Field and excitation dependent ultrasonic attenuation in3He-B

Sound absorption of³He-B at 0 bar was studied at a frequency of 10 MHz. We performed pulsed experiments with different pulse lengths (4 to 15 s) and pulse powers (0.1 to 160 W) in the temperature range 0.2 < T/T_C < 2. For pulse power less than pth 50 W, and in the temperature range 0.4 to 0.8 T_c and zero field, the attenuation coefficient a decreases monotonically at about 0.2 cm^–1 per decade of power. Above pth. increases up to values of 3.5 cm^–1 and 1.9 cm^–1 at highest power for temperatures of 0.8 T_c and 0.4 T_c, respectively. At pulse power around 100 W and at the lowest temperatures, the attenuation changes within the first 200 s after the application of the pulse; also increases with increasing field. In the normal fluid decreases with increasing power. All of our observations are lacking a rigorous theoretical understanding.     

Temperature dependence of electrical resistivity of deformed and undeformed V-rich V3Si single crystals

The electrical resistivity (T) of V-rich V₃Si single crystals (T _c-11.4 K) was measured from 4.2 to 300 K along the directions of [1 0 0] and [1 1 1] before and after plastic deformation at 1573 K. Anisotropy of (T) was observed although V₃Si has the cubic A15 structure. Plastic deformation does not affect the normal-state (T) behaviour but changes the normal-superconducting transition width T_c. At low temperatures (T _c<T 40 K), (T) varies approximately as T ⁿ where n-2.5 and this behaviour does not contradict the (0)- phase-diagram plot proposed by Gurvitch, where is the electron-phonon coupling constant and (0) is the residual resistivity.     

Angular dependence of the critical magnetic field in granular superconducting films

The critical magnetic fieldH _c () of granular Al films has been measured as a function of the angle between the field direction and the plane of the film at temperatures nearT _c0 .The film thicknessd is smaller than the temperature-dependent coherence length (T), the bulk electron mean free path1 is smaller than the BCS coherence length ₀, and 1 d. The experimental data onH _c () are well fitted by the Tinkham formula. However, the observed values ofH _c/H _care not always consistent with and increase with1/d. This fact suggests that the boundary scattering of electrons at the film surface enhancesH _c () and that the enhancement ofH _cis larger than that ofH _c.On leave from Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan.     

Equation of State and Thermodynamic Properties of Pure D2O and D2O + H2O Mixtures in and Beyond the Critical Region

A parametric crossover model is adapted to represent the thermodynamic properties of pure D₂O in the extended critical region. The crossover equation of state for D₂O incorporates scaling laws asymptotically close to the critical point and is transformed into a regular classical expansion far from the critical point. An isomorphic generalization of the law of corresponding states is applied to the prediction of thermodynamic properties and the phase behavior of D₂O + H₂O mixtures over a wide region around the locus of vapor-liquid critical points. A comparison is made with experimental data for pure D₂O and for the D₂O + H₂O mixture. The equation of state yields a good representation of thermodynamic property data in the range of temperatures 0.8T _c(x)T1.5T _c(x) and densities 0.35_c(x)1.65_c(x).     

Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Viscoelastic and rheological behavior of concentrated colloidal suspensions

Molecular approaches are discussed to the density (), viscoeleastic (), and rheological () behavior of the viscosity(,,) of concentrated colloidal suspensions with 0.3 < < 0.6, where, is the volume fraction, the applied frequency, and ; the shear rate. These theories are based on the calculation of the pair distribution functionP ₂(r,,), wherer is the relative position of a pair of colloidal particles. The linear viscoelastic behavior(,,=0) follows from an equation forP ₂(r,,) derived from the Smoluchowski equation for small, generalized to large by introducing the spatial ordering and (cage) diffusion typical for concentrated suspensions. The rheological behavior(,,=0) follows from an equation forP ₂(r,) of a dense hard-sphere fluid derived from the Liouville equation. This leads to a hard-sphere viscosity^hs(,) which yields the colloidal one(,) by the scaling relation(,) ₀=^hs(,) _B, where ₀ is the solvent viscosity. _B is the dilute hard-sphere (Boltzmann ) viscosity and the's are appropriately scaled,(,) and(,) agree well with experiment. A unified theore for(,,) is clearly needed and pursued.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994. Boulder, Colorado, U.S.A.     

