayleigh instability in the field of gravity for the superfluid–crystal 4He interface provided that the heavier 4He crystal phase occupies the space over the lighter superfluid phase. We find that the conditions and onset of the gravitational instability are different in kind above and below the roughening transition temperature when the crystal 4He surface is in the rough or in the smooth faceted state, respectively. In the rough state of the surface the gravitational instability is fully analogous to the classical case of the fluid–fluid interface. In contrast, in the case of the crystal faceted surface the onset of the gravitational instability is associated with surmounting some potential barrier. The potential barrier results from nonzero magnitude of the facet step energy. The size and the tilting angle of the crystal facet are also important parameters for developing the instability. The initial stage of the instability can be described as a generation of crystallization waves at the superfluid–crystal interface. In particular, we discuss the experiments (Demaria et al. in J. Low Temp. Phys. 89:385, 1992; Tsymbalenko in Fiz. Nizk. Temp. 21:162, 1995; Tsymbalenko in Low Temp. Phys. 21:120, 1995) which may concern the gravitational instability of the superfluid-crystal 4He interface.