Neutron induced disorder in superconducting A-15 compounds

The effect of high energy neutron (E>1 MeV) irradiation at 60°C on the superconducting critical temperature, Tc, the upper critical field, Hc2, the lattice parameter, ao, and the degree of Long Range Order has been measured for Nb and V based A-IS superconducting compounds. Large reductions in Tc, and Hc2are observed for fluences up to 5.0 × 10¹⁹n/cm². For Nb3Al aoincreases and the degree of Long Range Order is significantly reduced as Tcis depressed. The results are discussed in terms of atomic ordering in the A-15 structure.     

Superconductivity in new A-15 niobium alloys

A number of previously unreported A-15 Nb alloys have been studied, using samples prepared by dual target sputtering.T _c was measured resistively and structure determined by x-ray diffraction. Samples were “chemically” analyzed by anodization. New alloys include A-15 Nb₃Si and pseudobinary derivatives, as well as some derivatives of “Nb₃P.”T _c and the A-15 lattice parameter were surveyed for these, and for previously studied alloys related to Nb₃Al, Nb₃Ga, and Nb₃Ge. The “chemical” variation ofT _c was slight, except near pure Nb₃Si and for alloys based upon “Nb₃P,” where the samples show considerable disorder. Maxima inT _c occur for the alloys Nb₃Al_0.7Ge_0.3 and Nb₃Al_0.5Ga_0.5. The first is well known; trends measured here indicate that the second may be equally high. It is proposed that the dominant factor forT _c in this group of alloys is the state of order achieved in the samples. No evidence was seen to associate enhancedT _c with A-15 phase boundaries.     

Low temperature thermal expansion of A-15 vanadium-gallium alloys

The thermal expansion of A-15 VGa alloys relative to room temperature was measured from near 4.2 °K to 300 °K using a powder X-ray diffraction technique. The data were fitted to a polynomial function of temperature, from which the instantaneous coefficients of linear expansion were calculated. No unambiguous evidence for a low-temperature martensitic transformation was detected.     

The physical and structural properties of superconducting A15-type Nb-Sn alloys

Bulk samples covering the entire homogeneity range of the Nb-Sn A15-phase were prepared by a new method: levitation melting under high argon pressure. The variations of the lattice parameter, superconducting transition temperature, resistivity and critical field slope were measured as a function of composition. A low-temperature X-ray diffraction study was undertaken in order to fix the compositional limit of the tetragonal phase. The theoretical expectations for the critical field slopes at the transition temperature, T _c, based on actually-observed alloy parameters, were found to be in good agreeement with measured values.     

Defects in A-15 superconductors

Evidence is now emerging of a universal defect behaviour in A-15 compounds which has considerable importance to the superconducting as well as the normal state behaviour.The susceptibility of these materials to the defect formation may be another manifestation of their structural instability. While the nature of the defect is still unknown it apparently can greatly influence the properties of superconductor we make, and the problems for superconductor we cannot make.     

Effect of annealing on the superconducting properties of two amorphous alloys: Nb70Zr15Si15 and Zr85Si15

