Acoustic Emission by Quartz Tuning Forks and Other Oscillating Structures in Cryogenic 4He Fluids

We report on experimental investigations of acoustic emission by quartz tuning forks resonating at frequencies 32 kHz, 38 kHz, 77 kHz and 100 kHz immersed in cold gaseous ⁴He and its normal and superfluid liquid phases. Frequency dependence of the observed low-drive-linewidth at 350 mK together with the temperature and pressure dependences (1.3 K < T < 4.2 K, 0 < p < 25 bar) of the observed damping of the high frequency (77 and 100 kHz) resonators measured in normal liquid ⁴He and its superfluid phase provide strong and direct evidence of the importance of sound emission by these tuning forks. Three analytical models of acoustic emission by vibrating tuning forks are developed and compared with the experimental results. We also discuss the importance of sound emission for experiments with the commonly used 32 kHz tuning forks as well as other oscillating structures??spheres, wires, grids and various micromachined sensors. We compare the relative importance of dissipative losses due to laminar viscous/ballistic drag and acoustic emission in liquid and superfluid ⁴He.     

The Fulde–Ferrell–Larkin–Ovchinnikov State in Pnictides

We present experimental results on crosstalk of non-electrical origin between high frequency quartz tuning forks immersed in the same volume of helium gas, liquid or superfluid. We compare these results with various observations of other groups and propose an explanation of this puzzling phenomenon. To the best of our knowledge, notable crosstalk has only been observed in superfluid helium both in the two-fluid regime and at very low temperatures, but was rarely seen to behave in a systematic way. We demonstrate some of its most significant properties—amplitude dependence within a short time span, long-term temporal instability, effects of the geometry of the setup and of obstacles placed between the tuning forks. Although the results are not fully understood, as the most likely explanation, we ascribe the observations to the coupling of tuning forks to standing acoustic modes inside the experimental volume, emphasizing the importance of second sound for understanding the observations at temperatures within the two-fluid regime (1 K<T<2.17 K). Finally, we suggest simple precautions leading to suppression of excessive acoustic crosstalk between oscillating objects in He II.     

Quartz Tuning Fork Viscometers for Helium Liquids

Mechanical resonators, in the form of vibrating wires or torsional oscillators, have long been employed as sensors in liquid ³He and ³He–⁴He mixtures. The damping of resonators is due to the viscosity of the surrounding liquid which is a strong, well-known function of temperature for bulk Fermi liquids. It is therefore possible to use the viscous damping for thermometry in the millikelvin regime. An alternative sensor is the small quartz tuning fork which is driven by the piezoelectric effect and requires no external magnetic field. In this paper, we present measurements of the viscous damping of such a tuning fork when immersed in a 6.2% ³He–⁴He mixture, between 3 and 100 mK, and at zero and high (10 T) magnetic field. The measurements indicate that damping of the tuning fork resonance is dominated by the liquid helium properties and is insensitive to the applied magnetic field. The response of the tuning fork to the saturated helium mixture demonstrates that it could potentially be used for thermometry in any magnetic field. There is evidence of slip at the interface between the fork and the helium suggesting specular scattering from the smooth surface of the quartz. The fork is also able to detect the superfluid transition in pure liquid ³He.     

Mass Flow through Solid 4H

We continue our solid ⁴He flow experiments in which we grow solid helium samples at constant temperature in the hcp region of the phase diagram. We exploit the properties of liquid helium in a confined geometry (porous Vycor glass), and induce a mass flow through the solid at pressures higher than the bulk melting pressure. We previously observed flow, but our temperature was limited to T≥350 mK. At T≈400 mK it was found that the flow ceased at P≈27 bar, and no flow was observed for T>550 mK. We have begun to extend our measurements to lower temperatures, and our data show that at lower temperatures we observe flow at higher pressures.     