Investigation of UBe13 and other beryllium and uranium compounds in normal and superconducting states

The Hall voltageU _xy (H), magnetoresistance (H), magnetization in the superconducting stateM(H), and the second superconducting critical magnetic field of UBe₁₃ have been investigated. It is found thatU _xy (H) is not linear, but has a maximum nearH=70 kOe atT=1.9 K. When the temperature rises from 1.9 to 100 K, the Hall coefficientR(H0) decreases about 20 times from 2.5×10^–10 to 1.35×10^–11 -cm/Oe. The rise of the magnetic field causes a strong decrease of the electrical resistance: atT=1.7 K, (0)/(210kOe)5.8. From theH _c2 investigation for single crystals it can be seen that near T_c the anisotropy ofH _c2 is absent (it becomes visible only upon loweringT to 0.9T _c ). TheM is similar to the typical dependence for type II superconductors. The thermodynamic critical fieldH _c (0)1 kG, the Ginzburg-Landau parameter x 60, and the penetration depth 4.10^–5 cm. The effects of alloying a small quantity of iron and of neutron irradiation are investigated. The effects of alloying with other compounds of U and Be are also discussed. It is possible to suppose that UBe₁₃ has two groups of carriers, heavy and light, with the anomalous properties of UBe₁₃ caused by the specificity of the interaction between these two groups of carriers.     

Magnetic field dependence of the density of states of YBa2Cu3O6.95: Implications for the vortex structure

The total specific heat of YBa₂Cu₃O_6.95 single crystals includes contributions from phonons and spin-1/2 particles, as well as electronic contributions. The electronic specific heat is described by a quadratic term T² in zero field and a linear term [(0)+(H)]T which is increased when a magnetic field H is applied perpendicular to the CuO₂ planes. In agreement with d-wave superconductivity, we find that _n/T_c and (H)_n(H/H_c2)^1/2, where _n is the coefficient of the normal-state linear term. The H^1/2 dependence of the density of states at the Fermi level was predicted by G. Volovik for lines of nodes in the gap: the quasiparticles which contribute to this density of states are close to the nodes in momentum space and are located outside the vortex core.     

Shear viscosity of the B phase of superfluid3He

The shear viscosity (T) in the Balian-Werthamer (BW) state of superfluid ³ He is calculated variationally throughout the region 0t 1(t=T/T _c) from the transport equation for Bogoliubov quasiparticles. Coherence factors are treated exactly in the calculation of the collision integral. The numerical result for =_s= _s(T)/_n(T_c) agree very well with experiment in the range 0.8t1.0. Analytic expressions = 0.577 (1–1.0008t) and =1–(23/64) [=(T)/k _B T] are obtained in the low-temperature region and in the vicinity ofT _c, respectively. From the numerical analysis it is shown that the latter equation is valid only in the temperature range 0.9997t1.0.Supported by the Research Institute for Fundamental Physics, Kyoto University.     

The specific heat and critical magnetic field of superconducting PdH(D)

From the solution of the Eliashberg equations on the imaginary axis, the thermodynamic properties, specific heat, and critical magnetic field of PdH(D) have been calculated. The Eliashberg kernels ²()F() were constructed using a published value of ²(), and F() was obtained from inelastic neutron scattering data. The results for the specific heat are in good agreement with published experimental data. The critical magnetic field shows a nearly parabolic behavior as a function of temperature, in disagreement with the linear experimental behavior. The deviation function D(t) and the ratios C(T _c)/T _c and [T _c/H _c(0)]² indicate that the PdH(D) system is BCS-like. The functional derivative of T _c with respect to changes in the kernel is also calculated.On sabbatical leave from the Instituto de Investigaciones en Materiales, UNAM, Mexico.     

Thermal Expansion and Isothermal Compressibility of TlIn1 – xNdxSe2 (0 ≤ x≤ 0.08) Crystals

The thermal expansion coefficient () and isothermal compressibility ( _T ) of TlIn_{1 – x} Nd _x Se₂(0 x 0.08) crystals were measured between 77 and 400 K. In the range 77–160 K, both and _T increase with temperature, the increase in being much steeper. At higher temperatures, and _T change very little. The observed composition dependences of and _T are interpreted in terms of energy-band structure.     

The transverse acoustic impedance of He II

The complex shear acoustic impedance of liquid He II has been measured at frequenciesf(=/2) of 20.5, 34.1, and 47.8 MHz from 30 mK to the -point T (2.176 K). The impedanceZ was found from the temperature dependence of the quality factor and the resonant frequency of a thickness shear mode quartz crystal resonator immersed in the liquid. The relationship for a hydrodynamic viscous liquidZ(T)=(1–i)(f _n )^1/2 was used to measure the temperature dependence of the viscosity (T) using tabulated values of the normal fluid density _n (T). Deviations from hydrodynamic behavior occurred when the viscous penetration depth was less than the superfluid healing length, the phonon mean free path, and the roton mean free path. Near the -point,Z(T)/Z(T) was frequency dependent and a value for the superfluid healing lengtha=(0.10±0.01)^–2/3 nm was found, where =(T–T)/T. The effects of van der Waals forces near the crystal surface were also observed and a layer model was used to interpret the measurements. Below 1.8 K only rotons contribute significantly toZ and we determined the roton relaxation time as _r =8.5×10^–14 T ^–1/3 exp (8.65/T) sec. Below 1.2 K, _r >1 and we investigated the breakdown of hydrodynamics in this region. ForT<0.6 K the resonant frequency of the crystals decreased by f/f=2×10^–7, but the origin of this effect is not yet known.Financial support provided by the SERC, Bedford College, and the Central Research Fund, University of London.     

