Dependence of the flux flow viscosity coefficient on the Ginzburg-Landau parameter κ in superconducting indium films

The flux flow viscosity coefficient b ^–1 (in units of ₀ H _{c n} ^–1 c ^–2) of vacuum-deposited indium thin films with low values (1.0–2.8) is measured at temperatures between 0.5T _cand 0.98T _cin the weak magnetic field region. At each temperature, b ^–1 decreases as increases for larger than 1.7. The decrease of b ^–1 with increasing is more rapid as the temperature increases. From an analysis of the present results as well as the existing data on intermediate- and high- superconducting alloys, the relation between b ^–1 and is established over a wide range of . The dependence of b ^–1 on is qualitatively explained by taking into account the contribution of the normal electron dissipation to the viscosity coefficient in the Bardeen-Stephen model.Financial support provided by the Fonds National Suisse de la Recherche Scientifique.On leave from the Department of Electronic Engineering, Faculty of Engineering, Kyushu Industrial University, Fukuoka, Japan.     

The Thermal Conductivity and Thermal Diffusivity of Liquid n-Alkanes: C n H2n+2 (n=5 to 10) and Toluene

Experimental values of the thermal conductivity and the thermal diffusivity of six pure liquid n-alkanes (C _n H_2n+2; n=5 to 10) and toluene are presented in the temperature range of –20 to 70°C under atmospheric or saturation pressure. Measurements were made with the transient hot-wire method, and in the analysis, the temperatures T and T (associated with both and ) were used. In the present work, the values of thermal diffusivity were corrected by the factors k _f (=1.0076 to 0.9892) for data sets obtained with different configurations of the experiment, in which the factors were determined by reference to the thermal diffusivity of n-heptane [= _s/(c _p )_s] at 298.15 K calculated from the volumic heat capacity (c _p )_s as a reference material for heat capacity and the experimentally obtained thermal conductivity _s. The uncertainty of the data is estimated to be 0.48% for the thermal conductivity (absolutely measured) and about 1.8% for the thermal diffusivity (with a coverage factor of k _p =2; p=95%).     

Relaxation times and mass diffusion in superfluid dilute3He-4He mixtures

Relaxation times are reported from the transients observed during thermal conductivity _eff and thermal diffusionk _T ^* measurements in superfluid mixtures of³He in⁴He with a layer thickness of 1.81 mm. The experiments extend from 1.7 K toT and over a³He concentration range 10^–6X<5×10^–2. The agreement between the measured and the predicted from the two-fluid thermohydrodynamic equations is satisfactory forX>10^–3 but deteriorates for smaller³He concentrations. This situation is similar to that for _eff andk _T ^* results and indicates that the transport properties in very dilute mixtures with layers of finite thickness are not well understood. ForX>10^–3, the mass diffusion coefficientD _iso for isolated³He in⁴He has been determined from and from _eff measurements. There is an inconsistency by a constant numerical factor between these determinations. This problem might be related to the observations that in the superfluid phase, the relaxation times for different cell heightsh do not scale withh ². FromD _iso derived via the _eff data, the³He impurity-roton scattering cross section is determined. Comparisons with previous work are made.     

Thermal transport properties and size effects in very dilute superfluid mixtures of3He in4He

The effective thermal conductivity _eff has been measured for 1.6 K for mixtures with 10^–6–2. Both _eff and the derived impurity mass diffusion coefficient D_iso show an unexpected dependence on the height h of the fluid layer. A scaled representation of D_iso leads to a purely phenomenological model involving an effective length scale, proportional to X^–1 and temperature independent. The relations so obtained are consistent with the observations as well as with the observed transition curve Q_C(X) to non-linear behavior.     

Heat conduction in Ba1?xKxBiO3

We have investigated heat conduction of single crystal Ba_1–xK_xBiO₃ in the temperature range of 2–300 K and in a magnetic field of up to 6 Tesla. Temperature dependence of thermal conductivity(T) reveals the participation of both electrons and phonons with their relative contributions that depend critically on the potassium doping concentration. Crystals underdoped with potassium (samples with higherT _c) exhibit a strong suppression of and a glass-like temperature dependence. In contrast, those with a higher potassium content (lowerT _c) show an increase as temperature decreases with a peak near 23 K. Field dependence of(H) is also very sensitive to the level of potassium doping. Crystals exhibiting a large phonon contribution show an initial drop in(H) at low fields followed by a minimum and then a slow rise to saturation as the field increases. The initial drop is due to the additional phonon scattering by magnetic vortices as the sample enters a mixed state. The high field behavior of(H), arising from a continuous break-up of Cooper pairs, exhibits scaling which suggests the presence of an unconventional superconducting gap structure in this material.     