NMR Studies of 3He Droplets in Dilute 3He-4He Solid Solutions

We have performed measurements of the temperature dependence of the nuclear spin-lattice relaxation times (T ₁) for a wide range of ³He concentrations for dilute mixtures of ³He in solid ⁴He. The temperatures for phase separation are determined for ³He concentrations 500<x ₃<2000 ppm for a molar volume V _M =20.7 cm³. We report the temperature dependence of the nuclear spin-lattice relaxation times for ³He in the droplets formed after phase separation at low temperatures. The temperature dependence suggests that the interface ³He atoms responsible for the relaxation are degenerate, not solid-like.     

3He-3He and 4He-4He Cross Sections in Matter at Low Temperature

The Galitskii-Migdal-Feynman (GMF) formalism is applied to liquid ³He and (for the first time) to liquid ⁴He. The effective total, diffusion and viscosity cross sections, as well as the effective scattering length and the effective range, are calculated. For liquid ³He, it is found that S-wave scattering dominates for wave number k<0.5 Å^?1. At the Fermi momentum k _F, the effective partial cross section σ _? (and thus the total cross section σ _T) has a singularity (virtual state). This singularity may be interpreted as a signature of superfluidity or a quasi-bound state. For k>2 Å^?1, the effective total cross section is nearly constant. On the other hand, it is found in liquid ⁴He that S-wave scattering dominates for k<0.3 Å^?1, and a peak exists in σ _T arising from a peak in the effective D-wave cross section. This resonance corresponds to a quasi-bound state trapped by the ?=2 centrifugal barrier. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the matter cross section at low temperatures. This effect is absent in the ³He gas. It is, therefore, a purely many-body effect in liquid ³He. With increasing energies, the matter results approach the vacuum results. This indicates that the high-energy behavior is dominated by the self-energy contribution; the many-body effects can be neglected.     

Unusual Behavior of a MEMS Resonator in Superfluid 4He

Novel mechanical resonators based on micro-electro-mechanical systems (MEMS) technology were developed for the study of superfluid ⁴He. The MEMS device is composed of two parallel plates, the movable plate suspended by four serpentine springs above the substrate, forming a shear mechanical oscillator. A specific device with a 1.25 μm gap was tested in the superfluid phase of ⁴He. At temperatures below 400 mK the device exhibits nonlinear and hysteretic behavior when the excitation exceeds a threshold. The anomalies are reminiscent of quantum turbulence and vorticity effects observed in other mechanical oscillators such as tuning forks or vibrating grids.     

Transition to Turbulence and Critical Velocity in Superfluid Solution of 3He in 4He

By the method of oscillating tuning fork, we carried out researches of the transition to turbulence in superfluid solution of 5% ³He in ⁴He at temperatures of 100 mK–300 mK. The critical velocity υ _c of the turbulence appearance is determined through measuring the volt-ampere characteristics. It is established that in the mixture the temperature dependence of the critical velocity is non-monotonous and differs strongly from that in pure ⁴He. Unlike ⁴He, the step-like anomalies on resonance curves were observed which, presumably, is connected with instability of the vortex system under the conditions where the core of the vortex is filled by the atoms of ³He. It is shown that such anomalies appear at the temperatures below 0.9 K, at the same time at temperatures below ～0.5 K they appear even at υ<υ _c .     

Hysteresis,Switching and Anomalous Behaviour of a Quartz Tuning Fork in Superfluid 4He

We have been studying the behaviour of commercial quartz tuning forks immersed in superfluid ⁴He and driven at resonance. For one of the forks we have observed hysteresis and switching between linear and non-linear damping regimes at temperatures below 10 mK. We associate linear damping with pure potential flow around the prongs of the fork, and non-linear damping with the production of vortex lines in a turbulent regime. At appropriate prong velocities, we have observed metastability of both the linear and the turbulent flow states, and a region of intermittency where the flow switched back and forth between each state. For the same fork, we have also observed anomalous behaviour in the linear regime, with large excursions in both damping, resonant frequency, and the tip velocity as a function of driving force.     