Zero Sound Attenuation Near the Quantum Limit in Normal Liquid 3He Close to the Superfluid Transition

The zero sound attenuation of normal liquid ³He has been studied over a range of temperatures from slightly above the superfluid transition temperature, T _c, to approximately 10mK at the constant pressures of 1 and 5bar. Using longitudinal LiNbO₃ transducers, operating both on and off resonance, the experiment was performed at 15 discrete frequencies located in several broadband frequency windows, including 16–25, 60–70, and 105–111MHz. The results are compared to Landau's prediction for the attenuation of zero sound in the quantum limit, (k _B Tk _B T _F), where ₀(P,T, )= (P) T ²{1+(/2k _B T)²}. Calibration of the received zero sound signals was performed by measuring the temperature dependence of the first sound attenuation from 30 to 800mK at those same frequencies and pressures. The data are compared to previous results.     

The flux-line lattice in high-Tc superconductors

The flux-line lattice in type-II superconductors has unusual nonlocal elastic properties which make it soft for short wavelengths of distortion. This softening is particularly pronounced in the highly anisotropic high-T _c superconductors (HTSC) where it leads to large thermal fluctuations and to thermally activated depinning of the Abrikosov vortices. Numerous transitions are predicted for these layered HTSC when the temperatureT, magnetic inductionB, or current densityJ are changed. In particular, the flux lines are now chains of two-dimensional (2D) pancake vortices which may evaporate by thermal fluctuations or may depin individually. At sufficiently highT, ohmic resistivity(T, B) is observed down toJ 0. This indicates that the flux lines are in a liquid state with no shear stiffness and with small depinning energy or that the 2D vortices can move independently. At lowerT, (T, B, J) is nonlinear since the pinning energy of an elastic vortex lattice or vortex glass increases with decreasingJ as predicted by theories of collective pinning and by vortex glass scaling.     

The transverse acoustic impedance of dilute solutions of3He in superfluid4He

The transverse acoustic impedanceZ=R–iX of dilute solutions of³He in superfluid⁴He has been measured at a frequency (/2) of 20.5 MHz at temperaturesT from 30 mK to the transition at T. The³He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of³He quasiparticles, and in the collisionless limit, 1 ( is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient (c, T) and (c, T). The relaxation times were in good agreement with previous work, while (c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the³He quasiparticles and the thermally excited rotons are in the hydrodynamic region, 1. Values of the total viscosity (c, T) were obtained and analyzed to give the³He gas viscosity and the³He-³He and roton-³He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the point we founda=(0.1±0.03)^–2/3 nm, where =1–T/T, proportional to the phase coherence length . Our data are consistent with the hypothesis that _s/T is a universal constant for superfluid dilute solutions, where _s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in³He-⁴He films.     

Temperature dependence of resistivity for thermally diffused V3Si multilayer films

Results concerning V₃Si films produced by a simple annealed multilayer technique are reported together with X-ray diffraction patterns, Auger spectroscopy, and Rutherford backscattering analysis. Low-temperature electrical resistivity measurements are discussed. It is found that the V₃Si films exhibit aT ² dependence in the temperature rangeT _c T23 K and aT ^2.6 dependence in the rangeT _c T40 K. The normal-state resistivity in the whole temperature range (T _c T600 K) is analyzed in the framework of Cote-Meisel theory. Consistent values of the saturation resistivity _m and of the Debye temperature are obtained by fitting the experimental data with the Cote-Meisel expression for (T).     

