A15 Superconductors Research Articles

A universal lattice parameter-superconducting transition temperature correlation in A15 superconductors?

A relationship between the superconducting transition temperature T c and the lattice constant “ a”, for irradiated A15 compounds is derived on the basis of the nature of the defects observed previously in these materials using Electron Microscopy. The universality of this relationship for any kind of damage as proposed by Noolandi and Testardi is discussed.

Effect of strain on the critical current and critical field of B1 structure NbN superconductors

The effect of uniaxial strain on the critical current of NbN superconductors has been measured at 4.2 K in magnetic fields from 6 to 22 T. Unlike A15 superconductors, the critical current of B1 structure NbN shows no measurable dependence on elastic strain, even at fields as high as 22 T. Furthermore, the bulk upper critical field determined from the high-field critical current data is independent of uniaxial strain within experimental error (±0.5%). The irreversible strain limit εirrev where the superconductor is permanently damaged was measured to be greater than 0.7% (0.5% intrinsic strain) in 0.2-μm-thick film samples. Values of εirrev were observed to correlate with the microstructure of the NbN films as well as with the onset of substrate yielding.

Effect of impurities on the thermodynamics of A15 superconductors

The authors have derived a model theory for the superconductivity of A15 compounds, with normal and paramagnetic impurities, which is based on a generalised version of the Eliashberg equation that includes the possibility of energy dependence in the electron density of states. This variation is simulated by a Lorentzian distribution symmetric about the chemical potential and superimposed on a constant background density. To be specific, parameters similar to those characteristic of Nb3Sn are used but with a high and narrow peak in the density of states.

On the analysis of tunneling data for A15 superconductors

We examine the applicability of the standard McMillan inversion of Eliashberg's equations for superconductors with a nonconstant electronic density of statesN(e). We do this usign simple models forN(e) and a realistically shapedN(e) taken from recent band structure work for Nb3Sn. It turns out that peak structure inN(e) near eF may lead to gross errors in the derived Eliashberg function α2F(θ) when the energy dependence ofN(e) is omitted in the inversion procedure. For Nb3Sn, this leads to a 40% overestimate of λ when α2F(θ) is evaluated via the standard McMillan program.

Atomic disorder and superconductivity in A15 materials

The validity of a modified linear chain model for describing the properties of A15 superconductors is discussed in detail. Using this simple model for the electronic density of states, we calculate the critical temperature and the Fermi level as functions of atomic disorder with concentrationc within the framework of the BCS theory. Thereby the experimentally observed saturation effect of the critical temperature is reproduced by taking into account the contribution of three-dimensional electronic states. The microscopic versions of the Ginzburg-Landau equations for systems with a strongly varying electronic density of states and a strongly varying electron velocity are derived for clean and dirty superconductors in order to calculate the Ginzburg-Landau parameter, the coherence length, the penetration depth, and the upper critical field as functions of atomic disorder. It is shown that these quantities depend strongly on the values inserted for the mean free electron pathl(c). Good agreement between theoretical and experimental results is obtained by an appropriate choice ofl(c). In contrast, the thermodynamic critical field is nearly independent ofl(c). In all cases we derive a depression of the pinning forces and the critical current densities with increasing atomic disorder in good agreement with the experiments.

Radiation effects on superconductivity in A15 materials

At present the A15 superconductor Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn is one of the most attractive materials for the design of magnet systems for fusion reactors. There the materials are exposed to a high flux of neutrons up to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> -10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sup> n/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> during a continuous fusion reactor operation within ten years. As a result the critical parameters of the superconducting materials are changed rather drastically, which must be taken into account when designing reliable magnet systems. The neutron radiation damage in A15 materials thereby is characterized by small highly disordered regions within a less disordered matrix. The highly disordered regions are responsible for the increase of the critical current density after low-dose neutron irradiation of non-optimized materials and have an influence on the superconducting transition width. In contrast, the change of the superconducting parameters after high-dose irradiation may be understood essentially by considering the properties of the matrix alone.

Critical temperature and critical current of V 3Si with voids induced by fast neutron fluence of 10 21 cm -2

Investigating the correlation between the critical current density and the defect structure of A15 superconductors V 3Si crystals were irradiated with fast neutrons in order to produce voids. Due to a high irradiation temperature the decrease of the critical temperature is completely prevented by self-annealing. Pinning by the void structure does not obey a temperature scaling relation.

