Simulations of the effects of tin composition gradients on the   superconducting properties of Nb3Sn conductors
  In powder-in-tube (PIT) Nb3Sn composites, the A15 phase forms between a central tin-rich core and a coaxial Nb tube, thus causing the tin content and superconducting properties to vary with radius across the A15 layer. Since this geometry is also ideal for magnetic characterization of the superconducting properties with the field parallel to the tube axis, a system of concentric shells with varying tin content was used to simulate the superconducting properties, the overall severity of the Sn composition gradient being defined by an index N. Using well-known scaling relationships and property trends developed in an earlier experimental study, the critical current density for each shell was calculated, and from this the magnetic moment of each shell was found. By summing these moments, experimentally measured properties such as pinning-force curves and Kramer plots could be simulated. We found that different tin profiles have only a minor effect on the shape of Kramer plots, but a pronounced effect on the irreversibility fields defined by the extrapolation of Kramer plots. In fact, these extrapolated values H_K are very close to a weighted average of the superconducting properties across the layer for all N. The difference between H_K and the upper critical field commonly seen in experiments is a direct consequence of the different ways measurements probe the simulated Sn gradients. Sn gradients were found to be significantly deleterious to the critical current density Jc, since reductions to both the elementary pinning force and the flux pinning scaling field H_K compound the reduction in Jc. The simulations show that significant gains in Jc of Nb3Sn strands might be realized by circumventing strong compositional gradients of tin. 
L. D. Cooley, C. M. Fischer, P. J. Lee, and D. C. Larbalestier