2 GLYPH<s48> GLYPH<s49> GLYPH<s50> GLYPH<s51> GLYPH<s52> GLYPH<s45>GLYPH<s50> GLYPH<s48> GLYPH<s50> GLYPH<s52> GLYPH<s54> GLYPH<s56> GLYPH<s68> GLYPH<s112>GLYPH<s44> GLYPH<s32> GLYPH<s109> GLYPH<s98>GLYPH<s97>GLYPH<s114> GLYPH<s116>GLYPH<s44>GLYPH<s32>GLYPH<s109> GLYPH<s115>GLYPH<s101>GLYPH<s99> FIG. 1: The growth of a $^{4}$He crystal at 0.47 K and initial overpressure 5.2 mbar. The left frame corresponds to 0.19 ms after nucleation. The right frame is taken 80 ms later when the net pressure is already close to the melting pressure. The vertical size of the frames is 2.4 mm. FIG. 2: The deviation of the pressure from equilibrium vs time during crystal growth at 0.48 K and initial overpressure 7 mbar. The left insert shows a crystal at 0.64 ms after nu- cleation. The time at the right insert is 16 ms. The vertical size of the frames is 2.4 mm. 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. 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. 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 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