Effect of Crystal Growth Rate on Liquid-like Droplets Formation in the hcp Solid Helium

The samples of hcp solid helium (1% $^3$He in $^4$He) are studied by NMR technique. The samples are grown by the blocking capillary method at different growth rates (about 8, 2, and 0.08 mK/s). The NMR technique is used for phase identification by measurements of the diffusion coefficient $D$ and the spin-spin relaxation time $T_2$ at temperatures of $1.3-2.0$ K and pressures of 34-36 bar. Along with $D$ and $T_2$ for the hcp phase, we simultaneously observe the $D$ and $T_2$ typical for a liquid at growth rates 8 and 2 mK/s. It means that liquid-like inclusions are quenched from the melting curve during fast crystallization of the samples. It is also shown that the slower growth rate corresponds to a smaller size of liquid-like droplets. It results from lower spatially restricted values of $D$ and, finally, absence of these inclusions at the longest crystallization times. The diffusion coefficient measured for liquid-like droplets is also decreasing during the NMR experiment at constant temperature which indicates the reduction of the size of these droplets. Liquid-like droplets are shown to disappear after sample annealing near the melting curve.