Effect of strain content on the ultrasonic attenuation in the intermediate state of type I superconductors

The attenuation of longitudinal ultrasonic waves has been measured in single-crystal indium doped with 0.002 at % of bismuth in various physical states of the specimen in the intermediate state over the frequency range 23–30 MHz. Two phases have been identified in the superconducting layers. The fundamental frequency v₀ for one phase is approximately constant for various physical states of the specimen for the same field, but increases with increase in magnetic field from 0.7H _cto 0.9H _c; the fundamental frequency v₀ for the other phase decreases with decrease in dislocation density. The origin of the first phase is due to the laminar structure of the intermediate state. The second phase is due to the formation of microstructure in the superconducting layers due to the impurity and strain content in the specimen. The thickness of the microstructure has been calculated utilizing Granato and Lucke's vibrating string model of dislocation for various physical states of the specimen.     

Ultrasonic attenuation in the intermediate state of tin

Attenuation of ultrasound has been measured in the intermediate state of single crystals of tin at 3.3 MHz in the temperature range 1.5–3.7 K. A small measurable change of the frequency v_O of the collective modes of excitations has been observed very near the critical magnetic field.     

Dynamic resistance of the current-induced intermediate state in superconductors

We have measured the in-phase component of the low-frequency ac impedance of the dc current-induced intermediate state in wires of pure and impure type I superconductors. We find that this dynamic resistance of the intermediate state is greater than the normal state resistance of the wire. The linear response theory for the dynamic resistance developed by Gauthier and Rochon provides a reasonable qualitative understanding of our experimental results.This work has been supported by the Chief of Research and Development, Department of National Defence, Canada through his contribution No. 3610-320.     

Current hysteresis in the intermediate state of thin-film superconductors

We have studied the current hysteresis at 4.2 K in the intermediate state of superconducting lead films using electrical resistance measurements and high-resolution magnetooptical observations of the magnetic flux structure. At low magnetic fields the liquidlike arrangement of the flux structure in the form of multiquanta flux tubes was found to persist following the application of a high electrical transport current with an average current density of 10⁵–10⁶ A/cm². In this field range areduction of the resistive voltage was observed following the application of a high transport current. This inverse current hysteresis appears to be associated with a shift of the magnetic flux structure in the direction of the current-induced flux motion resulting in an extended fluxfree region along the sample edge where flux tubes enter the film during flux motion. At higher magnetic fields, where the laminar flux structure is the stable configuration, the usual resistive voltage enhancement has been observed following the application of a high transport current. In this regime the laminae rearrange themselves under the influence of a transport current resulting in a preferential orientation perpendicular to the current.Based on work performed under the auspices of the U.S. Atomic Energy Commission.     

The vortex morphology model of ultrasonic attenuation in the mixed state of high-Tc superconductors

This paper presents the vortex morphology model concerning the ultrasonic attenuation in the mixed state of high-T_c superconductor. This model pointed out that under different magnetic field and temperature, different vortex morphology appeared in the high-T_c superconductors. There are three factors that can determine ultrasonic attenuation, which are temperature, magnetic field and anisotropy of superconductors’ structures.     

Longitudinal ultrasonic attenuation coefficient for high-T K Kondo superconductors

The ultrasonic attenuation coefficients for longitudinal waves in bulk superconductors containing high-T _K Kondo impurities and in proximity effect sandwiches containing the Kondo impurities in the normal layer are obtained using the Matsuura, Ichinose, and Nagaoka approach to treat the scattering by the Kondo impurities. The attenuation coefficients are obtained for temperatures close toT _c by suitably renormalizing the propagators and vertices appearing in the leading graphs in the expansion of the density-density correlation function appearing in the definition of the longitudinal attenuation coefficient for the case ql1. Closed-form expressions for the attenuation coefficient for the bulk superconductor case are obtained.     