Ultrasonic dispersion and attenuation near the liquid-gas critical point of 3He

We report ultrasonic dispersion and attenuation measurements near the liquid-gas critical point of ³He at frequencies from 0.5 to 5.0 MHz and densities from 0.89 _c to 1.15 _c . The singular part of the sound attenuation and the dispersion on the critical isochore _c = 0.0414 g/cm³ are analyzed in terms of the Kawasaki-Mistura theory. If the Ornstein-Zernike order parameter correlation function is assumed in the analysis, good agreement with our data is achieved, except close to the critical temperature T _cin the high-frequency region, where ^* = /_D 1. Here _D is the characteristic relaxation rate of the critical fluctuations. From a fit of the theory to our data, and assuming the inverse correlation length is expressed by = ₀, where = (T–T_c)/T_c with = 0.63, we obtain ₀ = (3.9 ± 0.4) × 10⁹ m^–1. It is found that a more realistic form of the correlation function, as proposed by Fisher and Langer and calculated by Bray, yields even poorer agreement with out data than does the classical Ornstein-Zernike form for ^* > 10. The same difficulties appear in the analysis of the available data for xenon. Thus, the present mode coupling theory is unable to satisfactorily describe the acoustic experiments on fluids near the liquid-vapor critical point over a large range of reduced frequencies ^*. In the appendix, we reanalyze previously reported ultrasonic data in ⁴He, taking into account the nonsingular term of the thermal conductivity. Using = 0.63, we obtain a good fit of the experiment to the theory in the hydrodynamic region with ₀ = (5.5 ± 1) × 10⁹ m^–1.Supported by a grant from the National Science Foundation.     

Elastic energy of the vortex state in type II superconductors. I. High inductions

The elastic properties of the flux line lattice (FLL) in type II superconductors are calculated from the linearized Ginzburg-Landau (GL) theory for large inductionsBH _c2 . They appear to be strongly nonlocal, i.e., the elastic modulic ₁₁ andc ₄₄ for homogeneous deformations do not apply if the strain field varies over distances /(1–B/H _c2 )^1/2 d ( is the penetration depth,d is the FL distance). For smaller strain wavelength,c ₁₁ andc ₄₄ are smaller by factors (1–B/H _c2 )²/2 ² and (1–B/H _c2 )/ 2 ² , respectively. The order parameter and local field of a deformed FLL exhibit the expected spatial frequency modulation, but also a pronounced amplitude modulation whose degree of modulation increases with the strain wavelength. The results of further calculations avoiding the linearization of the GL theory are given.     

Asymptotic Bethe-Ansatz results for a Hubbard chain with 1/sinh-hopping

We investigate spin-1/2 electrons with local Hubbard interaction and variable range hopping amplitudes which decay like sinh()/sinh(r). Using Sutherland's Asymptotic Bethe Ansatz we derive the generalized Lieb-Wu integral equations from the two-particle phase shift. For half-filling we obtain a closed expression for the ground state energy density. Due to the nesting property there is a metal-to-insulator transition at U_c(> > 0) = 0⁺.In the singular limit = 0the charge gap opens when the interaction strength equals the bandwidth, U _c( = 0) =W.We would like to thank P. Nozières and A. Gogolin for stimulating discussions. F. G. thanks all his colleagues at the ILL Grenoble for their kind hospitality during a stay in 1993/94.     

Grain growth in the two-phase Al-Cu alloys

Grain and phase growth in the two-phase Al-Cu alloys containing 6, 11, 1 7, 24 and 33 wt % Cu were investigated by annealing at 535 °C for 0.5–100 h. The grain and phase sizes of the phase are seen to be larger than that of the phase. The size of phase decreases whereas the size of phase increases with increasing copper content in the alloy. As such, the phase- and grain-size distributions are broader than the phase- and grain-size distributions, but the size range depends on annealing time and alloy composition. The grain sizes of the ,d , and ,d , phases can be related to the volume fraction of the phase,f , according to the equationd = 0.497d /f .     

Temperature dependence of the experimental penetration depth of superconducting thin films

Experimental magnetic field penetration depths (t, d, H) of the stable and superheated Meissner state were calculated as a function of temperature for various applied magnetic fields and various film thicknesses for two cases: (1) (t)/d and (2) 2(t)/d ( is the Ginzburg-Landau penetration depth,d is the film thickness, is the GL parameter). The results of the first case should be a useful tool for obtaining (0) of amorphous superconducting thin films.¹ This work was supported in part by NSF Grant No. INT 8006927.     