The changes in the superconducting and electronic properties of amorphous Nb₇₀Zr₁₅Si₁₅ and Zr₈₅Si₁₅ alloys with annealing were examined with an aim to evaluate the effect of structural relaxation on the superconductivity of metal-metalloid type amorphous alloys.T _c rises once from 3.99 to 4.42 K on annealing at temperatures below about 473 K for the Nb-Zr-Si alloy and from 2.71 to 2.75 K at temperatures below about 373 K for the Zr-Si alloy, and with further rising annealing temperature,t _d, lowers monotonically to a final relaxed value (3.15 K for Nb₇₀Zr₁₅Si₁₅ and 2.49 K for Zr₈₅Si₁₅), which is independent of the previous thermal cycling. These results indicate that the thermal relaxation of an amorphous phase occurs through at least two stages. The lowering ofT _c occurs exponentially witht _d, and an activation energy for the relaxation process and the frequency of jump over the barrier were estimated to be about 2.03 eV and 2.4×10¹⁴ sec^–1 for Nb₇₀Zr₁₅Si₁₅ and about 1.28 eV and 1.2×10¹¹ sec^–1 for Zr₈₅Si₁₅, respectively. The high frequencies indicate that the relaxations occur more or less independently of each other in a non-co-operative manner. The dressed density of electronic states at the Fermi level,N(E _f) (1+), which was calculated from the measured values of _n and (dH _c2dT)T_c, exhibited a similar annealing temperature dependence to that ofT _c. From this the change inT _c on thermal relaxation was interpreted as due to the changes in and/orN(E _f). From the depressions ofJ _c(H) and fluxoid pinning force on annealing in a temperature range of 473 to 873 K, it was concluded that the structural relaxation from a less homogeneous quenched-in state to a homogeneous stable state occurred on the scale of coherence length (7.5 nm) during the annealing.     

Effect of neutron irradiations on superconducting properties of A-15 compounds undoped and doped with 10B and 235U

The effect of lattice damage caused by room temperature irradiations with products of ¹⁰B(n, )⁷ Li reactions and ²³⁵U fissions and with fast neutrons on transition curves, quenching curves, and lattice constants of Nb₃Sn, Nb₃Al, Nb₃(Al, Ge), and V₃Si have been investigated. The critical currents in transverse magnetic fields could be increased up to more than one order of magnitude. For heavily irradiated samples drastically reduced values for the critical currents, the upper critical fields, and the transition temperatures were observed. The lattice constants were increased up to 0.5%; by irradiation.Some of the results in this paper were presented at the International Discussion Meeting on Flux Pinning in Superconductors, St. Andreasberg, West Germany, September 23–27, 1974.Part of this work was performed while the author was a Guest Scientist at the Brookhaven National Laboratory, Upton, New York, and at the Francis Bitter National Magnet Laboratory, which is supported at M.I.T. by the National Science Foundation.Work supported by the Deutsche Forschungsgemeinschaft.Work supported by the U. S. Atomic Energy Commission.     

Diffusionlike equation for superconducting binary alloys

A diffusionlike equation is derived within the coherent potential approximation (CPA) for type II (or inhomogeneous), superconducting binary alloys. Diagrammatic formulation of the CPA is employed to extend the derivations of Eilenberger and Usadel to nondilute random substitutional alloys A _1?s B _s having arbitrary concentrations and scattering strength. The generalized diffusion coefficient satisfies a simple algebraic equation, the coefficients of which are connected to measurable physical quantities. The diffusionlike equation is valid for arbitrary values of the order parameter at arbitrary temperatures belowT _c . When the order parameter Δ is small, simple expansions in terms of Δ would lead immediately to the generalized Landau-Ginzburg equations. The upper critical magnetic field and magnetization are expressed as functions of concentrations of the binary alloy.     

Low-temperature plasticity observations of superconducting Pb-Sb alloys

Plasticity of quenched and aged Pb-Sb alloys of various Sb concentrations and the _ns value of the creep strain jump at transition to the superconducting state have been studied. It is shown that the jump value for the quenched state is in inverse proportion to the hardening coefficient. In the aged alloy the _ns value decreases with the impurity concentration increasing, and at 3 at. % of Sb it becomes equal to zero. The results obtained are compared with Natsik's theory considering thermally activated unpinning of dislocations from obstacles, which is more probable in the superconducting state. The comparison demonstrates a good qualitative agreement of theory with experiment.     

