Phonon-Impuriton Relaxation and Transport in 3He-4He Superfluid Solutions

No Heading The measurements of the effective thermal conductivity coefficient of a superfluid³He-⁴He mixture with initial concentration of 9.8% ³He are carried out in the temperature range 70 – 500 mK. The results obtained and the other experimental data available on effective thermal conductivity, shear viscosity, and spin diffusion are interpreted within the kinetic theory of phonon - impuriton system of superfluid solutions. It is shown that all experimental data can be explained by taking into account the following relaxation processes: longitudinal phonon relaxation, phonon scattering by impuriton, phonon absorption and emission by impuriton, and impuriton - impuriton interaction. The last process is characterized by different relaxation times for each transport phenomenon: transfer of mass, momentum, and nucleus spin. The impuriton - impuriton and phonon - impuriton relaxation times are estimated and the hierarchy of relaxation times in such system is established. The phonon longitudinal relaxation time in phonon diffusion process should be taken into account. The phonon and impuriton contributions to thermal conductivity, viscosity, and mass diffusion are estimated.PACS numbers: 66.20.+d, 67.60–g, 64.75+g, 67.40.Pm, 66.60+a, 66.30.Xj     

Investigation of the lifetime of longitudinal phonons at GHz frequencies in liquid and solid4He

The attenuation of longitudinal 1-GHz phonons was measured as a function of temperature in liquid ⁴ He at svp and at 23 bar as well as in hcp ⁴ He at 36 bar. The lifetime of the phonons which were generated by stimulated Brillouin scattering was determined optically by a probing light pulse. The results in liquid ⁴ He are discussed in terms of relaxation processes in the phonon and roton gas and are in good agreement with existing work. The attenuation in hcp ⁴ He, which approximately shows aT ⁴ temperature dependence, is attributed to three-phonon processes with longitudinal thermal phonons. A quantitative comparison with Landau-Rumer theory gives satisfactory agreement with the data. No effect of phonon dispersion on sound attenuation is found down to 0.8 K.     

Sound and dissipation coefficients in the phonon-impurity system of 3He-4He solutions

The phonon-impurity system of dilute solutions of ³He in ⁴He is studied experimentally and theoretically using an acoustic technique. The sound velocity and absorption measurements make it possible to identify the theoretically predicted new mechanism of phonon relaxation with anomalous dispersion in the presence of impurities. A kinetic problem for arbitrary frequencies is solved, which also enables us to obtain all the dissipation coefficients of the solutions and to explain the experimental data on second-sound absorption, thermal conductivity, and heat pulse propagation. The relation is considered between relaxation processes in a phonon-impurity system and the phonon spectrum dispersion in ³He-⁴He solutions.     

Thermal conductivity and isotopic impurities in single crystals of helium

We have utilized the enhancement of thermal conductivity by Poiseuille flow of the phonon gas to obtain highly sensitive measurements of phonon scattering by isotopic impurities in single crystals of helium. Crystal orientation, size, and quality may be inferred from the thermal conductivity data themselves. Our hcp ⁴ He crystals were grown at a constant pressure of 85.1 atm using apparatus and techniques that made possible some control over crystal orientation. An isotopic impurity concentration of 1.0×10^–5 decreases the peak conductivity in these crystals by a factor of 1.9 along a direction perpendicular to thec axis. In the Poiseuille region a relaxation time limit has been achieved experimentally that allows our data to be fitted as a function of temperature and concentration with only one parameter. The observed scattering strength is a factor of 2.7 greater than can be explained in terms of mass-defect scattering alone. A number of current theories are examined in the light of this result. Our pure ⁴ He data strongly support aT ^–3 dependence for the normal-process relaxation time. Measurements of the thermal conductivity parallel to thec axis reveal no anisotropy in either the normal-process relaxation time or the isotopic scattering strength.This work was supported in part by the National Science Foundation and the Office of Naval Research.     

