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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In this work, the transport and magnetization properties of distributed-barrier Rod-inTube (RIT) strands and Tube Type strands are studied. While Tube Type strands had smaller magnetizations and thus better stabilities in the low field region, their 12 T non-Cu J c s were somewhat smaller than those of the RIT strands. Microstructures were investigated in order to find out the reasons for the difference in non-Cu J c values. Their grain size and stoichiometry were found to be comparable, leading to similar layer J c s. Accordingly it was determined that the lower A15 area fraction rather than the quality of A15 layer was the cause of the discrepancy in non-Cu J c . Subsequently, the area utilizations of subelements were investigated. While for a RIT strand the fine grain (FG) A15 area occupies ~60% of a subelement, for a Tube Type strand it is no more than 40%. Further analysis indicates that the low FG area fraction in a Tube Type strand is attributed to its much larger unreacted Nb area fraction. Finally, a simple change in strand architecture is proposed to reduce the unreacted Nb area fraction.

In this letter we demonstrate the development of ternary Nb3Sn multifilamentary conductors with artificial pinning centers (APC) which achieve high critical fields. These recently-developed conductors were tested in a 31 T magnet, and the results showed that their upper critical field (Bc2) values at 4.2 K are 27-28 T, and irreversible field (Birr) values are above 26 T, values similar to or higher than those of best RRP conductors. The non-Cu Jc has been brought to nearly 1200 A/mm 2 at 16 T and 4.2 K, comparable to RRP, in spite of the fact that the fine-grain Nb3Sn fractions in filaments are still low (20-30%) and the grain sizes are still not fully refined (70-80 nm) due to conductor designs and heat treatments that are not yet optimized. The Nb3Sn layer Jc at 4.2 K, 16 T is 4710 A/mm 2 for the APC wire with 1%Zr, about 2.5 times higher than RRP conductors, in spite of the fact that its grain size is not yet fully refined due to insufficient oxygen and unoptimized heat treatment. An analysis is presented about the non-Cu Jc that can be achieved by further optimizing the APC conductors and their heat treatments.

In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb3Sn superconductors. In the first part, the governing equations for the bulk diffusion and inter-phase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether it is the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that “frozen” bulk diffusion leads to unique composition characteristics that the bulk composition of a compound layer remains unchanged after its initial formation instead of varying with the diffusion reaction system; here the model is modified for the case of grain boundary diffusion. Finally, we apply this model to the Nb3Sn superconductors and propose approaches to control their compositions.