Crystallization waves of solid-liquid interface of 4He

In title, numerals are subscripts.I have systematically studied the growth resistance of $sp4$He crystals with $sp3$He concentrations X$sb3$ from 0.3 ppb to 158 ppb at temperatures below 0.5 K by measuring the damping of crystallization waves. For $sp3$He concentrations $Xsb3 le 7$ ppb, my data indicate that the presence of $sp3$He has a negligible effect on the growth resistance. At temperatures below 0.25 K, my data agree with the calculations of Bowley and Edwards that the growth resistance is dominated by the collisions between phonons and the moving interface. The data also indicate that the crystal phonons crossover from a ballistic regime to a hydrodynamic regime at temperatures above 0.25 K. For $sp3$He concentrations $Xsb3 ge 12$ ppb, my data show that the growth resistance increases dramatically with increasing $sp3$He concentration. This excess growth resistance can be explained by an additional dissipation that is due to $sp3$He diffusing within the solid and $sp3$He diffusing across the interface