Thermal conductivity and quantum diffusion in solid H2

The thermal conductivity of solid H₂ and the NMR absorption signal of isolated o-H₂ were measured simultaneously along isotherms 0.07<T<1.5 K as a function of time after a rapid cooldown from 2 K. The o-H₂ concentration ranged from 3.4% to 0.4%, and the pressure was 90 atm. During the measurements, clustering of o-H₂ particles occurred as seen from the changes both of the NMR signal amplitude and of with time t. The difference ^–1 = ^–1 ()– ^–1(0) between the thermal resistivity ^–1 (t=0) just after cool down and in equilibrium, ^–1 (), was found to change sign near 0.23 K, and this result is discussed with respect to previous experiments. The equilibrium resistivity attributed to the o-H₂ impurities, , is derived and is compared with previous determinations and with predictions. An analysis of the equilibration process for ^–1 and for the NMR signal amplitude is presented. It shows that the characteristic times are of comparable but not equal magnitude. Comparison of the derived from NMR data atP=90 and 0 atm favors resonant ortho-para conversion over quantum tunneling as the leading mechanism for quantum diffusion.     

On type-II superconductors with a first-order transition at the lower critical field

The free energy of a superconductor in the mixed state is obtained to first order in 1–(T/T _c) and – in terms of the solutions of the Ginzburg-Landau equations for = . The circular cell approximation is used to evaluate the lower critical field and the discontinuity in the magnetization at this field for those type-II materials displaying a first-order transition at the field of first flux penetration; the cases of both singly quantized and doubly quantized vortices are considered. The main result of the numerical calculations is that the critical value of for a first-order transition is identical to the critical value of for an attractive interaction between widely separated vortices.Supported in part by the National Research Council of Canada.     

Thermal conductivity and heat capacity of titanium hydrides

We have measured the thermal conductivity and the heat capacity C of Ti, TiH _0.82 , TiH _1.7 , and TiH ₂ at 0.35 K T 4 K. Whereas (TiH _0.82 ) and (TiH _1.7 ) are substantially smaller than (Ti), we find (TiH ₂ ) – 3 (Ti). This latter remarkable result may arise from the enhanced electronic density of states — which is shown by the heat capacity data — and from a rather large electronic mean free path in this stoichiometric compound.     

Plane thermal stresses around holes under steady distribution of temperature

Summary A method for determining the plane thermal stress distribution in a multiply connected region under steady distribution of temperature is presented. The analysis is based on the complex variable approach and permits, if the thermal field is known, the simple determination of theKolosoff functions. The method is illustrated using two examples.

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Zusammenfassung Es wird eine Methode zur Bestimmung des ebenen Wärmespannungszustandes in einem mehrfach zusammenhängenden Bereich unter stationärer Temperaturverteilung angegeben. Die Analyse benützt die komplexe Darstellung und erlaubt die einfache Bestimmung derKolosoff-Funktionen, wenn das Temperaturfeld bekannt ist. Die Methode wird anhand von zwei Beispielen illustriert.

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Notation c constant which take valuesc=E/(1–) for plane strain and - c E for plane stress - Re{} real part of - u, v components of displacement vector - T temperature - z complex variable (x+i y) - coefficient of thermal expansion - complex variable in a mapped plane - boundary value ofz or - Kolosoffs constant which takes values =3–4 for plane strain and =(3–)/(1+) for plane stress - shear modulus of elasticity - Poissons ratio - _xx,_yy,_xy components of stress tensor - () mapping function     

Thermal transport properties in helium near the superfluid transition. III. Dilute3He-4He mixtures in the normal phase

An experimental study is presented for the thermal conductivity and the thermal relaxation for dilute mixtures of³He in⁴He with concentration 9×10^–4X(³He)5×10^–2 at saturated vapor pressure and in the normal phase near the superfluid transition. The conductivity results for are compared with predictions by Dohm and Folk from field-theoretic renormalization group(RG) theory. The conductivity _s =[^–1(T)–^–1(T)]^–1, is compared with Ahlers' phenomenological arguments, and also with predictions by Dohm and Folk and by Onuki. The temperature difference transient T(t) across the fluid, measured as a function of timet after switching on and off the heat current, is analyzed. The thermal diffusion ratiok _T and the mass diffusion coefficientD are obtained by fitting the calculated transient to the experimental one. The results are compared with the predictions that follow from the RG approach by Dohm and Folk. Very good agreement is obtained fork _T. The transient is not very sensitive toD, and hence the determination is not accurate. Yet within the uncertainty, the deducedD also agrees with predictions. Appendices give (1) the corrections to from finite heat effects, (2) the calculation of the concentration susceptibility (X/) _T,P , and (3) the calculation procedure for ,k _T, andD using the RG approach of Dohm and Folk.     