Volume pinning force and upper critical field of irradiated Nb3Sn

Irradiation by neutrons and ions in A15 superconductors (Nb3Sn, V3Ga) exerts a stronger influence on the pinning behavior than in nonordered alloys (NbTi). In this work it is shown for deuteron irradiated Nb3/Sn wires prepared by the bronze process that the dose curve of the volume pinning force PV can be conveniently described by a sum of two terms, due to the grain boundary pinning and to the radiation pinning, respectively. After deduction of the contribution by the radiation-induced pinning centers, good agreement is obtained between the measured PV values and those calculated using the upper critical field Bc2 and the transition temperature Tc on the basis of the irradiation fluence. The use of a theoretical relationship between Bc2 and Tc is supported by measured values. Application to multifilamentary superconductors with high current carrying capabilities simplifies the calculation of PV, since the radiation induced volume pinning force can be neglected.

Cw laser annealing of Nb3Al and Nb3Si

cw laser annealing has been applied to synthesize the metastable A15 superconductors, Nb3Al and Nb3Si. Qualitative agreement with the equilibrium phase diagrams have been obtained for the Nb-Al system. Laser annealing permits the high-temperature A15 phase to be fast quenched to room temperature without decomposition. Subsequent use of multiple low-temperature laser scans raises the superconducting transition temperature, probably by improving the atomic order. For the Nb-Si system, a single-phase nonstoichiometric A15 structure is formed from the amorphous phase upon laser annealing.

Critical current density and superconducting parameters T&amp;lt;inf&amp;gt;c&amp;lt;/inf&amp;gt;, H&amp;lt;inf&amp;gt;c2&amp;lt;/inf&amp;gt;, and k in neutron-irradiated and annealed V&amp;lt;inf&amp;gt;3&amp;lt;/inf&amp;gt;Si

Single and polycrystalline V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Si was neutron irradiated at 240°C up to a fluence of 1.2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> and subsequently isochronally annealed up to 1330°C. Measurements include the critical current density, j <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , the critical temperature, T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , the upper critical field, H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c2</inf> , and the residual resistance. Dislocation loops are identified by TEM as the part of the radiation induced defects responsible for j <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> . Two different annealing temperatures are found for T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> and j <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , respectively. Due to the high irradiation temperature, T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> recovery occurs in one stage only, corresponding to thermally produced vacancles. All samples exhibit a scaling behavior of the volume pinning force between 0.9 and 0.6 reduced temperature. A j <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> (H) peak is observed at low fluences and high annealing temperatures. The explanation for this behavior is based on a concentration dependent reduction of the theoretical threshold. A saturation behavior of the volume plnning force for high fluences and low annealing temperatures is observed, which is in quantitative agreement with the high-field mechanism of Kramers model above 0.8 reduced field. With these results we can explain the field dependent enhancement of j <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> after neutron irradiation of A15 superconductors with grain boundary pinning.

Microstructure and properties of A15 superconductors formed by direct precipitation

Superconducting materials were made by quenching supersaturated solutions of V-Ga and Nb-Al, deforming the quenched specimens, and then precipitating the A15 phase by aging at intermediate temperature. The critical current characteristics of the product materials depend both on the inherent properties of the A15 phase, which presumably reflect its composition, and on the details of the precipitation process, which determine the grain size, continuity, and volume fraction of the A15. These features of the precipitation process differ qualitatively between V-Ga and Nb-Al. They are described and used to interpret the critical current characteristics.

The effect of neutron irradiation upon the superconducting critical temperature of some transition-metal carbides, nitrides, and carbonitrides

Samples of TiN, NbC, and Nb(CN) have been irradiated to various neutron doses in the Brookhaven High Flux Beam Reactor. Their superconducting critical temperatures are reduced at a rate which is much less than that for similarly irradiated high-Tc A15 superconductors. A dose of 1.5×1020 n/cm2 (E≳1 MeV) causes a reduction in Tc of 6–27%. This reduction may be explained in terms of the production of metal-lattice vacancies.

Field dependent change of the critical current density in neutron irradiated A15 superconductors with grain boundary pinning

The dependence of the upper critical field (Hc2) and the critical current density ( jc) on fluence has been measured up to 1.2×1019 cm−2 (E≳1 MeV) for V3Si bulk material irradiated with neutrons at ambient reactor temperatures. Dislocation loops are identified by TEM as the part of the radiation induced defects responsible for jc. Using these results it is shown that the increase in jc of irradiated A15 superconductors with grain boundaries is not due to the raised Hc2 but corresponds to the radiation induced dislocation loops. The volume pinning force of these defects has the same temperature dependence but quite a different field dependence than the grain boundary pinning. By superposing the dislocation loop pinning on the grain boundary pinning we obtain an enhancement of jc which increases with increasing field in excellent agreement with the observed field dependent increase of jc in neutron irradiated A15 superconductors. Deviations from the experimental values for high-jc materials and consequences for the high field mechanism of Kramer’s model are discussed.

