Attenuation and dispersion of first sound near the superfluid transition of 3He-4He mixtures

The attenuation α, the velocity u, and the dispersion D = u (ω) - u (0) of first sound have been determined in 3He-4He mixtures (molar 3He concentrations X3 = 0, 0.070, 0.194, 0.377, and 0.517) at frequencies 2.3 < or = ω/2π < or = 627 kHz, and in the termperature range 1 μK < or = absolute value (T - T/sub lambda/ ) < or = 10 mK. From the measured velocities we calculate the thermodynamic velocity u (0), as well as (partialS/partialP)/sub lambda/ and (partialV/partialP)/sub lambda/. The attenuation and the dispersion are considerably reduced when the 3He concentration is increased. They are interpreted as arising from a relaxation process occurring only below T/sub lambda/, and a fluctuation process occurring on both sides of the lambda transition. Both contributions have about equal strength. The strength A/subR/ of the relaxation process decreases by more than three orders of magnitude with increasing X3 in our concentration range. Using the obtained relaxation time tau' = tau'0t-/subx//sup prime/ (with t = absolute value( T - T/sub lambda/ )/T/sub lambda/), and published data for the correlation length xi', and for the second-sound velocity u2, we find tau' = xi'/u2 for T < /T/sub lambda/. The amplitude tau'0 increases more than one order of magnitude with increasing X3 in the investigated concentration range. For T > T/sub lambda/, our absorption and dispersion data for all ω and X3 can be scaled with functions of ωtau over four decades of ωtau. This scaling analysis shows that the time tau characterizing the critical attenuation and dispersion at T < T/sub lambda/ has the same temperature and concentration dependence as the relaxation time tau' at T < T/sub lambda/; these two times differ at most by a constant multiplicative factor. Below T/sub lambda/, the data are represented by the sum of the contribution represented by the scaling function plus the contribution from order parameter relaxation