Superconducting A-15 compounds: A review

The critical superconducting parameters of A-15 compounds are reviewed, and the trends analysed in order to predict maximum values. Experimental data on critical temperature is summarized and compared with theory. The ability to form the stoichiometric, well-ordered materials required for maximum T_c is discussed in terms of the thermodynamic stability of the A-15 phase. It is concluded that critical temperatures in excess of 25 K, in the A-15 structure, are unlikely.The upper critical field data show that, whereas the vanadium-based compounds are paramagnetically limited, the niobium-based compounds are not. The relation between critical current and microstructure is explored. Best data on critical current densities and ac losses is presented.Finally an account is given of the various methods by which actual conductors, both tapes and multifilamentary wires, are made.     

On a weak-coupling theory of superconducting magnetic alloys

The interaction of electrons with magnetic impurities in superconducting magnetic alloys is calculated to second order in the spin exchange coupling. Its effects on the transition temperature, the order parameter, the density of states, and the conductance are studied. The results are as follows. (1) The variation of the transition temperature with impurity concentration is the same as in the Abrikosov-Gor'kov theory; that of the order parameter is similar. (2) The density of states is finite at all nonzero impurity concentrations. Superconductivity with magnetic impurities is always gapless. (3) There are far more states about the Fermi level than in the Abrikosov-Gor'kov theory. At an impurity concentration equal to two-thirds its critical value, the density of states at the Fermi level surpasses one-half the normal value. The conductance curve loses all semblance of an energy gap.     

On properties of superconducting alloys containing Kondo impurities

The phase transition temperature T _c and the specific heat discontinuity C of a superconductor containing Kondo impurities are expressed self-consistently in terms of the t-matrix for Kondo scattering, which has been calculated within the Tomonaga approximation, thereby taking care of the infrared singularities. The approximation contains the Abrikosov-Gor'kov theory and the exact result for the classical spin as limiting cases. The initial slopes of T _c and C as a function of antiferromagnetic exchange coupling have a maximum, and the zero-temperature transition concentration has a minimum, showing that the impurity undergoes a magnetic-nonmagnetic transition when the coupling is increased. This agrees with previous results for the impurity spin susceptibility. The condition for a reentrant phase boundary is discussed in connection with its implications for the specific heat jump. The results are compared quantitatively with experimental data for LaAl₂ containing Ce and Gd impurities and qualitatively with recent data for the (La _1-x Th _x )Ce system.     

Effect of cold rolling on the superconducting and electronic properties of two amorphous alloys; Nb50Zr35Si15 and Nb70Zr15Si15

The effect of cold rolling on the superconducting properties was examined for amorphous Nb₅₀Zr₃₅Si₁₅ and Nb₇₀Zr₁₅Si₁₅ superconductors. Cold rolling to 10 to 20% reduction in thickness results in a rise of superconducting transition temperature (T _c) and a decrease in transition width (T _c), upper critical field gradient near , critical current density [J _c(H)] and normal electrical resistivity (_n). Changes of about 7% forT _c 33% for T _c, 12% for and 70% forJ _c(H) are found. The rise ofT _c upon cold rolling was considered to originate from the increase in the electron-phonon coupling constant () due to an increase in the electronic density of states at the Fermi level [N(E _f)] and a decrease in the phonon frequency (), while the decreases in T_c,J _c(H) and _n were attributed to the decrease in fluxoid pinning force due to an increase in homogeneity in the amorphous structure. From the results described above, the following two conclusions were derived: (a) cold rolling causes changes in electronic and phonon-states in the quenched amorphous phase, and (b) deformation upon cold rolling occurs not only in the coarse deformation bands observable by optical microscopy, but also on a much finer scale comparable to the coherence length (7.7 nm).     

Atomic ordering and superconductivity in A-15 compounds

Twenty-six different binary A-15 compounds were investigated to determine if superconductivity could be related to the degree of long-range atomic ordering on the crystallographic lattice sites. Significant changes in the superconducting transition temperatures and critical fields were produced by quenching from high temperatures followed by low-temperature annealing. These changes inT _cwere accompanied by changes in the degree of long-range ordering as determined using x-ray diffraction methods. The results can be interpreted within the framework of Weger's linear-chain model only when the B-element is a nontransition element. When both the A-and B-components are transition elements, however, the superconducting behavior will apparently depend on the nature of d-electron interactions between the component atoms. Complete ordering is not always an essential requirement for optimizing the superconducting properties.     