The Decay of Forced Turbulent Coflow of He II Past a Grid

We present an experimental study of the decay of He II turbulence created mechanically, by a bellows-induced flow past a stationary grid in a 7×7 mm² superfluid wind tunnel. The temporal decay L(t) originating from various steady-states of vortex line length per unit volume, L ₀, has been observed based on measurements of the attenuation of second-sound, in the temperature range 1.17 K<T<1.95 K. Each presented decay curve is the average of up to 150 single decay events. We find that, independently of T and L ₀, within seconds past the sudden stop of the drive, all the decay curves show a universal behavior lasting up to 200 s, of the form L(t)∝(t?t ₀)^?3/2, where t ₀ is the virtual origin time. From this decay process we deduce the effective kinematic viscosity of turbulent He II. We compare our results with the bench-mark Oregon towed grid experiments and, despite our turbulence being non-homogeneous, find strong similarities.     

The Frequency Dependence of the Added Mass of Quartz Tuning Fork Immersed in He II

We measured the dependences of the resonance frequency of tuning forks immersed in liquid helium at \(T = 0.365\hbox { K}\) in the pressure interval from saturated vapor pressure to 24.8 atm. The quartz tuning forks have been studied with different resonance frequencies of 6.65, 8.46, 12.1, 25.0 and 33.6 kHz in vacuum. The measurements were taken in the laminar flow regime. The experimental data allow us to determine the added mass of a quartz tuning fork in He II. It was found that the added mass per unit length of the prong fork is frequency dependent. Some possible qualitative explanations for such dependence are proposed. In addition, we observed, at \(T = 0.365\hbox { K}\), the changes in added mass with pressure according to the pressure dependence of He II density.     

The Damping and Drag Coefficient of Quartz Tuning Fork in Superfluid $$^{3}\hbox {He}$$–$$^{4}\hbox {He}$$4He Solutions in the Laminar Flow

The \(^{3}\)He impurity influence on the oscillations of a quartz resonator and thus its drag coefficient in a laminar flow of a superfluid \(^{3}\)He–\(^{4}\)He mixture has been investigated. The temperature dependences of the resonance curves were measured on quartz tuning forks with a resonance frequency 32 kHz in vacuum in superfluid mixtures with \(^{3}\)He concentrations of \(x_{3}=0.05\) and 0.15 in a wide range of driving forces at temperatures from 0.5–2.5 K. The results obtained were used to plot the temperature dependence of the drag coefficient. With the help of the normalization on the effective area of the oscillating body, the concentration dependence of the drag coefficient of the quartz tuning fork and the vibrating sphere in superfluid solutions has been constructed and analyzed.     

Thermodynamic Diagrams of 3He from 0.2 K to 300 K Based Upon its Debye Fluid Equation of State

On the basis of the equation of state and the phase equilibrium equations of helium-3 (³He), a computer program for calculating the thermodynamic properties of ³He has been created. With this program, many iso-property tables were prepared for generating p–h and T–s diagrams of ³He over the range of temperature from 0.2 K to 300 K and pressures up to 300 MPa. Compared with the previous diagrams plotted with interpolated experimental data sets, the new ones are more thermodynamically consistent and cover a broader temperature and pressure range. The estimated overall random errors of the diagrams are within 2 %.     

Thermodynamic Properties of Liquid 3He-4He Mixtures Between 0–10 bar below 1.5 K

The thermodynamic properties of liquid ³He-⁴He mixtures at pressures of up to 10 bar and temperatures below 1.5 K are determined. The calculations are based on previously determined thermodynamic properties of ³He-⁴He mixtures at saturated (zero) pressure, and available experimental measurements of the molar volume, which are used to determine an expression for the molar volume. Since available experimental data for mixtures at higher pressures are restricted to low temperatures (below about 0.7 K), the calculated molar volumes at high pressure and high temperature are largely based on pure ³He and pure ⁴He data.     

Slippage of 4He Films and Precursor Phenomenon of Superfluidity

We have carried out quartz crystal microbalance (QCM) experiments for ⁴He films on an exfoliated single-crystalline graphite using a 32 kHz tuning fork, and have measured the temperature dependence of the resonance frequency and the Q value for various areal densities and oscillation amplitudes. Comparing with the previous experiments for Grafoil, the decoupling of the films due to the slippage or the superfluidity was larger than that of Grafoil, and the competition between the slippage and the superfluidity was observed in three-atom thick films. Furthermore, it was found that the slippage is suppressed gradually at higher temperature than the superfluid onset T _c , and that the relaxation time decreases at low temperatures while it obeys the Arrhenius law at high temperatures. These results suggest a precursor to the superfluidity of ⁴He films.     

