Fourth Sound Velocity Research Articles

Search for fourth sound propagation in supersolid He4

A systematic study is carried out to search for fourth sound propagation solid He4 samples below 500mK down to 40mK between 25 and 56bar using the techniques of heat pulse generator and titanium superconducting transition edge bolometer. If solid He4 is endowed with superfluidity below 200mK, as indicated by recent torsional oscillator experiments, theories predict fourth sound propagation in such a supersolid state. If found, fourth sound would provide convincing evidence for superfluidity and a new tool for studying the new phase. The search for a fourth sound-like mode is based on the response of the bolometers to heat pulses traveling through cylindrical samples of solids grown with different crystal qualities. Bolometers with increasing sensitivity are constructed. The heater generator amplitude is reduced to the sensitivity limit to search for any critical velocity effects. The fourth sound velocity is expected to vary as ∝ρs∕ρ. Searches for a signature in the bolometer response with such a characteristic temperature dependence are made. The measured response signal has not so far revealed any signature of a new propagating mode within a temperature excursion of 5μK from the background signal shape. Possible reasons for this negative result are discussed. Prior to the fourth sound search, the temperature dependence of heat pulse propagation was studied as it transformed from “second sound” in the normal solid He4 to transverse ballistic phonon propagation. Our work extends the studies of [V. Narayanamurti and R. C. Dynes, Phys. Rev. B 12, 1731 (1975)] to higher pressures and to lower temperatures. The measured transverse ballistic phonon propagation velocity is found to remain constant (within the 0.3% scatter of the data) below 100mK at all pressures and reveals no indication of an onset of supersolidity. The overall dynamic thermal response of solid to heat input is found to depend strongly on the sample preparation procedure.

Sound Experiments on Superfluidity of 3He in Highly Porous Aerogels

We have carried out sound experiments on superfluid 3 He in three highly porous aerogels with different porosities. Two of the acoustic cells contain aerogels inside the pores in roughly sintered silver powder to avoid the vibration of the aerogel. In these acoustic cells we have detected fourth sound, and extracted the superfluid density from the fourth sound velocity. The effect of the sintered silver on superfluid 3 He was examined by using another acoustic cell which contains the sintered silver without aerogel. The size of the pores in the sintered silver was large enough not to show the size effect of superfluid 3 He and small enough to observe fourth sound of 3 He. In another cell without sintered silver, we have observed second-sound-like signal. The superfluid transition temperatures of 3 He are suppressed more in higher density aerogel. The aerogel density dependence of the suppression of the superfluid transition temperature of 3 He in aerogel can be explained qualitatively by the simple s-wave scattering approximation. However, the superfluid density shows quite different pressure-dependence in different porous aerogels. The reason of this phenomenon is not understood yet.

The Observed Properties of Liquid Helium at the Saturated Vapor Pressure

The equilibrium and transport properties of liquid He4 are deduced from experimental observations at the saturated vapor pressure. In each case, the bibliography lists all known measurements. Quantities reported here include density, thermal expansion coefficient, dielectric constant, superfluid and normal fluid densities, first, second, third, and fourth sound velocities, specific heat, enthalpy, entropy, surface tension, ion mobilities, mutual friction, viscosity and kinematic viscosity, dispersion curve, structure factor, thermal conductivity, latent heat, saturated vapor pressure, thermal diffusivity and Prandtl number of helium I, and displacement length and vortex core parameter in helium II.

Observation of the Sliding Mode in Incommensurate Intergrowth Compounds: Brillouin Scattering from the Inclusion Compound of Urea and Heptadecane.

The anisotropy of the speeds of sound is reported for the incommensurate heptadecane/urea inclusion compound as measured by Brillouin scattering. In addition to the three normal acoustic modes, the results show the presence of a fourth sound velocity, corresponding to the so-called sliding mode (phason). A simple model for the elasticity of incommensurate crystals is used to discuss the polarizations of the sliding mode and the other acoustic modes.

