A multiphase diffusion model was constructed and used to analyze the growth of the e- and η-phase intermetallic layers at a plane Cu-Sn interface in a semi-infinite diffusion couple. Experimental measurements of intermetallic layer growth were used to compute the interdiffusivities in thee andη phases and the positions of the interfaces as a function of time. The results suggest that interdiffusion in the e phase(≈De) is well fit by an Arrhenius expression with D0 = 5.48 × 10−9 m2/s andQ = 61.9 kJ/mole, while that in the η phase (≈Dη) has D0= 1.84 × 10−9 m2/s andQ = 53.9 kJ/mole. These values are in reasonable numerical agreement with previous results. The higher interdiffusivity in theη phase has the consequence that theη phase predominates in the intermetallic bilayer. However, the lower activation energy for interdiffusion in theη phase has the result that thee phase fills an increasing fraction of the intermetallic layer at higher temperature: at 20 °C, the predicted e-phase thickness is ≈10 pct of that ofη, while at 200 °C, its thickness is 66 pct of that ofη. In the absence of a strong Kirkendall effect, the original Cu-Sn interface is located within theη-phase layer after diffusion. It lies near the midpoint of theη-phase layer at higher temperature (220 °C) and, hence, appears to shift toward the Sn side of the couple. The results are compared to experimental observations on intermetallic growth at solder-Cu interfaces.

Analysis of low-temperature intermetallic growth in copper-tin diffusion couples

Significant efforts can be found throughout the literature to optimize the current-carrying capacity of Nb3Sn superconducting wires. The achievable transport current density in wires depends on the A15 composition, morphology and strain state. The A15 sections in wires contain, due to compositional inhomogeneities resulting from solid-state diffusion A15 formation reactions, a distribution of superconducting properties. The A15 grain size can be different from wire to wire, and is also not necessarily homogeneous across the A15 regions. Strain is always present in composite wires, and the strain state changes as a result of thermal contraction differences and Lorentz forces in magnet systems. To optimize the transport properties, it is thus required to identify how composition, grain size and strain state influence the superconducting properties. This is not possible accurately in inhomogeneous and spatially complex systems such as wires. This article therefore gives an overview of the available literature on simplified, well-defined (quasi-)homogeneous laboratory samples. After more than 50 years of research on superconductivity in Nb3Sn, a significant amount of results are available, but these are scattered over a multitude of publications. Two reviews exist on the basic properties of A15 materials in general, but no specific review for Nb3Sn is available. This article is intended to provide such an overview. It starts with a basic description of the niobium–tin intermetallic. After that, it maps the influence of Sn content on the electron–phonon interaction strength and on the field–temperature phase boundary. The literature on the influence of Cu, Ti and Ta additions will then be summarized briefly. This is followed by a review of the effects of grain size and strain. The article concludes with a summary of the main results.

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A Review of the Properties of Nb3Sn and Their Variation with A15 Composition, Morphology and Strain State

Sn wires and include recent findings on the variation of the upper critical field (Hc2) with temperature (T) and A15 composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available Hc2(T) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, Hc2*(T) results and can be approximated by , with t = T/Tc. Knowing Hc2*(T) implies that Jc(T) is also known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct Jc(T) dependence. Available Jc(H) results indicate that the magnetic field dependence for all wires from T up to about 80% of the maximum Hc2 can be described with Kramer's flux shear model, if nonlinearities in Kramer plots when approaching the maximum Hc2 are attributed to A15 inhomogeneities. The strain () dependence is introduced through a temperature and strain dependent Hc2*(T,) and Ginzburg–Landau (GL) parameter κ1(T,) and a strain dependent critical temperature Tc(). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependences on Hc2*(T) and Hc2*(). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkably simple relation , where C is a constant, s() represents the normalized strain dependence of Hc2*(0) and h = H/Hc2*(T,). Finally, a new relation for s() is proposed, which is an asymmetric version of our earlier deviatoric strain model and based on the first, second and third strain invariants. The new scaling relation solves a number of much debated issues with respect to Jc scaling in Nb3Sn and is therefore of importance to the applied community, who use scaling relations to analyse magnet performance from wire results.

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A general scaling relation for the critical current density in Nb3Sn

The last couple of years have seen an expansion on both applications and market development strategies for SMES (superconducting magnetic energy storage). Although originally envisioned as a large-scale load-leveling device, today's electric utility industry realities point to other applications of SMES. These applications-transmission line stabilization, spinning reserve and voltage control-are likely to open the door to SMES commercialization in the electric utility sector. In the industrial sector, power quality concerns are already driving the development of a market for micro-SMES devices, and load-leveling at an industrial scale is fast becoming a potential application. Work recently completed as part of the US SMES program, as well as ongoing design activities, point to self- (or cold-) supported SMES as the design option in the near-future. This is a major departure from the earth-supported SMES systems first envisioned 25 years ago for utility load-leveling. The path to commercialize SMES is not likely to include a large 'demonstration' unit, or model, but rather follow an evolutionary process in which bigger and better units will be fielded in response to specific applications. This paper reviews the developments in the US SMES program that have taken us to where we are today, briefly reviews SMES-related activities around the world, and points out trends in applications and development of SMES.

