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requirement for the interface instability as well as the initial stage of fingering process, as is shown in [16], is sensitive to the state of a crystal facet, rough or smooth, and to the size of a facet. 

Recently [17], it has been demonstrated that the Fara- day instability is also inherent in the superfluid-solid $^{4}$He interface. Crystallization waves at the horizontal inter- face between superfluid and solid $^{4}$He are generated by a periodic vibration of an experimental cell in the ver- tical direction. In accordance with expectation [18] the amplitude of the waves excited at one-half of the driv- ing frequency decreases for higher temperatures due to reduction of the interface growth coefficient describing dissipative properties of the interface. From general ar- guments the Faraday instability can be viewed as a par- ticular case of the Taylor instability for the periodically driven interface. 

On the other side, the spectrum of crystallization waves remains invariable for the steady flow of a super- fluid in the direction normal to the interface [12]. At first sight this implies that the growth of a solid should not bring the superfluid-solid interface to instability. How- ever, in the experiments on free growth of a $^{4}$He crystal initiated at the needle point immersed into the overpres- surized liquid bulk [19, 20] one can observe a destruc- tion of the regular shape of the crystal triggered under sufficiently large overpressure exceeding about 6 mbar. Immediately after nucleation the crystal seed has a clear hexagonal prism-like shape with slight ripples. Soon af- terwards by 0.1–0.2 ms the shape of the crystal becomes round with a highly irregular outline. Far later by 100– 150 ms, as the net overpressure vanishes and the pressure in the cell becomes phase-equilibrium, the shape of the grown crystal relaxes to a regular hexagonal prism. We put two images of a crystal in Fig. 1. 

For overpressures higher than 6 mbar, see Fig. 2, we discover more exotic patterns by the same time interval 0.1–0.2 ms after the voltage pulse which triggers nucle- ation. The interfacial irregularities become more pro- nounced and acquire a mushroom-like shape. Appar- ently, the fluid moves into the crystal between the neigh- boring spikes, resulting eventually in generation of liquid 

<img src='content_image/396495.jpg'>

<img src='content_image/396496.jpg'>

bubbles inside the crystal. 

In addition, in Fig. 2 we show the behavior of the pres- sure in the course of the crystal growth. After nucleation of a crystal seed the overpressure in the cell drops and then gradually vanishes, oscillating around zero value corresponding to the equilibrium pressure. The pres- sure oscillations are due, in the first turn, to the finite- ness of the experimental volume and the finiteness of sound velocity. The point is that the appearance of a solid seed and its next growth are accompanied by varia- tions of the density and the volume in which the density changes. The change of the seed volume results in ex- citing and emitting the sound waves which propagate in the direction to the container walls with the next back- ward reflection from the walls to the solid seed. E.g., the first- and second-sound emissions with an expanding $^{3}$He-concentrated drop in a superfluid $^{3}$He-$^{4}$He mixture has been analyzed in Ref. [21]. The excitation and emis- sion of sound become more and more effective as the interface rate and acceleration increase. Eventually, we obtain acoustic damping oscillations of the liquid inside the cell [22]. In some sense the damping of the pressure oscillations represents a quality factor of a liquid/solid or melting/freezing resonator. In the lack of any dissipative processes in the system the pressure oscillations will last infinitely long. 

The pressure in the cell becomes equilibrium pressure in 2 ms and the driving force vanishes. Finally at 16 ms, the crystal relaxed and acquired the regular hexagonal shape. However, we still observe the liquid bubbles em- bedded into the crystal bulk. 

If we roughly estimate the velocity which the interface 