Effective interactions and transport properties of degenerate spin-polarized3He-4He mixtures

We present calculations of the thermal conductivity, viscosity, and longitudinal spin diffusion of degenerate³He-⁴He mixtures as a function of spin polarization. Physical arguments and sum rules are used to describe qualitatively the behavior of the effective interactions between two³He quasiparticles. A recently proposed potential model is consistent with these expectations and provides the momentum- and polarization-dependent transition probabilities that enter into transport calculations. In the limit of small³He concentrations, our results agree with previous calculations based on the hard sphere model. For concentrations nearing saturation, however, we find structure in the thermal conductivity as a function of polarization with the³He density kept fixed. While the behavior of the viscosity remainsqualitatively similar to that at low concentration, the spin diffusion coefficient is qualitatively different. This behavior of the transport coefficients is largely a consequence of the strongly polarization dependentm _z =1 triplet scattering rate which becomes comparable to that in the singlet channel at large polarizations.     

The coupled phonon spectrum in3He-4He solutions

A simple extension of a model previously used for³He-⁴ He solutions is presented, in which the effective vertex functions between³ He and⁴ He density fluctuations are assumed to depend only on the momentum transfer. The possible zero-concentration³ He quasiparticle spectra are divided into two classes, those that do and those that do not intersect the⁴ He phonon spectrum. The present model calculations of the coupled phonon spectrum demonstrate that as the temperature is decreased the behavior of the shifts in the phonon spectrum can be considered as a signature of the class of³ He quasiparticle spectrum used. Comparison with recent scattering experiments, however, indicates that the existing data are not sufficient to distinguish unambiguously between the two classes of³ He spectrum. It is suggested that a low-temperature neutron scattering experiment be performed to settle this question.     

Umklapp region thermal conductivity of body-centered-cubic3He

The thermal conductivity of body-centered-cubic³He has been measured in isotopically pure samples. In agreement with previous measurements in impure samples, the thermal conductivity in the bcc phase of³He does not obey the simple Umklapp temperature dependence which is found in the higher density hexagonal-close-packed phase. The calculated phonon mean free paths also do not obey a simple Umklapp temperature dependence, providing evidence that the high-temperature specific heat anomaly in bcc³He is not directly responsible for the anomaly in the thermal conductivity.Work supported by grants from the National Science Foundation and the Army Research Office (Durham).     

Search for evidence of the influence of vacancies on the thermal conductivity of solid4He

We have measured the thermal conductivity of high quality low density hcp⁴He Crystals. The behavior is well described by standard phonon thermal conductivity theory. We discuss the limits that these measurements set on the thermal conductivity due to vacancies.     

Effective Heat Conductivity and Relaxation Processes in Superfluid Mixtures of 3He-4He

The effective thermal conductivity coefficient'ceff in superfluid ³He-⁴He mixtures with concentration of 9.8% ³He has been studied experimentally between 100 and 500 mK, where the main contribution to the kinetic processes is made only by phonons and ³He impurity excitations. In this case the effective thermal conductivity is a combination of diffusivity, thermal conductivity and thermal diffusion. The κ _eff value was found from stationary measurements of the temperature gradients caused by the thermal flow and from the temperature relaxation kinetics. Both the methods provide consistent resugts which also agree with those on effective thermal conductivity calculated in terms of the kinetic theory of phonon-impuriton system.     

Temperature,pressure, and concentration dependence of the thermal conductivity of very dilute solutions of3He in superfluid4He

The thermal conductivity of³He–⁴He solutions at saturated vapor pressure has been measured for the concentration range 0.011–1.3 mole %³He and the temperature range 84–650 mK. Measurements were made at 10 and 24 atm for several of the concentrations. The thermal conductivity of solutions at 24 atm does not differ greatly from the thermal conductivity of pure⁴He at this pressure. Qualitative agreement with the Baym and Ebner theory is achieved only if the boundary scattering of phonons is treated in a different manner than suggested by them.     