Superconducting storage systems: an overview

We review the scaling relations for the critical current density (Jc) in Nb3Sn wires and include recent findings on the variation of the upper critical field (Hc2) with temperature (T) and A15 composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available Hc2(T) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, Hc2*(T) results and can be approximated by Hc2(t)=Hc2(0) = 1-t1.52, with t = T=Tc.Knowing Hc2*(T) implies that also Jc(T) is known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct Jc(T) dependence. Available Jc(H) results indicate that the magnetic field dependence for all wires from mu0H = 1 T up to about 80 percent of the maximum Hc2 can be described with Kramer's flux shear model, if non-linearities in Kramer plots when approaching the maximum Hc2 are attributed to A15 inhomogeneities. The strain (e) dependence is introduced through a temperature and strain dependent Hc2*(T,e) and Ginzburg-Landau parameter kappa1(T,e) and a strain dependent critical temperature Tc(e). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependencies on Hc2*(T) and Hc2*(e). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkable simple relation Jc(H,T,e)= (C/mu0H)s(e)(1-t1.52)(1-t2)h0.5(1-h)2, where C is a constant, s(e) represents the normalized strain dependence of Hc2*(0) andh = H/Hc2*(T,e). Finally, a new relation for s(e) is proposed, which is an asymmetric version of our earlier deviatoric strain model and based on the first, second and third strain invariants. The new scaling relation solves a number of much debated issues withrespect to Jc scaling in Nb3Sn and is therefore of importance to the applied community, who use scaling relations to analyze magnet performance from wire results.

The superconducting phase within a bronze‐process, multifilamentary Nb3Sn superconducting wire is formed by reaction at the interface between the Nb filaments and the bronze matrix. The maximum current that can be carried by the wire is known to depend on the time and temperature of the heat treatment as well as on the transverse magnetic field. In the work reported here a commercial Airco wire containing 2869 Nb filaments of 3–5 μm diameter in a matrix with a bronze/Nb ratio of three was given a variety of reaction heat treatments. The microstructure of the reacted layer was analyzed as a function of heat treatment, and found to be divisible into three concentric shells that are morphologically distinct. The central shell consists of fine equiaxed grains. Its areal fraction, grain size, and composition depend on the heat treatment, and appear to determine the critical current. The best combination of grain size and composition, and the highest critical current, is obtained with an intermediate reaction temperature (700–730 °C). A further improvement in both microstructure and critical current is achieved by double‐aging the wire, starting the reaction at 700 °C and finishing it at 730 °C. The relation between microstructure and heat treatment is interpreted in light of the apparent mechanism of the reaction, which is revealed by high resolution analyses of the reacted layer. The relation between microstructure and properties is consistent with current understanding of the influence of grain size and stoichiometry on the behavior of type II superconductors.

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The microstructure and critical current characteristic of a bronze‐processed multifilamentary Nb3Sn superconducting wire

A review is presented of the characteristics of large-scale toroidal and solenoidal coils (>10 MWh, or 36 GJ) to establish a basis for quantitative estimates of the material requirements for these two SMES (superconducting magnetic energy storage) systems. The size dependence, the scaling features, and the estimated costs for major material components are compared. Results show that requirements for major materials in the toroid exceed those for the solenoid by factors from two to more than five, depending on size and assumptions.

A comparison of large-scale toroidal and solenoidal SMES systems

The critical current density (J c ) of internal tin wires is increased when low-temperature diffusion heat treatments are performed prior to a high temperature reaction. To determine the variation of J c with pre-reaction heat treatments a copper-stabilized IGC internal tin wire with an outside diameter of 0.267mm was studied. The wire has 2 to 2.5 μm diameter filaments, and within the Ta barrier, the area ratio of the copper matrix and Sn core to Nb is about 2.2. Due to the character of the Cu-Sn phase diagram, heat treatments at a series of temperatures below the Nb 3 Sn reaction temperature affect the local Sn concentration in the matrix about the Nb filaments. The variation in J c resulting from these heat treatments is a consequence of the microstructural state of the conductor and the morphology of the Nb 3 Sn layer produced. The results of this work show that the internal tin and bronze-processed wires have different J c (H) characteristics. The two processes have comparable critical currents at high fields, suggesting the same H c2 , while at low fields the internal tin wire is superior, suggesting a better grain morphology.

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The critical current density and microstructural state of an internal tin multifilamentary superconducting wire

Results show that Mg may be used to improve J/sub c/ in multifilamentary wire, and that the increase is large (60 to 100%). Chemical analysis reveals that the Mg segregates to the reacted layer, and resides principally in the bulk Nb/sub 3/Sn. The microstructural analyses suggest that its principal effect is to suppress coarsening of the Nb/sub 3/Sn grains and establish a uniformly grained layer. Preliminary data also suggests that Mg decreases the minimum Nb/sub 3/Sn grainsize and improves the overall stoichiometry of the reacted layer. The samples used had very high bronze to Nb ratios (R). Since the increase in J/sub c/ apparently depends on the concentration of Mg in the reacted layer, and since virtually all the Mg accumulates there, it may prove difficult to achieve comparable results at lower R values without substantially raising the Mg content of the bronze, or changing to an external bronze process. 6 figures.

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The influence of magnesium addition to the bronze on the critical current of bronze-processed multifilamentary Nb 3 Sn

The central or two-dimensional field of a dipole magnet can be calculated with some precision. The fields at the end of the magnet, which are three-dimensional in nature, provide a more complicated problem. Starting with an end design that produced a relatively good end in terms of multipole components, a method of extending parts of the straight section was used to reduce the most important harmonics, the sextupole and decapole, to a negligible level. In addition, the effect of extending an iron yoke over the ends of a magnet was investigated and it was found to have little effect on the harmonics, though it will raise the dipole field. These results are encouraging as they imply that good ends can be developed with relative ease should the two dimensional cross-section of a dipole magnet such as the SSC have to be changed.

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W. Hassenzahl

Papers

The microstructure and critical current characteristic of a bronze‐processed multifilamentary Nb3Sn superconducting wire

A comparison of large-scale toroidal and solenoidal SMES systems

The critical current density and microstructural state of an internal tin multifilamentary superconducting wire

The influence of magnesium addition to the bronze on the critical current of bronze-processed multifilamentary Nb 3 Sn

Field quality of the end sections of SSC dipoles