Thermal conductivity of superconducting UPt3

The thermal conductivity of the heavy-fermion superconductor UPt₃ has been measured on two single crystals of different quality as a function of temperature and applied magnetic field for different orientations of the heat current relative to both the field and the crystalline axes. The temperature dependence of is far from exponential and nearly the same for both crystals, in which the heat current is, respectively, parallel and perpendicular to the hexagonalc axis, suggesting a gap structure with nodes in the basal plane and normal to it. The field dependence of is strongly anisotropic. In the best sample at low fields, where the scattering of heat carriers by vortices is thought to be important, (H) depends on the relative orientation of field and current. On the other hand, at high fields nearH _c2 (in both samples), (H) depends on the relative orientation of field and crystalline axes, reflecting an anisotropy in the gap structure and in the Fermi velocities.     

Resistive behavior of the superconducting surface sheath of alloys

Measurements are reported of the surface resistance of dirty type-II superconductors driven into the surface-sheath regime by a static magnetic field,H ₀ parallel or nearly parallel to the sample surfaces and transverse to the microwave current, in which condition the latter can excite fluctuations of the order parameter. A recent calculation by Maki has suggested that the surface resistance would be influenced by the presence of Kulik's vortex state even when the sample surface is polished and is as nearly as possible parallel toH ₀. It is therefore proposed that the sample surface should be decomposed into elements which make different angles withH ₀, and the distribution of these angles described by a Gaussian. ₂ (t) is deduced from the surface-resistance measurements nearH _c3, so interpreted, and a temperature variation, ₂ (t)/₂(1), is found which agrees reasonably with theory and with magnetization data, [₂(1)=lim_{t 1} (₂)]. It is suggested that the anomalously large variation of ₂ (t) reported by Fischer and Maki may have resulted from failure to take Kulik's vortices into account. In magnitude, present ₂(1) data agree with theory but not with magnetization data.     

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 .     

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 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.     

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.     

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.     

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.     

Spin Gap and Hole Pairing of Sr14−x A x Cu24O41(A = Ca and La) Single Crystals Studied by the Electrical Resistivity and Thermal Conductivity

We have measured the electrical resistivity and the thermal conductivity of Sr _14–x A _x Cu ₂₄ O ₄₁(A = Ca and La) single crystals. The Arrhenius plot of ln vs T ^–1 gives two kinds of activation energy with a boundary temperature T . The activation energy at T < T is in approximate agreement with the spin gap in the ladder estimated from the NMR measurements, suggesting that holes in the ladder are paired and localized at T < T. The observed has been analyzed to be composed of _ph , _spin and _hole due to phonons, spins and holes, respectively. The _ph exhibits a small peak at 30 K in every direction of every single-crystal. The contribution of _spin is observed along the c-axis except for x(Ca) 6, and the spin gap, which corresponds to the spin excitation from spin-singlet to spin-triplet, has been estimated to be 420 K. For x(Ca) 6, the spin gap, which corresponds to the destruction of spin-singlet pairs i. e. the dissociation of hole pairs, has been estimated from along the c-axis at T > T to decrease with increasing x(Ca).     

Enhanced Phonon Scattering Below T c Caused by Zn and Ni Substitution in La1.85Sr0.15CuO4

The thermal conductivity has been measured for La _2-X Sr _X CuO ₄ and La _1.85 Sr _0.15 Cu _0.98 M _0.02 O ₄ (M; Zn, Ni). The characteristic enhancement in below T _c was confirmed for La _1.85 Sr _0.15 CuO ₄ . The phonon scattering mechanisms were analyzed in detail and the electron-phonon coupling constant was estimated to be 0.05. The enhancement becomes indetectable on Zn or Ni substitution for Cu, which indicated survival of the phonon scattering by charge carriers down to lower temperatures as a result of reduced T _c .     

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

Measurements of the average thermal conductivity _exp hQ/T and of the thermal relaxation time to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of³He in⁴He. Hereh is the cell height,Q is the heat flux, andT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10^–9<X(³He)<3×10^–2 and with heat fluxes 0.3<Q<160 µW/cm². Assuming the boundary resistanceR _b , measured forX<10^–5, to be independent ofX over the whole range ofX, a calculation is given for _exp. ForQ smaller than a well-defined critical heat fluxQ _c (X) X ^0.9, _exp is independent of Q and can be identified with the local conductivity _eff, which is found to be independent of the reduced temperature = (T–T)/T for –10^–2. Its extrapolated value at T is found to depart forX10^–3 from the prediction X ^–1 , tending instead to a weaker divergence X ^–a witha0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q _c (X), a nonlinear regime is entered. ForX10^–6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX2×10^–7. The results for _exp(Q),Q _c (X), and _eff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times (X) in the linear regime are found to be consistent forX>10^–5 with the hydrodynamic calculations using the measured _eff(X). ForX<10^–5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.     

