Instability of a crystal 4He facet in the field of gravity

TL;DR

This paper investigates the gravitational instability of the superfluid-crystal helium-4 interface, highlighting how surface state (rough or faceted) affects the instability mechanism and identifying key parameters influencing its onset.

Contribution

It provides a theoretical analysis of gravitational instability differences between rough and faceted helium-4 crystal surfaces, including potential barriers and initial wave generation.

Findings

Instability mechanism differs above and below the roughening transition.

Faceted surfaces exhibit a potential barrier due to facet step energy.

Initial instability involves crystallization wave generation.

Abstract

We analyze 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 half-space over the lighter superfluid phase. The conditions and the 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 similar 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 linear 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. The experiments which may concern the gravitational instability of the superfluid-crystal 4He interface are discussed.