On intrinsic and extrinsic effects in the surface impedance of cuprate superconductors

Surface impedance measurements in the normal and superconducting state are an excellent method to study conduction electron dynamics and extended defects. Electron dynamics show up most clearly in the relaxation range, i.e., for distances traveled in one rf periods= _F/ ( _F Fermi velocity) being smaller or of the order of the penetration depth and mean free pathl. For materials with _F10⁷ cm/sec the relaxation range is easily accessible forf0.1 THz. Then, in the normal state, relaxation defines the surface impedance with an intrinsic penetration depth _I approaching the London penetration depth _L andR _{I 0 L}/ 2 as surface resistance, allowing measurement of _L and relaxation time(T, ). In the superconducting state the photon interaction scales with _L/ _L=1/( _F dimension of Cooper pairs forl) and causes at low frequencies an absorption rate growing with, which is decreasing with _F/l. The rate increase proportional to turns to a decrease above 0.1 THz, which is accompanied by a decrease ofA with frequency which is stronger for large and small _F/l. These characteristic dependences allow measurement of material parameters, anisotropy, and dynamics of electrons, especially the relaxation rate. But presently, the rf surface impedanceZ is still shrinking with material improvements, which shows, clearly, that theZ=Z _I+Z _res is still dominated by extrinsic properties summarized inZ _res. We present evidence thatZ _res is due to the large leakage currentj _bl and the smallj _cJ of weak links where the latter destroys the intrinsic shielding from a _I-thin seam _J deep into the bulk. This causes rf residual lossesR _res( ₀)² _J ³ _bl/2.R _res stays finite atT-0 due to _bl(T0) _bl(j _bl) being amplified by ( _J/ _I)³>10³ as a weighting factor. The appropriate measure of weak links are the grain-boundary resistanceR _bn((0)) enhancing _JR _bn andR _resR _bn ² . Thus,Z _res is minimal for minimal extrapolated resistivity(T0).To identify the weak links as a new entity, the H-field dependence is most helpful, because at very low fieldsH _c 1J1/ _J Josephson fluxons penetrate into the weak links. These Josephson fluxons show negligible flux flow or flux creep, and enhanceZ _res by _J(H, T) . The measuredj _cJ(H, T) andj _bl values explainZ _res quantitatively as well as in temperature (a+T ⁿ ) (n1,T<T _c /2) and in field (b+H ⁿ ) (n1,H>H _c1J) dependence. The strength of the field dependencedZ _res/dHZ _res(H _c1J )/H _c2J(T) is not only a measure ofZ _res andH _c2J(T) but is crucial for nonlinear effects and (fluxon) noise also, which limit the performance of rf devices.     

High-resolution measurements of the heat capacity of MnBr2·4H2O near its Néel temperature

The heat capacityC _P of the antiferromagnet MnBr₂ ·4H₂O has been measured for polycrystalline and single-crystal samples nearT _N(2.123 K) with temperature resolution of 1×10^–6 K. Similar rounding of the lambda anomaly is found in both cases. For |1 –T/T _N| 10^–1 all data can be well fitted by assuming the samples to consist of many independent subsystems obeying the same power laws but with a Gaussian distribution ofT _N's having a width of 1.1×10^–3 K. ForT>T _N, we findC _P ^–0.12, essentially as predicted for three-dimensional Ising models in the critical region. ForT<T _N and 10^–3 10^–1,C _P ln , which approximates Ising model behavior in this interval but is not expected to be valid for 10^–4. ForT>T _N and 2.5×10^–1, C_P agrees well with predictions for the classical Heisenberg model. This crossover at 10^–1 is consistent with the known anisotropy of the salt and with present theory. The data forT>T _N in the interval 10^–4 10^–3, while not in the range of obvious rounding, appear to be strongly influenced by the mechanism responsible for that rounding.Work supported by the National Science Foundation and the Office of Naval Research. Based on a thesis submitted by L.W.K. to Carnegie-Mellon University in partial fulfillment of the requirements for the Ph.D. degree. A preliminary account of this work was presented at the Atlantic City meeting of the American Physical Society, March 1972 [Bull. Am. Phys. Soc. 17, 299 (1972)].     

Dielectric Permittivity of Eight Gases Measured with Cross Capacitors

A four-ring, toroidal cross capacitor was used to measure accurately the relative dielectric permittivity (p,T) of He, Ar, N₂, O₂, CH₄, C₂H₆, C₃H₈, and CO₂. ( is often called the dielectric constant.) The data are in the range from 0 to 50°C and, in many cases, extend up to 7 MPa. The accurate measurement of (p,T) required a good understanding of the deformation of the gas-filled capacitors with applied pressure. This understanding was tested in two ways. First, the experimental values of (p,T) for helium were compared with theoretical values. The average difference was within the noise, _expt– _theory=(–0.05±0.21)×10^–6, demonstrating that the four-ring cross capacitor deformed as predicted. Second, (p,T) of argon was measured simultaneously on three isotherms using two capacitors: the four-ring capacitor, and a 16-rod cross capacitor made using different materials and a different geometry. The results for the two capacitors are completely consistent, within the specifications of the capacitance bridge. There was a small inconsistency that was equivalent to 1×10^–6 of the measured capacitances, or, for argon, 3×10^–5 A , where A is the zero-density limit of the molar polarizability (–1)/[(+2)].