Superfluid fraction of4He from 1.5 K toT ?(P) and from vapor pressure to the melting curve

New measurements of the first-, second-, and fourth-sound velocities are reported and used to obtain the superfluid fraction ρ s /ρ at pressures from vapor pressure to the melting curve and from 1.5 K to within 1% of the superfluid transition temperatureTλ(P). Close toTλ, the new results agree very well with previous measurements by Greywall and Ahlers. At low temperatures they agree well with the tabulations by Maynard; but in the range within 10% or so ofTλ(P) and at the higher pressures they differ from Maynard's values by several percent.

Pressure dependence of size effects in superfluid 4He

We show that the depression of the fourth sound velocity due to size effects over the range 1.4 ⩽ T ⩽ 1.8 K and 0 ⩽ P ⩽ 25 bar can be represented by a function of the displacement thickness δ of Roberts et al. A simple phenomenological model yields values of the healing length which agree with δ within a normalization constant.

Surface magnetic relaxation and fourth sound of 3He-A1

Surface magnetic relaxation is shown to constitute the main mechanism for absorption of fourth sound in 3 He-A 1 . The damping due to both this process and the usual intrinsic dissipation was calculated and compared. It is found that, depending on the values of T 1 (the wall-induced longitudinal magnetic relaxation time), the relaxation mechanism is up to two orders of magnitude stronger than the dissipative one. In addition, it leads to a markedly different frequency dependence of the damping and a measurable dispersion of the fourth sound velocity.

Surface magnetic relaxation and fourth sound of 3He-A1

Abstract Surface magnetic relaxation is shown to constitute the main mechanism for absorption of fourth sound in 3 He-A 1 . The damping due to both this process and the usual intrinsic dissipation was calculated and compared. It is found that, depending on the values of T 1 (the wall-induced longitudinal magnetic relaxation time), the relaxation mechanism is up to two orders of magnitude stronger than the dissipative one. In addition, it leads to a markedly different frequency dependence of the damping and a measurable dispersion of the fourth sound velocity.

Fourth sound velocity and two-scale-factor universality in 4He near Tλ

Abstract Measurements of the fourth and first sound velocities near the superfluid transition temperature at several pressures in 4 He show that the error in the amplitude of the superfluid fraction ϱ s /ϱ derived from second sound velocities is not more than 3% and too small to explain apparent departures from two-scale-factor universality along the λ-line.

Observation of step-wise solid layer nucleation of 4He on grafoil

We have used fourth sound to investigate the formation of solid layers of 4 He on Grafoil, and have observed step-wise solid layer nucleation. A periodic pressure dependence in the fourth sound velocity indicates an average single layer thickness of 2.3±.2Å, which is slightly less than the one-half c-axis length for the He hcp structure. Measurements were made below the hcp and bcc regions, and no significant differences were evident. No pressure hysteresis was observed when the fourth sound signal was present, but there was an indication of capillary condensation of solid in the Grafoil.

Temperature dependence of the Landau critical velocity in He II

The temperature dependence of a superflow-induced downshift of the fourth sound velocity in He II confined in various restrictive media has been observed. The results are interpreted in terms of local superfluid velocities approaching the Landau critical velocity and therefore constitute the first measurements of the temperature dependence of the Landau critical velocity.

PRECISION, SELF-CONSISTENT THERMODYNAMICS FOR SUPERFLUID HELIUM FROM SOUND VELOCITY MEASUREMENTS

Measurements of the different sound velocities of superfluid 4He have been used to sell-consistently determine all the equilibrium thermodynamic properties of the superfluid. The precision of the results, typically 0.3%, represents an order-of-magnitude improvement over a significant portion of the existing data and has eliminated some discrepancies as large as (10-15)%. The sound velocity data consists of first-, second-, and fourth-sound velocities measured simultaneously at more than 400 points in the P-T plane about 1.2 K. Equations of two-fluid hydrodynamics are used to convert the sound velocities to thermodynamic quantities, including the density, thermal expansion coefficient, normal-fluid fraction, entropy, specific heats, and compressibility.