Landau intermediate state structure in type I superconductors

Landau laminar structures are discussed for cases where the normal-superconducting (N-S) boundary is curved and where it is straight throughout a sample. A numerical calculation shows that the free energy for a curved N-S boundary is less than that for a straight one, except for values ofd/ less than about 8 and a small region of magnetic fields close toh . Here is the surface energy parameter andh is the perpendicular critical field corresponding to a sample thicknessd. The expression forh for the straight N-S boundary is different from that obtained by Simonin and López. It is shown that the data ofh reported to date are insufficient to verify the formation of laminar structures with a straight N-S boundary.This work was supported by the Fonds National Suisse de la Recherche Scientifique.On leave from the Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan.     

The resistivity of the intermediate state of type-I superconductors

The interaction between transport current and flux spots in the intermediate state of a superconductor is investigated. It is shown that the force on the flux spots depends on factors such as current lead configuration, and it is therefore not possible to define a unique flow resistivity for type-I superconductors. The conclusions are supported by experimental evidence.     

On the london model of the intermediate state in current-carrying superconductors

The London picture for the destruction of superconductivity by a current is considered. Equipotential S regions are taken as being placed periodically along the wire, and the magnetic field at the phase boundary is taken to have the critical value. From a solution of the Laplace equation for the electric potential near the contact point of two S regions a relationship between the angular aperture of the conical S region and the period of the structure is found. A numerical solution is given for the phase boundary and for the resistance at large currents. The volume of the S phase is found to be much smaller than that in the original London model. As a consequence the resistance of the wire after destruction of the uniform S state differs from that for the uniform N state by only a few percent.     

High resolution magneto-optical studies of the intermediate state in thin film superconductors

The structure of the intermediate state in superconducting lead films has been investigated as a function of magnetic field and film thickness. The detection system utilized the high specific Faraday rotation in thin films of a mixture of EuS and EuF₂ in combination with a polarizing microscope, yielding a resolution of about 1 μm. The thickness of the Pb films ranged between 0.7 and 9 μm, thus including the critical film thickness at which the transition from the intermediate state to the vortex state occurs. At low fields a liquid-like mixed state of multi-quanta flux tubes was observed which appeared to be stable up to increasing magnetic fields with decreasing film thickness. The diameter of these flux tubes varied approximately with the square root of the film thickness. At intermediate fields the intermediate state pattern was found to persist down to a film thickness of 0.7 μm, the smallest thickness investigated. The periodicity length of the intermediate state structure was in reasonable agreement with the non-branching model of Landau. Just below H_c, small superconducting domains were observed in increasing field, whereas long threads of superconducting material were formed abruptly in decreasing field. These superconducting threads were absent in the specimentsthinner than 1–2μ, being replaced by a liquid-like mixed state of superconducting tubes. After the passage of a sufficiently high electrical current through the specimen, the flux structure was found to be rearranged into long domains oriented predominantly perpendicular to the current, leading to current hysteresis effects. Finally, some dynamic observations were made during current induced flux flow.     

Ultrasonic attenuation in the superconducting and intermediate states of pure and doped type I superconductors

The attenuation of longitudinal ultrasonic waves has been measured in single crystals of indium (99.999%), indium doped with 0.003 at % of tin, and indium doped with 0.002 at % of bismuth in the intermediate and superconducting states over the frequency range 10–30 MHz. For the bismuth-doped indium specimen, measurements were taken for three different physical states, i.e., for three different dislocation densities, and for the indium and the tin-doped indium specimens, measurements were for one physical state. For a particular measurement, the same physical state was maintained both in the intermediate and superconducting states. A temperature-dependent oscillatory behavior of the ultrasonic attenuation was observed in the intermediate state in all the three specimens, but in the superconducting state the oscillatory behavior was observed only in the bismuth-doped specimen. Two phases have been identified in the superconducting layers of the intermediate state and there is only one phase in the superconducting state of the bismuth-doped sample. The origin of the two phases in the intermediate state and that of the single phase in the superconducting state of the bismuth-doped sample are discussed. A qualitative explanation is presented for the occurrence of oscillatory attenuation in the intermediate state irrespective of the nature of the dopant and the selective occurrence of oscillatory attenuation in the superconducting state due to the nature of the dopant.     

