  At the superfluid-solid 4He interface there exist crystallization waves
having much in common with gravitational-capillary waves at the interface
between two normal fluids. The Rayleigh-Taylor instability is an instability of
the interface which can be realized when the lighter fluid is propelling the
heavier one. We investigate here the analogues of the Rayleigh-Taylor
instability for the superfluid-solid 4He interface. In the case of a uniformly
accelerated interface the instability occurs only for a growing solid phase
when the magnitude of the acceleration exceeds some critical value independent
of the surface stiffness. For the Richtmyer-Meshkov limiting case of an
impulsively accelerated interface, the onset of instability does not depend on
the sign of the interface acceleration. In both cases the effect of
crystallization wave damping is to reduce the perturbation growth-rate of the
Taylor unstable interface.

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