Low-Temperature Specific Heat of Graphite and CeSb2: Validation of a Quasi-adiabatic Continuous Method

We present the application of a fast quasi-adiabatic continuous method to the measurement of specific heat at ⁴He temperatures, which can be used for the study of a wide range of materials. The technique can be performed in the same configuration used for the relaxation method, as the typical time constants between calorimetric cell and thermal sink at 4.2 K are chosen to be of the order of τ～30 s. The accuracy in the absolute values have been tested by comparing them to relaxation-method results obtained in the same samples (performed in situ using the same set-up), with a deviation between the absolute values <3 % in the whole temperature range. This new version of the continuous calorimetric method at low temperatures allows us to completely characterize and measure a sample within a few hours with a high density of data points, whereas when employing other methods we typically need a few days. An exhaustive study has been performed for reproducibility to be tested. In the present work, we have applied this method to two different substances: CeSb₂, which exhibits three magnetic transitions at 15.5 K, 11.7 K and 9.5 K, and graphite, both highly-oriented pyrolytic graphite (HOPG) and natural crystals. Our results on these graphites are discussed in comparison with previous published data on different kinds of graphite samples.     

Vibrating Wire Thermometry in Superfluid 3He

We report systematic measurements of the response of a Vibrating Wire Resonator (VWR) in normal and superfluid liquid ³He. Special attention has been paid to the hydrodynamic regime of the superfluid B-phase, where the response parameters of the VWR do not follow a simple law. We show that a simple interpolation between the region where first order slip-corrections can be applied and the ballistic regime is insufficient. Measuring an empirical effective viscosity, we propose a temperature calibration method which allows the use of VWRs as a secondary thermometer at intermediate and high pressures in the temperature range 0.2 T _c < T < 50 mK.     

Evidence for a Self-bound Liquid State and the Commensurate–Incommensurate Coexistence in 2D 3He on Graphite

We made heat-capacity measurements of two dimensional (2D) ³He adsorbed on graphite preplated with monolayer ⁴He in a wide temperature range (0.1≤T≤80 mK) at densities higher than that for the 4/7 phase (=6.8 nm^?2). In the density range of 6.8≤ρ≤8.1 nm^?2, the 4/7 phase is stable against additional ³He atoms up to 20% and they are promoted into the third layer. We found evidence that such promoted atoms form a self-bound 2D Fermi liquid with an approximate density of 1 nm^?2 from the measured density dependence of the γ-coefficient of heat capacity. We also show evidence for the first-order transition between the commensurate 4/7 phase and the ferromagnetic incommensurate phase in the second layer in the density range of 8.1≤ρ≤9.5 nm^?2.     

High Quality Tuning Forks in Superfluid 3He-B Below?200?��K

We have investigated the influence of the damping force acting on high quality tuning forks (Q??10⁶) of different sizes and geometries in superfluid ³He-B at temperatures below 200 ??K and a pressure of 0.1 bar. The measurements show that at low velocities, the damping of the largest fork expressed in terms of its resonance characteristic width ??f ₂ rises up as its velocity increases. This is in contradiction to the damping of the fork due to Andreev reflection and it may be caused by the interaction of this fork with excitations trapped in the Andreev bond states. We present our preliminary experimental results.     

Quantum Crystal Oscillations in a Superfluid Liquid

We study the hydrodynamics of quantum ⁴He crystal oscillations in a superfluid liquid with involving the dynamics of atomically rough surfaces. It is shown that, due to enhancement of the kinetic growth coefficient as the temperature lowers, the reaction force of the liquid applied to the ⁴He crystal changes its character from the inertial to the viscous one vanishing as T→0. The model is confirmed by the experiments on the oscillations of the ⁴He crystal within the temperature range 0.54–1.43 K at frequencies 484 and 211 Hz. New type of a hydrodynamic instability is found. The instability occurs provided that the oscillation amplitude of the velocity becomes higher than ～3 cm/s.