Anomalous size dependence of the thermal conductivity of graphene ribbons

We investigated the thermal conductivity K of graphene ribbons and graphite slabs as the function of their lateral dimensions. Our theoretical model considered the anharmonic three-phonon processes to the second-order and included the angle-dependent phonon scattering from the ribbon edges. It was found that the long mean free path of the long-wavelength acoustic phonons in graphene can lead to an unusual nonmonotonic dependence of the thermal conductivity on the length L of a ribbon. The effect is pronounced for the ribbons with the smooth edges (specularity parameter p > 0.5). Our results also suggest that, contrary to what was previously thought, the bulk-like three-dimensional phonons in graphite make a rather substantial contribution to its in-plane thermal conductivity. The Umklapp-limited thermal conductivity of graphite slabs scales, for L below ～30 μm, as log(L), while for larger L, the thermal conductivity approaches a finite value following the dependence K(0) - A × L(-1/2), where K(0) and A are parameters independent of the length. Our theoretical results clarify the scaling of the phonon thermal conductivity with the lateral sizes in graphene and graphite. The revealed anomalous dependence K(L) for the micrometer-size graphene ribbons can account for some of the discrepancy in reported experimental data for graphene.     

The attenuation of second sound in dilute3He-4He solutions below 1 K

The attenuation of second sound in dilute solutions of³He in⁴He has been measured from the width of standing wave resonances. Results are presented here for³He molar concentrations of 1.3% and 5% in the temperature range 50 mK to 1 K at pressures of 0 and 10 atm. The results are compared with the theory of Saam, Baym, and Ebner and suggest that theoretical values of the phonon thermal conductivity lifetime are too great. Comparison is also made with recent measurements of the second-sound damping constant in very dilute solutions (X0.5%); our result shows no sign of the anomalous peak in the damping constant observed for such concentrations. The shear viscosity of the dilute solutions is also computed and found to be in agreement with the capillary flow measurements of Kuenhold, Crum, and Sarwinski.This work was supported in part by a grant from the Research Corporation.     

Breaking the Minimum Limit of Thermal Conductivity of Mg3Sb2 Thermoelectric Mediated by Chemical Alloying Induced Lattice Instability

Thermal properties strongly affect the applications of functional materials, such as thermal management, thermal barrier coatings, and thermoelectrics. Thermoelectric (TE) materials must have a low lattice thermal conductivity to maintain a temperature gradient to generate the voltage. Traditional strategies for minimizing the lattice thermal conductivity mainly rely on introduced multiscale defects to suppress the propagation of phonons. Here, the origin of the anomalously low lattice thermal conductivity is uncovered in Cd-alloyed Mg₃Sb₂ Zintl compounds through complementary bonding analysis. First, the weakened chemical bonds and the lattice instability induced by the antibonding states of 5p-4d levels between Sb and Cd triggered giant anharmonicity and consequently increased the phonon scattering. Moreover, the bond heterogeneity also augmented Umklapp phonon scatterings. Second, the weakened bonds and heavy element alloying softened the phonon mode and significantly decreased the group velocity. Thus, an ultralow lattice thermal conductivity of ≈0.33 W m⁻¹ K⁻¹ at 773 K is obtained, which is even lower than the predicated minimum value. Eventually, Na_0.01Mg_1.7Cd_1.25Sb₂ displays a high ZT of ≈0.76 at 773 K, competitive with most of the reported values. Based on the complementary bonding analysis, the work provides new means to control thermal transport properties through balancing the lattice stability and instability.     

Transport properties of spin polarized3He-4He mixtures

We have calculated the viscosity, thermal conductivity, and longitudinal spin diffusion coefficient in³He-⁴He mixtures which are spin polarized. The calculation applies to all temperature regimes. We have also calculated the Onsager cross coefficient which arises because of the coupling between heat and longitudinal spin currents. The interaction between³He quasiparticles is taken to be a constant as a first approximation. We have also investigated the changes brought about by allowing the interaction to vary with the momentum of the quasiparticle.     

Measurements of Torsional Oscillations and Thermal Conductivity in Solid 4He

Polycrystalline samples of hcp ⁴He of molar volume 19.5?cm³ with small amount of ³He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of ³He, x ₃, were studied: isotopically purified ⁴He with the estimated x ₃≤10^?10, ‘well-grade’ helium with x ₃～3×10^?7 and a specially prepared mixture with x ₃=2.5×10^?6. The torsional oscillator response and thermal conductivity were investigated before and after annealing. The temperature and width of the torsional anomaly increase with increasing x ₃. Annealing resulted in an increased phonon mean free path but often in little change in the torsional oscillator response. While the magnitude of the torsional anomaly and phonon mean free path can be very different in different samples, no correlation was found between them; this implies that these two properties are controlled by different types of crystal defects. It seems plausible that the mean free path of thermal phonos at ～200?mK is controlled by vibrating dislocations while the magnitude of the frequency shift of torsional oscillations is governed by static defects such as pinned dislocations and grain boundaries.     

