Two phonon pair breaking in superfluid3He-B

We report on pulsed zero sound experiments in the B-phase of ³ He down to 0.6 mK. The investigated pressure and frequency range was 5 to 16 bar and 10 to 70 MHz, respectively. The dissipated energy during the sound pulses was between 0.4 to 90 nJ. The resolution in damping was about 0.1 cm ^–1 . Within the range of our experimental parameters we never observed two phonon absorption resulting from non-linear coupling of zero sound to the J =2⁺ mode. However, with pulses of single frequency a new peak structure was found at temperatures corresponding to (T) = . This behavior is attributed to pair breaking by two phonons of the same energy. The attenuation increased with increasing pulse power, but also depended on pulse duration. In addition to that, we found at all pressures and frequencies an unreproducible attenuation structure close to the position of the J=2⁺ mode.     

Thermal expansion in the superconducting state

We present a model for the electronic contribution to the thermal expansion in the superconducting state based on the weak coupling BCS theory. A simple scaling parameter is introduced to accommodate strong coupling. We find satisfactory agreement between the model's predictions and experimental measurements for a number of materials exhibiting qualitatively different expansion behavior.Supported by the Australian Research Grants Committee.     

Hysteresis in the phase-slip state of superconducting filaments

Recently some papers on measurements of the I-V characteristics (where V is the time-averaged voltage) of superconducting indium microbridges ¹ as well as tin and zinc whiskers ^2,3 driven by a dc current into the phase-slip state have appeared. Special emphasis was placed on a discussion of the hysteresis, which is well-known in such experiments (see, e.g., Refs.1–18 in Kramer and Rangel ⁴ ). The hysteresis was compared with the predictions of the generalized time-dependent Ginzburg-Landau (GTDGL) equations for dirty superconductors in local equilibrium. ^4,5 Unfortunately these predictions represent the only results in this context derived ultimately in a rigorous fashion from the standard microscopic theory of superconductivity. Comparison was also made with a model by Kadin, Smith, and Skocpol (KSS), ^6,7 which gives a much smaller hysteresis. The authors of Ref. 1 found good agreement with the KSS model. The authors of Refs. 2 and 3 found a hysteresis which is larger than that of the KSS model, but still considerably smaller than predicted by GTDGL theory. They proposed a generalization of KSS which can be fitted to the data.     

Anisotropy-enhanced deviation functions in superconducting zinc and cadmium

The thermodynamic critical fields of zinc, cadmium, and molybdenum were measured down to 25 mK using an ac susceptibility method. Considerable downward shifts of the deviation function were found for Zn and Cd and analyzed in terms of anisotropic Eliashberg theory with large electron-phonon coupling anisotropy parameters a ². In contrast to these two elements, isotropic behavior was found in superconducting molybdenum.     

Suppression of electronic friction on Nb films in the superconducting state

Investigations on the origins of friction are still scarce and controversial. In particular, the contributions of electronic and phononic excitations are poorly known. A direct way to distinguish between them is to work across the superconducting phase transition. Here, non-contact friction on a Nb film is studied across the critical temperature TC using a highly sensitive cantilever oscillating in the pendulum geometry in ultrahigh vacuum. The friction coefficient Γ is reduced by a factor of three when the sample enters the superconducting state. The temperature decay of Γ is found to be in good agreement with the Bardeen-Cooper-Schrieffer theory, meaning that friction has an electronic nature in the metallic state, whereas phononic friction dominates in the superconducting state. This is supported by the dependence of friction on the probe-sample distance d and on the bias voltage V. Γ is found to be proportional to d-1 and V2 in the metallic state, whereas Γ～d-4 and Γ～V4 in the superconducting state. Therefore, phononic friction becomes the main dissipation channel below the critical temperature.     

The intermediate state in superconducting mercury

Using the magneto-optic technique, an extensive study has been made of the intermediate state in single crystals of superconducting mercury. A regular laminar structure, closely approaching that envisaged by Landau, was realized in the thinnest sample examined (47 Μm). The field dependence of the lamina periodicity displays excellent agreement with the Landau model and the deduced surface energy is in good agreement with the Ginzburg-Landau theory. At applied magnetic fields very close to the critical one, the stable magnetic structure consists of isolated superconducting filaments. A number of observations are reported on their growth and stability.     