Anomalous phonon damping in insulating cuprates

Measurements of the in-plane (_ab) and out-of-plane (_c) thermal conductivity for insulating cuprate crystals are discussed along with new measurements for YBa₂Cu₃O₆, and PrBa₂Cu₃O₆, where both _ab and _c are twice the magnitude previously reported for this material. An unusual temperature (T) dependence of _ab in cuprates with apical oxygen indicates the onset of strong phonon damping for T < 200–250K. Along with dielectric and elastic anomalies reported in this regime, the data suggest the occurrence of a structural phase transition, involving rotations of the CuO polyhedra about an in-plane axis. The role of such local distortions in the thermal transport of superconducting compounds and the superconducting-state enhancement of _ab are discussed.     

Thermal Conductivity of Sm3S4 System with Mixed Valence Sm Ions

The thermal conductivity () and electrical resistivity () of mixed-valence compound Sm₃S₄ have been measured in the temperature range 5 to 300 K. The present results and those presented previously [1] for the thermal conductivity between 80 to 850 K are interpreted in terms of the temperature-dependent fluctuating valence of Sm ions. Sm₃S₄ crystallizes in the cubic Th₃P₄ structure, and the cations with different valences occupy equivalent lattice sites. Divalent and trivalent Sm ions are randomly distributed in the ratio of 1:2 over all possible crystallographic cation positions (Sm²⁺ ₂Sm³⁺ ₂S^2– ₄). The behavior of the Sm₃S₄ lattice thermal conductivity _ph is extraordinary since valences of Sm ions are fluctuating (Sm³⁺Sm²⁺) with a temperature dependent frequency. In the interval 20 to 50 K (low hopping frequencies), _ph of Sm₃S₄ varies as _ph T ^–1 (it is similar to materials with static distribution of cations with different valences): at 95 to 300 K (average hopping frequencies 10⁷ to 10¹¹ Hz), _ph changes as _ph T ^–0.3 (it is similar to materials with defects). Defects in Sm₃S₄ appear because of local strains in the lattice by the electrons hopping from Sm²⁺ ions (with big ionic radii) to Sm³⁺ ions (with small ionic radii) and back (Sm²⁺Sm³⁺), at T>300 K (high hopping frequencies), _ph becomes similar to materials with homogenous mixed valence states [1].     

Thermal Conductivity Properties of Bi2-αTlαSr2Ca2Cu3O10+z Glass-ceramic HT c Superconductor Rods

The Glass rods with nominal composition of (Bi _2- Tl )Sr ₂ Ca ₂ Cu ₃ O _10+z , where =0.15, 0.25 and 0.35, have been prepared by melt casting technique. Preferably c-axis oriented grains were grown after the sintering process. The thermal conductivity (T) measurements were performed between 30K and 290K and calculations were made using Wiedemann-Franz law. The (T) values of the samples varied between 3.8 to 8.9 mW/cm.K and showed strong dependence to the heating temperatures and compositions. The best T _c and T _zero were obtained to be 122 K and 115 K respectively.     

Thermal Conductivity of the Four-Leg Spin-Ladder System La2Cu2O5 Single Crystal

We have investigated the magnetic susceptibility, , and the thermal conductivity, , in magnetic fields for the four-leg spin-ladder system La₂Cu₂O₅ single crystal. The in a magnetic field parallel to the ladder exhibits a kink at 130 K in correspondence to the magnetic ordering. The along the ladder exhibits a peak at 25 K and a shoulder at 14 K, which are probably related to the thermal conductivity due to magnons, _magnon, and that due to phonons, _phonon, respectively. The perpendicular to the ladder, on the other hand, exhibits only one broad peak related to _phonon. The observed large anisotropy of has been explained based upon the anisotropy of _magnon.     

Electron-phonon coupling as a mechanism for high-temperature superconductivity

We have solved the Eliashberg gap equations which are valid for arbitrary phonon frequency, (_ph), electron-phonon coupling constant, (), and screened Coulomb interaction, ( ^*). We have used values of (_ph),, and ( ^*) appropriate to the cuprate superconductors, and calculated the density of states, the pair potential., and the value of the gap at T=0 K. Using the linearized Eliashberg equations in the matrix representation, we have calculatedT _c and 2/k T _c . We have found that we can account for the highT _c 's in the cuprates with reasonable values for, ^*, and _ph.