Ultrasonic propagation in3He-4He mixtures near the tricritical point

Abstract

We present measurements of the singular sound attenuation αsing in liquid mixtures of3He and4He near the superfluid transition and at temperatures above the phase separation curve. The mole fractionX of3He ranged from 0.55 to 0.73 and the frequency ω/2π varied between 1 and 45 MHz. The temperature range was 0.75–1.4 K, with the greatest emphasis on the tricritical region nearX t=0.67 andT t=0.87 K. From the change in slopedU/dT of the sound velocityU, we present a new determination of the phase separation curve, which is compared with previous measurements. The sound attenuation peak along the superfluid transition becomes broader in temperature asT λ is decreased. In addition, there is also an increase in sound attenuation as the phase separation temperatureT σ is approached. ForX<X t these two peaks merge into one asX t is approached. For a given frequency, the attenuation has a maximum value at the tricritical point. Estimates of the contribution α D of mass diffusion to the attenuation for3He-4He mixtures with 0<X<0.55 and comparison with experimental values show that α D becomes relatively more important asX increases, and that atX=0.55 it effectively accounts for all of the observed singular attenuation, at least at megahertz frequencies. Hence we assume that for mixtures withX>0.55 the observed attenuation can be analyzed solely in terms of the diffusive relaxation mechanism. The mass diffusion parameterD is then determined from the data. AtX=0.55,D diverges asT λ is approached, which is consistent with theoretical expectations and experimental results. NearT t, there is a crossover to a tricritical regime, and it is found that approximatelyD∝(T−T t) Z withZ=0.32±0.1. Mode coupling predictions are thatZ=1/2 while recent renormalization group calculations giveZ=1/3. The attenuation curves in the tricritical region at the various frequencies can be represented satisfactorily but not perfectly by a scaling function with a characteristic relaxation time τ∝(T−T t) −x withx=1.7±0.15. This time corresponds to order-parameter fluctuations. Its temperature dependence is in excellent agreement with renormalization-group calculations that givex≈5/3, while expectations from dynamic scaling are thatx=3/2. Our analysis also gives the variation of the amplitudes of τ andD with the direction of approach toT t. A comprehensive theory for interpreting all the data, in the normal as well as in the superfluid phase, is lacking at this time.