De Haas-van Alphen experiments in the superconducting state

Landau quantum oscillations of the magnetization, commonly referred to as the dHvA effect, appear to be a general property of superconductors in the mixed state. This is both intriguing from a fundamental point of view, and fortunate in that it provides a microscopic probe with which to explore the many-body environment of a superconductor. The results of experiments to date can be understood rather well in terms of a general theory of the dHvA effect for an interacting system. We indicate the nature of this and comment on the implications for molecular and oxide superconductors.     

Dynamics of the intermediate state in a superconducting wire

A new approach to the dynamics of the intermediate state in a wire is presented. It represents a generalization of a recent theory for the dynamic resistance of the wire. It is shown that a large dynamic self-inductance also appears. The effects of the wire's environment on the intermediate state dynamics are discussed for the first time, and the classical skin effect is accounted for to all orders. A detailed analysis of the ac voltage response to mixed dc and weak ac current conditions is presented.Supported by CRAD Contributions 3610-609 (N.G.) and 3610-626 (P.R.).     

Thermal state of superconducting films on wide substrates

The stationary thermal state of a long superconducting film on a wide substrate is analyzed analytically. Expressions describing voltage-current characteristics and temperature-current dependence of the film are derived for the flux creep, flux flow and normal regimes. It is shown how the flux creep influences the conditions of the thermal stability. In particular, it is found that the bistability of the thermal state can appear in this regime. Under the boiling crisis, the temperature-current dependence for a film differs markedly from that for a wire and is characterized by a smooth temperature increase with the current. A “mixed” regime is analyzed where the flux flow and normal states exist simultaneously with the boundary between them parallel to the film axis.     

On the orientation of the moving flux line lattice in a superconducting film

The experimental counter-evidence is presented for Schmid and Hauger's theory which predicts the orientation of the moving flux line lattice relative to the direction of its flow. The pinning current and the current-versus-voltage characteristics of the flux flow state, together with the interference effects of the moving flux line lattice of indium films, are measured under two different experimental conditions, where either externally regulated dc voltage or current is supplied to the specimen. No difference is found between the two conditions. The theoretical arguments which predict a different orientation according to the conditions are no longer valid.     

Dissipative state of superconducting zinc whiskers

The current-induced breakdown of superconductivity in Zn and Zn-Ag alloy whiskers close to the critical temperature has been investigated. Above the critical current I _c the superconductor enters a dissipative state with characteristics showing a regular voltage step structure due to the appearance of phase-slip centers. For short samples there is an influence of the superconducting contacts. Unaffected phase-slip centers are only observed in long samples. For this case the temperature-independent quasiparticle relaxation time is found to be 3.2 × 10^–8 sec. For the zero-voltage intercept I ₀ a value of 0.56 I _c is obtained.     

Non-steady state solidification of superconducting oxides

The non-steady state solidification of RE123 (RE=Y, Nd) superconductive oxides was investigated by using an undercooling growth method. In both the Y- and Nd-systems, RE123 crystals grew steadily in the initial growth stage, but the growth rates decreased gradually in the later stage under the constant growth temperature. In the case of Nd-system, the substitution ratio of Hd/Ba in the grown Nd123 crystal was found to be gradually changed. The liquid compositions revealed that the liquid composition was close to the ternary equilibrium point after the growth rates decreased. This non-steady growth of Nd123 crystal is intrinsically caused since the composition of grown Nd123 solid solution is not on the 422-123 line and the residual liquid composition gradually shifts to the ternary equilibrium point to compensate for the mass balance during 123 growth. On the other hand, in the case of the Y-system, the evaluation of the volume fraction of Y211 particles showed that the volume fractions in the grown crystal were lower than those expected from the initial composition. On the contrary, those in liquid were higher and had similar values irrespective of the initial compositions and growth conditions. This accumulation of 211 phase particles near the 123/liquid interface would reduce the diffusion of the solute elements, which have the partition ratio of less than unity, away from the 123 interface. Therefore, such a large volume fraction would enhance the compositional shift close to the growth interface and cause locally a final transient to decrease the growth rate of the 123 crystal, if there is a compositional shift from the line connecting 123 and 211 compositions.     

Flux lattice dislocation motion in the mixed state

It is shown that flux lattice dislocations (FLDs) may be investigated by observing the alternating voltage accompanying an alternating current. This method has the advantage that the FLDs are trapped within the sample and the observed ac voltages are constant. In the dc case FLDs may give rise only to transient voltages, because the current sweeps the FLDs out of the sample. Measurement on Nb_0.5 Ta_0.5 strongly suggest that electric fields may arise in this material as a result of FLD motion. The density of FLDs appears to depend on the magnetic history of the sample. It may be increased by applying a pulse of direct current; apparently, a sufficiently large current may operate FLD sources so that the density of FLDs is increased. The FLD sources are probably not all alike, for the results suggest that a large current operates more sources than a small current. The experimental results support the hypothesis that certain peculiarities of the V/I characteristics are due to FLD multiplication.     