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.     

Hydrodynamic heat flow in very dilute superfluid3He-4He mixtures

The superfluid hydrodynamics of heat flow is examined for very small mass concentrationsc of³He in⁴He in an effort to better understand recent results for the effective heat conductivity _eff, which appear to be in conflict with predictions. The full hydrodynamics contains a thermal boundary layer; within this layer the temperature and concentration gradients differ from those in the bulk fluid. An examination of finite heating effects based on the ansatz _eff c ^–p for smallc shows distinctly different behavior for experimental determinations of _eff whenp<1,p=1, andp>1. Thus, finite heating can be used as a probe to evaluate the exponentp.     

Modified mixed oxide perovskites 0.7Sr(Al1/2B1/2) O3·0.3LaAlO3 and 0.7Sr(Al1/2B1/2) O3·0.3NdGaO3 (B=Ta5+ or Nb5+) for high-T c superconductor substrate applications

Single-crystal fibres of modified strontium aluminium tantalum oxide (1-x)Sr(Al_1/2Ta_1/2) O₃·xLaAlO₃(SAT-LA) and (1-x)Sr(Al_1/2Ta_1/2)O₃·xNdGaO₃ (SAT·NG), and modified strontium aluminum niobium oxide (1-x)Sr(Al_1/2Nb_1/2)O₃·xNdGaO₃(SAT·NG) and (1-x)Sr (Al_1/2Nb_1/2)O₃·xLaAlO₃ (SAN·LA) were grown using a laser-heated pedestal growth technique. 0.7SAT·0.3LA grows congruently and retains a twin free simple cubic perovskite structure (as the SAT) when cooled down to room temperature. 0.7SAT·0.3LA crystals have a moderate dielectric constant ( = 21.7) and low dielectric loss (tan = 7.5 × 10^–5) at 10 kHz and 90 K. The reduction problem of Ta⁵⁺ is eliminated (which is common in the case of SAT growth). 0.7SAT·0.3NG and 0.7SAN·0.3NG have lower melting temperatures and crystal growth is easier. NdGaO₃ addition to the SAT and SAN enhances the potential of SAT and SAN as large-area substrates for high-T _c superconductor growth. However, the dielectric constants increased from -12 to -16(0.7SAT·0.3NG) and from 18 to 23 (0.7SAN·0.3NG) as a result of NdGaO₃ incorporation.     

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].     

Specific heat of type-II superconductors in magnetic fields nearT c

The GLAG theory predicts that the value of the specific heatC _M in the mixed state just below the transition to the normal state, is a function of the Ginzburg—Landau (GL) parameter , even for vanishingly small magnetic fields(TT _c ).C _M is thus different from the specific heatC _S in the pure superconducting state(H=0) for all except 1.9. Experimental results of the authors generally confirm this paradoxical prediction which is not in contradiction with the thermodynamics of phase transitions. To experimentally clarify this behavior close toT _c , Nb₈₀Mo₂₀(4) and Pb₉₈In₂(0.8) specimens are studied in fields much smaller than those usually applied (down to17 Oe). A new method for measuring specific heat in decreasing as well as increasing temperature is introduced. Very good agreement with the theory is found for fields higher than 120 Oe while a deviation is observed close toT _c for lower fields where values of the Abrikosov lattice parameter would become larger than 1 µ. The sense and the magnitude of the deviation are such thatC _M andC _S would be equal for fields of 20 Oe and below. Possible explanations are discussed. It is suggested that a fundamental modification of the vortex state structure occurs in small fields close toT _c .     

Anisotropy of in-plane thermal conductivity in YBa2Cu3Oδδδ

The thermal conductivity of two untwinned single crystals of YBa₂Cu₃O_7-.     

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     

Microscopic calculation of the heat transfer between a granular structure and liquid3He

A recent formula for the heat transfer coefficient between ³He quasiparticles and phonons of a sintered metallic powder is evaluated using the phonon density of states of a microscopic model of a granular structure. The microscopic model describes a simple crystalline granular structure and contains extended modes only. When the dominant phonon wavelength is less than a typical grain size, possesses a low-temperature enhancement typical of a sintered metallic powder and over a limited range exhibits a linear variation with temperature.     

Thermal conductivity in theab-plane of a large single crystal YBa2Cu3O7−x with several oxygen contents

The ab-plane thermal conductivity _ab of a large single crystal of YBa₂Cu₃O_7-x has been studied as a function of annealing time in the temperature range from 10 up to 150 K. An observed anomaly in _ab below T_c is enhanced for short time annealing in an oxygen flow but the superconducting enhancement of _ab is rather suppressed for long-time annealing. The superconducting enhancement in _ab is suppressed in the over-doped regime in comparison with that on the optimized boundary. It is considered that this suppression in _ab originates in the screening effect on the electron-electron interaction due to charge carrier doping.