Vacancy diffusion and stress relaxation inHe4freezing in porous Vycor

We report results of ultrasonic-attenuation and -velocity measurements during freezing of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in porous Vycor glass. When solid helium is present, we observe attenuation peaks whose frequency and temperature dependences are characteristic of a thermally activated relaxation process. We identify the responsible mechanism as being the relaxation of ultrasonic stresses in the solid helium via vacancy diffusion. Since the pores of Vycor are very small (∼${10}^{\mathrm{-}6}$ cm), the relaxation time τ can be very short. For a sound wave with angular frequency ω, the resulting attenuation is largest at the temperature where ωτ=1. The activation energy for diffusion and the diffusion rates extracted from our measurements are consistent with those determined in other experiments on solid helium. In interpreting other freezing experiments in Vycor, it is important to consider mass transport due to this vacancy-diffusion mechanism, since it can allow pressure equilibrium to be maintained between the helium in the pores and bulk helium outside.