The lattice thermal conductivity of normal and superconducting niobium

The lattice thermal conductivity of superconducting and normal Nb as limited by the interaction of phonons with electrons has been deduced from measurements in the superconducting state. The results indicate that the mean free paths of transverse and longitudinal phonons are similar, ～4×10^?5 T ^?1 (cm K), in the normal state. Comparison is made with measurements on other metals. A compilation is included of the ratio of lattice conduction in the normal state to that in the superconducting state, based on the BCS theory of superconductivity.     

Eliashberg inversion of superconducting state thermodynamics

It is shown that the inversion of the Eliashberg equations currently used in tunneling spectroscopy may be applied to calorimetric data in the superconducting state. This method yields integrals of the spectral function of the electron-phonon interaction ² F(). Experimental results in pure Nb are presented.     

The mixed state of superconducting networks

The equilibrium phase of a superconducting network has been investigated below the superconducting critical temperature in the framework of the Ginzburg-Landau theory. It is found that the properties of the mixed state are entirely governed by the flux quantization effect in the loops of the array. Quantitative predictions are made for the spatial configuration of the order parameter, the supercurrents pattern, and the equilibrium magnetization in an extended square network.     

Superconducting fluctuations,pair breaking,and nuclear relaxation in small particles

A theoretical treatment of the combined effects of superconducting fluctuations and pair breaking on nuclear spin-lattice relaxation in small particles is described, in which the interaction of normal-state electrons with both fluctuations and impurities (i.e., renormalization of fermion propagators and impurity vertex corrections) is taken into account. The calculation is valid in the dirty limit and near the superconducting transition temperature, and exhibits qualitative agreement with presently available experimental results.Work supported in part by the U. S. Air Force Office of Scientific Research, Grant No. AFOSR 71-2077, and by the National Science Foundation.     

Cooper pair breaking and isotope effect coefficient variation in high-T c superconductors

The effect of pair breaking on the isotope effect coefficientα=?d lnT _c/d lnM in La_2?x Sr _x CuO₄ and Pr-, Ca-, and Zn-doped YBa₂Cu₃O_7?x and EuBa₂Cu₃O_7?x is studied using the generalized Abrikosov-Gorkov theory recently employed by Singh and Kishore for superconductivity. It is argued that the isotope effect coefficientα can be further enhanced, in agreement with experimental observations, by considering the dependence of the characteristic scattering timeτ _s for Cooper pairs on the concentrationn of impurities (both magnetic and nonmagnetic) and the disorder ignored by them (J. Supercond. 8, 9 (1995).     

Kinetic and isotherm studies of cadmium adsorption on manganese nodule residue

The adsorption equilibrium and kinetics studies of cadmium (Cd) ions from aqueous solutions on manganese nodule residue were carried out by considering the influence of various parameters, such as contact time, solution pH and initial metal concentration in solution, temperature and adsorbent quantity. The adsorption of Cd increased with an increase in the concentrations of this metal in solution. Presence of manganese and iron content in manganese nodule residue (MNR) played a significant role in Cd(II) ions removal. The linear forms of the Langmuir and Freundlich equations were utilized for experiments with metal concentrations of 200 mg/L for Cd(II) as functions of solution pH (2.0-6.0). First-order rate equation and pseudo second-order rate equations were applied to study adsorption kinetics. Mass transfer study was also done to know the reaction rate. Thermodynamic parameters, such as standard Gibb's free energy (deltaG(o)), standard enthalpy (deltaH(o)) and standard entropy (deltaS(o)), were also evaluated by Van't Hoff equation. Thus, adsorption of Cd on this adsorbent was found to be spontaneous and exothermic thermodynamically. The adsorption capacity for Cd was found to be 19.8 mg/g of MNR. Under the optimised conditions, cadmium level was brought down from 100 mg/L to Cd less than detection limits and from 200 to 2 mg/L. Thus, the wastewater after cadmium removal could be safely disposed off on to land or sewage. Finally, the metal loaded adsorbent was subjected to desorption using different mineral acids and leaching by using toxicity characteristic leaching procedure (TCLP), synthetic precipitation leaching procedure (SPLP) tests for its further treatment or its safe disposal.