Effect of electrical resistivity on ultrasonic attenuation in NpTe

Ultrasonic attenuation due to electron-phonon interaction (EPI) has been computed in semimetallic single crystal neptunium telluride (NpTe) in low temperatures 5-80 K. For the same evaluation, we have also evaluated ultrasonic velocity, electronic viscosity and second order elastic constants (SOEC). The SOEC of NpTe have been evaluated using the Born model of ionic solid. The behaviour of ultrasonic attenuation is quite similar to its inverse resistivity. The ultrasonic attenuation due to EPI is most significant at 40 K. Computed results of ultrasonic parameter have been compared and discussed.     

Effect of microstructure of low carbon steels on ultrasonic attenuation

The ultrasonic attenuation in low carbon steel with 0.04 wt% C to 0.80 wt% C was measured over a frequency range of 5 to 15 MHz, and the effects of the carbon content and normalizing temperature were analyzed. In pure iron, the attenuation is determined from the average grain size, which increases as the normalizing temperature increases; there is a noticeable effect caused by a few large grains. In the case of the hypoeutectoid steels, the proeutectoid ferrite grain, the size of which depends on prior austenite grain size, acts as the main scatterer. The prior austenite grain size increases as the carbon content decreases and the normalizing temperature increases. The colony is responsible for scattering in the eutectoid steel; scattering by pearlite is greater than that by ferrite.     

Effect of microstructure on attenuation mechanism of ultrasonic waves in carbon steels

Abstract

In this paper, fundamental concepts of ultrasonics and characteristics of distinctive microstructures have been used to simply explain the effect of microstructure on the attenuation mechanism of ultrasonic waves in carbon steels. In addition, it has been shown that application of the second medium hardness instead of the bulk hardness is more appropriate to correlate the sound velocity and the microstructure.     

Heat conduction in the intermediate state of superconductors: Observation of a new size effect in lead

Experimental evidence is presented for the existence of a size effect predicted by Andreev as a consequence of his quasiparticle reflection law at the superconducting-normal interphase boundaries. In high-purity lead we observe a reduction of the thermal conductivity in the intermediate state when the heat current is parallel to the laminar structure. This work was supported by the Fonds National Suisse de la Recherche Scientifique.     

Effect of matrix structure on ultrasonic attenuation of ductile cast iron

The ultrasonic attenuation of ductile cast irons with different matrices was investigated by means of ultrasonic echo waves. In the ductile cast irons with ferritic and pearlitic matrix structures, both of the ultrasonic attenuation increased with frequency. For similar frequencies, the ultrasonic attenuation of the pearlitic matrix was larger than that of the ferritic matrix. Based on the theory of ultrasonic attenuation in the solid, the mechanisms of ultrasonic attenuation in the ductile cast irons with different matrices were analyzed. It indicated that in the ductile cast irons with transformation of matrix from the ferrite to the pearlite, the mechanism of ultrasonic attenuation varied in the range of present frequencies. In the ferritic matrix, the total ultrasonic attenuation was mainly attributed to the scattering loss which included the stochastic scattering and the Rayleigh scattering. On the contrary, the absorption loss predominated in the total ultrasonic attenuation of the ductile cast iron with pearlitic matrix.     

Electromagnetic attenuation of shear waves in superconductors

A detailed analysis of the electromagnetic attenuation in superconductors has been carried out, with specific reference to type I materials. The rapid rise atT _c predicted by Cullen and Ferrell is found to be most pronounced in superconductors with low acoustic velocities. Also, the effect occurs at lowest frequencies in these materials. It is demonstrated how the shape of the transition curve reflects anisotropies in electronic and elastic properties. Very close toT _c the attenuation at low frequencies is inversely proportional to the real conductivity function, while at high frequencies it is proportional to that conductivity. Numerical results for Al, In, Pb, and Sn are presented. Although these materials are similar with regard to electronic structure, they are characteristically different with regard to electrodynamic properties as probed by ultrasonic phonons. From the present analysis it is concluded that ultrasonic probing of the electrodynamics of superconductors offers a sensitive and, at the present, unique way of determining the response of a superconductor to a single variable wave number. In addition the wave numbers available in this way are in a range where it has been most difficult to obtain such information by penetration depth studies, namely, in the transition region between pure local and nonlocal behavior.