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 .     

Singularity parametersε andκ for interface cracks in transversely isotropic piezoelectric bimaterials

Two parameters, and (Suo et al., 1992), are of key importance in fracture mechanics of piezoelectric material interfaces. In this paper, it is shown, for any transversely isotropic piezoelectric (TIP) bimaterial, that one of the two parameters and always vanishes but the other one remains non-zero. Physically, it means that the non-oscillating crack-tip generalized stress field singularity exists for some TIP bimaterials (with vanishing ). Consequently, TIP bimaterials can be classified into two classes: one with vanishing performed crack tip generalized stress field oscillating singularity and the other one with vanishing is independent from the oscillating singularity. Some numerical results for and are given too.     

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.     

Flux-line cutting in type II superconductors

Experimental evidence for flux-line cutting in superconductors (intersection and cross-joining of singly quantized vortices) is briefly reviewed. The interaction energy between two straight vortices tilted at an angle ( 0)is then shown to be finite in the London model, i.e., in the limit of vanishing core radius. Next, the activation energy and maximum interaction force are calculated for the vortices in an analytic approximation to the Ginzburg-Landau theory. Here two competing interactions determine the behavior. Electromagnetic repulsion (0 < < /2) varies as cos and decays over distances scaled by the penetration depth , while core attraction is independent of and varies over distances scaled by the coherence length . The force is always repulsive at large flux-line separation (0 < < /2) and its maximum decreases rapidly as decreases, so that flux-line cutting isexpected to be more probable in low- materials. The calculations provide a basis for explaining longitudinal flux-flow resistance as well as some intriguing magnetization behavior in the same configuration.This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences Division, and by the Deutsche Forschungsgemeinschaft.On leave from Max-Planck-Institut für Metallforschung, Institut für Physik, Stuttgart, West Germany.On leave from New University of Ulster, Coleraine, Northern Ireland.     

Thermal conductivity and phonon scattering mechanisms in La#x2212;x#x2212;x#x2212;xMxCuO4

The thermal conductivity of high density La_2–xM_xCuO₄ (M=Ba, Sr) sintered materials was measured between 15K and 150K for the various concentrations of Ba and the phonon thermal conductivity was analyzed comparing with that of Nd_2–xCe_xCuO₄. The pretty large value for pure La₂CuO₄ was drastically diminished by substituting La by a small amount of Ba atoms especially at low temperatures. It was found that a new type of the phonon scattering center such as a two-level tunneling must be taken account of in order to explain the observed reduction.     

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.     

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 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.     

Transport results from untwinned YBCO: Washboard frequency of the vortex lattice,and the quasiparticle mean free path

The washboard frequency of the moving vortex lattice in untwinned YBa₂ Cu₃ O_6.93 may be observed through mode-locking to an externally applied ac current of frequency _ext. The interference between and _ext results in jumps in the dc current-voltage characteristics when and _ext are harmonically related¹. The interference effect disappears in the vortex liquid state. The Hall conductivity _xy below T_c in YBCO contains contributions² from a positive quasiparticle (qp) term (H) and a negative vortex term (1/H). The qp term is surprisingly large well below T_c and implies a large gap anisotropy and a long qp mean free path (mfp). The thermal Hall effect³ _xy is closely related to the qp _xy; _xy is produced by asymmetric scattering of qp by pinned vortices. The qp mfp at H = 0, extracted from _xy and extended to low T by _xy, increases remarkably from 90 Å at T_c to more than 0.5m at 22 K.     

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 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 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.     

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.     

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     

Size-dependent Kohler slope in the transverse magnetoresistance of potassium

The Kohler slope of the linear magnetoresistance of potassium films measured in the Sondheimer geometry at 4.2 K depends on , the ratio of the film thickness to electron mean free path. The maximum value with a value of 0.1 occurs at =1. Calculations show that the slope decreases slowly from the maximum for smaller and larger values of . The slope is greater than 10^–3 for between 0.035 and 100. The dependence of the Kohler slope on the residual resistance ratio of annealed samples measured by Taub et al. is attributed to the dependence. The results show that samples of centimeter thickness are required to reduce significantly the size-dependent Kohler slope, and the slope must be shown to be independent of the sample thickness for the study of intrinsic effects.     

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.     

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.     

Nuclear spin-lattice relaxation in metals at low temperatures

In NMR experiments performed on metals at low temperatures, the analysis to obtain the nuclear spin-lattice relaxation time ₁ can be quite complicated. The electronic heat capacity ultimately becomes less than that of the nuclear spins, and the characteristic times for heat flow through the various resistances between the nuclear spins and the thermal bath can become long relative to ₁. This makes it necessary to solve the full set of coupled differential equations describing the thermal relaxation. This problem has been examined because ₁ is used as a thermometric parameter, and we consider the cases when the radiofrequency field penetrates the sample completely (powders and foils) and when only the skin-depth nuclei are excited (bulk specimens). Using our theoretical model, we analyze experimental results for platinum powder and a thallium bulk sample and obtain consistent values for =₁ T over a wide range of experimental conditions, even when thermal bottlenecks occur and the apparent relaxation time is much longer than ₁. These values are (Pt)=(34.2±0.6)×10^–3 sec K and (Tl)=(4.37±0.08)×10^–3 sec K.On leave from Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada.     

Eutectic solidification characteristics of Bridgman grown AI-3Fe-0.1V alloy

Eutectic solidification characteristics of Al-2.85 wt%Fe-0.12 wt% Valloy have been investigated by steady-state growth over the range of solidification front velocity from 51 to 1030m/s and temperature gradient 8 to 15 K/mm. Increasing growth velocity displaced the Al-Al3Fe eutectic by Al-AlxFe eutectic rather than by the Al-Al6Fe eutectic obtained for the binary Al-3 wt%Fe alloy. A fully Al-AlxFe eutectic structure has been obtained for the first time in the vanadium-containing alloy over the growth velocity range from 71 to1030m/s except at 100 and 510m/s where some Al dendrites were present in the eutectic matrix. TheAl-AlxFe eutectic was observed to undergo a morphological transition from lamellar to rod-like with increasing growth velocity concurrently with formation of a cellular eutectic structure. It was found that the relationship = Av–1/2, between eutectic spacing and growth velocity v, was applicable with A = 22.4 ± 1.8 and 13.8 ± 2.1 m3/2s–1/2 for lamellar and rod-like Al-AlxFe eutectics, respectively.     

Ultrasonic propagation in solid H2: The effects of orientational ordering

A report is given of the observation below 1 K of the sound attenuation expected from progressive orientational ordering in hcp H₂ with ortho concentrationsX<0.53. The experiments were carried out at 10 and 30 MHz. The amplitude of this effect depends on the coupling between the lattice vibrations and the molecular orientation, and should be maximum when the acoustic angular frequency is comparable with the orientational relaxation rate ^–1. The average rate can be roughly estimated from NMR longitudinal relaxation timeT ₁ measurements. Such a maximum for was indeed observed in the expected temperature range. At high enough temperatures, was found to be proportional toT ₁ ^–1 . which is consistent with predictions in the high temperature limit. Furthermore, the transition between the hcp and the fcc phases forX>0.53 is studied by means of the large changes in the sound propagation at the transition, and the phase diagram thus obtained is compared with results from x-ray and pressure measurements. The new observations explain some previous discrepancies in results using different methods. The difference between solid H₂ and D₂ regarding the stabilization of the cubic structure above the orientational ordering transition is also discussed. Calculations of the respective energy barriers E to be overcome during the martensitic transition are suggested.