Determination of the thermodynamics of He II from sound-velocity data

Recently measured sound-velocity data were used to completely determine the thermodynamics of superfluid helium at all temperatures above 1.2 K and at all pressures in the He II phase. The sound-velocity data consisted of first-, second-, and fourth-sound velocities measured simultaneously at more than 400 points in the $P$-$T$ plane. Equations of two-fluid hydrodynamics and a small amount of published data were used to convert the sound velocities to thermodynamic quantities. Because of the high precision of the data (0.2%) and the fine mesh of data points, it was possible to obtain continuous functions (of the variables $P$ and $T$) for the density, thermal-expansion coefficient, normal-fluid fraction, entropy, specific heats, and compressibility of He II. As an additional feature the correct asymptotic behavior near the $\ensuremath{\lambda}$ line was incorporated into the thermodynamic functions. These functions were used to generate tables of the thermodynamic quantities and smoothed values of the sound velocities. The precision of the results, typically 0.3%, represents an order-of-magnitude improvement over a significant portion of the existing data and has eliminated some discrepancies as large as (10-15)%.

Hydrodynamic theory applied to fourth sound in a moving superfluid

The hydrodynamic equations of superfluid $^{4}\mathrm{He}$ in a superleak are used to obtain an exact and general expression for the velocity of fourth sound in the presence of a steady superfluid flow. This expression, which depends only on the flow velocity and on static properties of the helium-superleak system, may be simplified when effects due to the finite-pore dimensions are negligible. In that case the fourth-sound velocity may be rewritten in terms of the flow velocity, thermodynamic properties of bulk helium and bulk filler material, and some purely geometric parameters. The expression obtained disagrees with the results of a previous calculation. A relation between the fourth-sound velocity at zero flow and the Doppler shift at finite flow, predicted by the present theory, is in conflict with existing experimental data. Possible explanations for this discrepancy are discussed.

Soundlike Collective Excitations in SuperfluidHe3

I discuss soundlike collective excitations in anisotropic superfluid Fermi liquids in both the collisionless and the hydrodynamic regimes. Expressions for the velocities of zero, first, second, and fourth sound are derived in terms of the Landau parameters of the normal state. The second- and fourth-sound velocities are found to vary appreciably with orientation.

Normal Fluid Density, Second Sound, and Fourth Sound in an Anisotropic Superfluid

In a superfluid with an anisotropic quasiparticle energy, the normal-fluid density is a diagonal tensor. The second and fourth sound velocities are distinctly anisotropic, so that heat-pulse or fourth-sound studies with an applied magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ may permit identification of the direction of the gap axis with respect to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$. High-frequency sound velocities may display a weaker anisotropy.

Experimental Determination of the Fourth Sound Velocity in Helium II

Fourth sound is a pressure and density wave in He II, in which only the superfluid is in motion. Using packed rouge to lock the normal fluid, the existence of this wave mode has been experimentally confirmed by measuring the temperature dependence of a plane-wave resonance in a closed-closed cylindrical acoustic resonator. The measured phase velocity has a temperature dependence which agrees within 1% with that predicted theoretically. Pulse measurements using 40-kc/sec sine-wave bursts further corroborate the existence of this type of wave. The absolute value of the fourth sound velocity is affected by the coherent multiple scattering of the wave from the superleak material. The results of Twersky's and Saxon's scattering theories are compared with the data. It is found that the equation $n={(2\ensuremath{-}P)}^{\frac{1}{2}}$, where $n$ is the index of refraction and $P$ is the porosity, fits the data within 3%. Values of the ratio of the superfluid to the He II density, derived from the fourth-sound data, agree within 2% with those obtained by other experimental techniques.

Fourth Sound In He II

Experimental results are presented to verify the existence of the unattenuated mode of wave propagation in helium II known as fourth sound. The experimental apparatus and procedure are described. A plot is given of the measured values of the fourth sound velocity from 1.19 to 2.1 deg K. For comparison the calculated curves of first and fourth sounds are given over the same temperature range. A brief discussion is given of the significance of the results. (H.D.R.)