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 accurately possible 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 this it maps the influence of Sn content on the 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 briefly summarized. This is followed by a review on the effects of grain size and strain. The article is concluded with a summary of the main results.

We review the scaling relations for the critical current density (J c ) in Nb 3 Sn wires and include recent findings on the variation of the upper critical field (H c2 ) with temperature (T ) and A15 composition. Measurements of H c2 (T ) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available H c2 (T ) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, H * c2 (T ) results and can be approximated byimplies that also J c (T ) is known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct J c (T ) dependence. Available J c (H) results indicate that the magnetic field dependence for all wires from µ 0 H ∼ = 1 T up to about 80% of the maximum H c2 can be described with Kramer's flux shear model, if non-linearities in Kramer plots when approaching the maximum H c2 are attributed to A15 inhomogeneities. The strain (ǫ) dependence is introduced through a temperature and strain dependent H * c2 (T, ǫ) and Ginzburg-Landau parameter κ 1 (T, ǫ) and a strain dependent critical temperature T c (ǫ). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependencies on H * c2 (T ) and H * c2 (ǫ). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkable simple relation J c (H, T, ǫwhere C is a constant, s(ǫ) represents the normalized strain dependence of H * c2 (0) and h = H/H * c2 (T, ǫ). Finally, a new relation for s(ǫ) 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 J c scaling in Nb 3 Sn and is therefore of importance to the applied community, who use scaling relations to analyze magnet performance from wire results.

The critical current (I c ) of six different Nb 3 Sn multifilamentary wires is investigated as a function of temperature, magnetic field, and strain. A relation for a critical temperature (T c ) that depends on the deviatoric strain is proposed and applied to interpret the results. First, a short review is given on the flux-pinning relations that are used to introduce a strain dependent T c in a relation for the I c as a function of field and temperature. The conductor samples are investigated in two different deformation states, namely, in a spiraled shape on a Ti sample holder and a straight section soldered onto a brass substrate. The brass substrate is used to apply a compressive or tensile axial strain to the conductor. The I c in the different samples prepared from a single conductor type can be described very well with a single set of critical properties and strain parameters. In particular, in the strain regime where the matrix deformation is limited and the superconductor is axially compressed, the proposed strain relation is very accurate. The small variation in the strain parameter between the six conductors investigated suggests that this strain parameter is an intrinsic property of Nb 3 Sn.

We have examined the upper critical field of a large and representative set of present multifilamentary Nb 3 Sn wires and one bulk sample over a temperature range from 1.4 K up to the zero-field critical temperature. Since all present wires use a solid-state diffusion reaction to form the A15 layers, inhomogeneities with respect to Sn content are inevitable, in contrast to some previously studied homogeneous samples. Our study emphasizes the effects that these inevitable inhomogeneities have on the field-temperature phase boundary. The property inhomogeneities are extracted from field-dependent resistive transitions which we find broaden with increasing inhomogeneity. The upper 90%-99% of the transitions clearly separates alloyed and binary wires but a pure, Cu-free binary bulk sample also exhibits a zero-temperature critical field that is comparable to the ternary wires. The highest 0 H c2 detected in the ternary wires are remarkably constant: The highest zero-temperature upper critical fields and zero-field critical temperatures fall within 29.5± 0.3 and 17.8± 0.3 K, respectively, independent of the wire layout. The complete field-temperature phase boundary can be described very well with the relatively simple Maki-DeGennes model using a two-parameter fit, independent of composition, strain state, sample layout, or applied critical state criterion.