Status of the development of high-field A15 superconductors

The status of the development of multifilamentary high-field A15 superconductors is reviewed briefly. Alternative techniques to circumvent the basic difficulty of fabricating a conductor with a brittle material are described and evaluated. The solid state diffusion or bronze route will remain the dominant technology for some years, however the “In Situ” technique is an attractive alternative with comparable J c and improved mechanical properties. Infiltration might find application in the development of materials for higher magnetic fields than possible with Nb 3Sn and V 3Ga. The future of powder technology is uncertain.

Properties of reactively sputtered superconducting films

A review of the applicability of reactive sputtering to the synthesis of several A15 and B1 superconductors was performed. Critical temperature, T c , of Nb 3 Ge and V 3 Si made by this method were found to be slightly lower than the highest reported values. T c 's of V 3 Ge and NbC films were higher than found in bulk samples. Nb-Si films were nonsuperconducting. The preparation of pseudo-binary alloys of the Nb-V-Ge, Nb-V-Si and the Nb-Ge-Si systems resulted in no improvements in T c 's. Fabrication of layered structures consisting of Nb-C-N and nonsuperconducting layers was investigated.

THE TUNNELING DENSITY OF STATES OF SUPERCONDUCTIVE Nb-Sn

THE TUNNELING DENSITY OF STATES OF SUPERCONDUCTIVE Nb-Sn

The sputtering of A15 Nb3Ge with controlled additions of oxygen

Abstract A series of experiments designed to investigate the role of oxygen during the sputtering of the A15 superconductor Nb3Ge is reported. The overall trend found by other workers, of oxygen enhancing the Tc of ‘Nb3Ge’ in certain circumstances, is confirmed: however, two additional and associated effects are observed with our particular configuration of target and substrate. First, a tendency for the oxygen impurity to reduce the room temperature resistance ratio, and secondly, the appearance of two A 15 phases of slightly differing lattice parameter which are most discernible when oxygen impurity is present. A discussion of these effects and a detailed analysis of X-ray diffraction measurements is presented. It is concluded that oxygen, though beneficial for the formation of ‘Nb3Ge', is not necessarily the most critical parameter in the formation of stoichiometric Nb3Ge.

The effect of gap anisotropy on radiation-induced [formula omitted] changes in the A-15 superconductors

The irradiation of A15 superconductors by energetic particles such as 4He or neutrons in the MeV range produces an unusually large depression of the transition temperature. It has been emphasized by Poate et al. [1] that this depression of T c , and also its saturalion at large fluences, can be correlated well with the associated variation of the electrical resistance ratio between 300 K and low temperatures. This correlation holds whether the defects are introduced by irradiation or in the process of sample preparation. We interpret this universality of behavior as strongly suggesting that the mean free path, l, is the factor that controls T c . Following the original ideas of Markovitz and Kadanoff [2], we propose that decreasing l caused by increasing defect concentration progressively reduces the effective anisotropy of the energy gap and consequently T c . Both the universality and the saturation flow naturally from this model without any adjustable parameters and we are able to account quantitatively for the T c depressions in V 3Ge, V 3Si, Nb 3Sn and Nb 3Ge. There is independent evidence for substantial anisotropy in a number of physical properties of these materials and in particular, measurements have been interpreted [3,4] as indicating that the energy gap varies over the Fermi surface by factors of 3 or 4 — an order of magnitude larger variation than is encountered in the elemental superconductors. A fuller account of our model has been published elsewhere [5]. Finally, the precise character of the radiation-induced defects in the A-15's appears to be still some-what uncertain. It is tempting to speculate that 〈100〉 crowdions may exist in these materials. Some qualitative considerations supporting this conjecture are discussed.

Influence of irradiation induced atomic disorder on H c2 of Nb 3Sn

A significant monotonous decrease of H c2 (0) almost proportional to T c has been observed after heavy ion irradiation of the A15 superconductor Nb 3Sn at low temperature < 30 K and isochronal annealing up to 300 K has been measured. The effects are discussed in connection with the Goodman—Gorkov-relation.

Internal friction in A15 and C15 superconductors in the temperature range 4-150K

Measurements of the internal friction for the propagation of longitudinal ultrasonic waves in the kHz range have been made for samples of Nb3Sn, V 25.25 at.% Si, HfV2 and ZrV2 all of which undergo lattice transformations above their superconducting transition temperatures. Large peaks in the internal friction are observed just below the lattice transformation temperatures of HfV2 and ZrV2, but not for Nb3Sn and V 27.25 at.% Si, though the latter does exhibit a much smaller peak at a temperature above the transformation.