The effect of a strong magnetic field on the damping of second sound in dilute3He-4He mixtures below 100 mK

We have measured the increase in damping of second sound in 0.1% and 0.05%³He-⁴He solutions upon application of a magnetic field of 10 T. The increase is caused by changes in the thermal conductivity and viscosity of the mixture as the system becomes spin polarized. We show how to fit the data for the viscosity in zero-field to obtain an estimate of the interaction between the³He quasiparticles. It is then possible to predict the viscosity in a field of 10 T using the calculation of Hampson et al. The data agree with the theory to within 2%.     

Thermal Conductivity of a Molecular Crystal with Rotational Degrees of Freedom: Orientational Defect Scattering

Measurements of thermal conductivity of solid methane-deuteromethane solutions at equilibrium vapor pressure in the temperature range 1.2÷20 K are reported. The obtained dependences of thermal conductivity on temperature and concentration can be explained qualitatively assuming that the dominant mechanism of phonon scattering is connected with the interaction of phonons with the rotational motion of the molecules in all of the three orientational phases of the CH₄-CD₄ system. The contribution of the orientational defect scattering to the thermal conductivity is discussed in frame of the model of local changes in the moments of inertia of molecules.      

Phonon scattering and thermal conduction mechanisms of sintered aluminium nitride ceramics

From thermal diffusivity measurements of sintered AIN at temperatures ranging from 100 to 1000 K, the phonon mean free path of AIN was calculated in order to investigate phonon scattering mechanisms. The calculated mean phonon scattering distance was increased with decreasing temperature. The mean phonon-defect scattering distances were respectively limited to about 50 nm at temperatures ranging from 100 to 270 K and about 30 nm at temperatures ranging from 100 to 700 K, for AIN specimens with a room-temperature thermal conductivity of 220 and 121 Wm^–1 K^–1 containing 0.1 and 1.4 wt % oxygen, respectively. These short phonon-defect scattering distances were considered to correspond to the separation of oxygen-related internal defects in AIN grains. Calculation of the mean phonon scattering frequencies indicated that the phonon scattering is dominated by phonon-defect scattering at temperatures below 270 K for an AIN specimen with an oxygen content of 0.1 wt %, and at temperatures below 350 K for an AIN specimen with an oxygen content of 1.4 wt %.     

Electro- and Heat Transfer in $$\mathbf{Cd}_{\mathbf{0.22}}\mathbf{\hbox {Hg}}_{\mathbf{0.78}}{} \mathbf{Te}$$ Single Crystals in the Temperature Range of Their Practical Applications

The thermal and electrical conductivity of a single-crystal \(\hbox {Cd}_{0.22}\hbox {Hg}_{0.78}\hbox {Te}\) was studied in the temperature range of practical applications (77–300 K). The sample has impurity conductivity, which is limited by the scattering of charge carriers by phonons. Heat in the sample is transferred by phonons and thermal conductivity is limited by phonon–phonon scattering. The electron contribution to the thermal conductivity can be neglected.     

Three-phonon vertex corrections to the excitation spectrum and liquid-structure function of liquid4He

The energy spectrum of elementary excitations and the liquid-structure function of liquid⁴He are calculated by means of the method of correlated basis functions in the approximation of second-order perturbation theory. The procedure is based on (i) the construction of phonon functions in terms of collective coordinates and the optimum Bijl-Dingle-Jastrow type of ground-state wave function and (ii) the evaluation of leading correction terms to the Bijl-Feynman excitation spectrum, which are generated by two types of three-phonon vertices. Numerical results are obtained using the optimum liquid-structure function computed by Campbell and Feenberg in the paired-phonon analysis.Research supported in part by the University of Kansas General Research Fund under grant No. 3235-5038.