Nb 3 Sn superconducting strands are the most practical conductors to generate high magnetic fields (12-16 T), and thus have significant applications in nuclear magnetic resonance (NMR), and great potential for fusion reactors and particle accelerator magnets. High critical current density (J c ) is a key parameter for such applications. Significant efforts towards optimization of various factors led to an 80% improvement in J c from the early 1990s to 2003, when the 4.2 K, 12 T non-matrix J c reached 3000 A/mm 2 (corresponding to 5000 A/mm 2 in Nb 3 Sn layer J c ). [1,2] However, further efforts over the past decade have failed to bring about further increase beyond this level, [3,4] leading some researchers to conclude that the J c of conventional Nb 3 Sn strands had reached its maximum. Here, however, by applying an internal oxidation method, we reduce the grain size by a factor of three and nearly double the 12 T J c . In this method, a Nb 3 Sn strand is fabricated with Nb-Zr alloy as starting material; with oxygen supplied properly via an oxide powder, the Zr atoms in the Nb-Zr alloy are internally oxidized, forming fine intra-granular and inter-granular ZrO 2 particles in Nb 3 Sn layer, which effectively refine Nb 3 Sn grain size. At a reaction temperature of 625 °C, grain size down to 20-50 nm (36 nm on average) has been achieved. For this sample the 4.2 K, 12 T Nb 3 Sn layer J c reached 9600 A/mm 2 .

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Nb3Sn superconductors have significant applications in constructing high-field (> 10 T) magnets. This article briefly reviews development of Nb3Sn superconductor and proposes prospects for further improvement. It is shown that significant improvement of critical current density (Jc) is needed for future accelerator magnets. After a brief review of the development of Nb3Sn superconductors, the factors controlling Jc are summarized and correlated with their microstructure and chemistry. The non-matrix Jc of Nb3Sn conductors is mainly determined by three factors: the fraction of current-carrying Nb3Sn phase in the non-matrix area, the upper critical field Bc2, and the flux-line pinning capacity. Then prospects to improve the three factors are discussed respectively. An analytic model was developed to show how the ratios of precursors determine the phase fractions after heat treatment, based on which it is predicted that the limit of current-carrying Nb3Sn fraction in subelements is ~65%. Then, since Bc2 is largely determined by the Nb3Sn stoichiometry, a thermodynamic/kinetic theory was presented to show what essentially determines the Sn content of Nb3Sn conductors. This theory explains the influences of Sn sources and Ti addition on stoichiometry and growth rate of Nb3Sn layers. Next, to improve flux pinning, previous efforts in this community to introduce additional pinning centers (APC) to Nb3Sn wires are reviewed, and an internal oxidation technique is described.Finally, prospects for further improvement of non-matrix Jc of Nb3Sn conductors are discussed, 2 and it is seen that the only opportunity for further significantly improving Jc lies in improving the flux pinning.

The impacts of heat treatment (HT) temperature and Ti doping on low-field flux jumping and 12 T J c of high-performance internal-Sn, distributed barrier (Nb-Ta) 3 Sn strands have been explored. It was found that higher HT temperatures could suppress low-field flux jumps by not only reducing the J c (B) curve slope, but also increasing the heat capacity and decreasing the dJ c / dT. A metric, J c,3 T /J c,12 T (the ratio of 3 T to 12 T J c ), was used to describe the slope of the J c (B) curve. In addition, an analytical equation was derived to predict the amplitude of a flux jump. The J c (B) curves were further analyzed in the form of Kramer plots to extract the irreversibility field, B irr , and the maximum bulk pinning forces, F p,max . The variations of B irr , F p,max and grain size, d, with HT and Ti doping were also analyzed. F p,max initially increasing linearly with 1/d, saturated at small values of d, possibly because the grains became columnar.

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