We study the hydrodynamics of quantum 4 He crystal oscillations in a superfluid liquid with involving the dynamics of atomically rough surfaces. It is shown that, due to enhancement of the kinetic growth coefficient as the temperature lowers, the reaction force of the liquid applied to the 4 He crystal changes its character from the inertial to viscous one vanishing as T → 0. The model is confirmed by the experiments on the oscillations of the 4 He crystal within the temperature range 0.54-1.43 K at frequencies 484 and 211 Hz. A new type of hydrodynamic instability is found. The instability occurs provided that the oscillation amplitude of the velocity becomes higher than ∼ 3 cm/sec.

The overpressurization of superfluid He 4 under crystallization is studied experimentally. The effect of a substrate and He 3 impurities on the nucleation rate W is observed. The dependence of the metastable state lifetime versus the overpressurization and temperature is measured in the range 10-7-1 s and 0.52-1.75 K. The results are compared with the theoretical predictions for the classic and quantum nucleation. The surface relief effect is considered. It is shown that relative to a flat surface, a cone-shaped pit is a site corresponding to a smaller nucleation energy. In this case a change of the nucleation rate versus the metastability degree and temperature in the classic region is analyzed. As a result, the most reliable qualitative manifestation of quantum nucleation is the independence of the metastable degree under the constant rate W upon temperature, which is observed below 1 K in the experiment.

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