$^4$He Crystal Quality and Rotational Response in a Transparent   Torsional Oscillator
  We have studied natural purity $^{4}$He single crystals and polycrystals between 10 and 600 mK using a torsional oscillator with a 2 cm$^{3}$ rigid cell made of sapphire with a smooth geometry. As the temperature was lowered, we observed sample dependent but reproducible resonant frequency shifts that could be attributed to a supersolid fraction of order 0.1%. However, these shifts were observed with single crystals, not with polycrystals. Our results indicate that, in our case, the rotational anomaly of solid helium is more likely due to a change in stiffness than to supersolidity. This interpretation would presumably require gliding of dislocations in more directions than previously thought. 
A. D. Fefferman, X. Rojas, A. Haziot, S. Balibar, J. T. West and M. H.   W. Chan
cond-mat.other