Coherent potential approximation for nonmagnetic weak-coupling superconducting alloys

With the aid of the Nambu formalism the coherent potential approximation (CPA) is applied to superconducting binary alloys of arbitrary composition. It will be shown that an approximation in which the order parameter does not depend on the space variable leads to a generalized Abrikosov relation, simplifying the CPA equations considerably. This relation yields the BCS equation forT _c , however, the density of states is determined by the CPA.     

Review on the fabrication techniques of A-15 superconductors

This Paper reviews the present state-of-the-art of preparing multifilamentary A-15 superconductors. The most common types, Nb₃Sn and V₃Ga, are presently produced by the so-called bronze process. The highest J_c (overall) = 3.5 × 10⁴ cm⁻² (at 15 T and 4.2 K), obtained for bronze processed Nb₃Sn composites through Ti addition, has pushed the useful limit of this material from 12 to 16 T. Similarly a J_c of 1 × 10⁵ A cm⁻² (at 20 T and 4.2 K) for the A-15 V₃Ga has been attained through elemental additions to the core and the bronze matrix. To circumvent the problem of work-hardening of the bronze, several variations of the bronze process such as the internal tin method, the Nb tube method, the ECN method and jelly roll method have also been upgraded to commercial scale. Composites of Nb₃Sn and V₃Ga have been recently produced successfully on a laboratory scale following the so called in situ technique. These composites not only have a superior J_c value but display improved strain tolerance due to the ultrafine nature of the filaments formed in situ. In situ filamentary A-15 composites with high J_c values have also been produced by following the powder metallurgy technique. The infiltration technique has been found useful for producing high field Nb₃(Al, Ge), Nb₃(Al, Si) and Nb₃Sn composite conductors with high ε_irr. Superior materials such as Nb₃Al, Nb₃Ga and Nb₃(Al,Ge) with high J_c performance have been synthesized using the laser beam technique. Nb₃Ge tapes with T_c = 21 K and J_c = 10⁵ A cm⁻² (at 18 T and 4.2 K) have been successfully produced on a laboratory scale by following the CVD technique. Thus, there are several available options from which to choose a technique for fabricating filamentary composites of ubiquitous Nb₃Sn and V₃Ga. New techniques for fabricating superior materials like Nb₃Al, Nb₃Ga, Nb₃Ge and Nb₃(Al, Ge) also seem to be at an advanced stage of development.     

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.     

Preparation of Cu-Nb alloys for multifilamentaryin situ superconducting wire

A study has been made of two techniques, chill casting and consumable arc melting, for preparing ingots of Cu-Nb alloy for production of multifilamentary Nb₃Sn superconducting wire. It was found that Y₂O₃, ThO₂ and graphite all make excellent crucible materials for melting Cu-Nb alloys at 1850° C. Some difficulty was found with Nb segregation in chill-cast 5 cm diameter ingots. The consumable arc casting technique was shown to produce a uniform Nb dendrite distribution with little macrosegregation in 5 cm diameter castings and is regarded as having excellent potential for scale-up production of uniform Cu-Nb ingots of 25 to 30 cm diameter.     

Critical field and specific heat of superconducting Tl-Pb-Bi alloys

The Eliashberg kernels ² ()F() obtained from tunneling experiments for a series of weak to strong coupling Tl-Pb-Bi alloys are used to calculate numerically on the imaginary axis the thermodynamic properties of these alloys in the superconducting state. The functional derivatives ofT _c andH _c with respect to changes in the kernel are also calculated.Research supported by the National Research Council of Canada.Partially supported by Conacyt, Mexico.