Study of Energy Dissipation in Solid $^4$He Samples as Measured by Compound Torsion Pendulum*

We have carried out a series of torsional oscillator experiments on solid $^4$He containing $^3$He-concentrations (with concentration x$_3$ = 0.3, 3, 6, 12, 25 ppm) using our compound torsional oscillator (TO). Our studies of the supersolid phenomenon focused on the energy dissipation change ($\sim\Delta$ Q$^{-1}$) as x$_3$ was varied. The unique compound TO design allows observations of identical samples at two distinct frequencies (f$_1$=493 and f$_2$=1165 Hz). When normalized as $\Delta Q^{-1}/\Delta Q^{-1}_{max}(x_3)$ the data collapse onto a universal bell-shaped function of $T/T_{max}(x_3)$ except for the f$_1$ mode in the 12 and 25 ppm samples and the f$_2$ mode in the 25 ppm sample. A clear deviation of $\Delta Q^{-1}$ in both modes from the other values of x$_3$ suggests some additional mechanism for the extra dissipation present in the 25 ppm sample.