Flux pinning in bronze-processed Nb3Sn

Publisher Website
Google Scholar
Abstract
Superconducting critical currents have been measured at 4.2 K and applied magnetic fields up to Hc2 for a series of solid‐state processed‐Nb3Sn conductors. Variations were made in the alloy content of the matrix and core as well as heat‐treatment times at 700 °C to produce a wide range of superconducting critical currents. The pinning‐force density, Fp (=Jc×B), plotted as a function of reduced field, h (=H/Hc2), exhibits a peak, Fpmax, at a reduced field hp. Fpmax varies from 81×108 dyn/cm3 at hp=0.2 to 18×108 dyn/cm3 at hp=0.32. The high values of Fpmax for these samples are related to Nb3Sn grain sizes which are 1000 Å or less. At 2 kG the flux‐line lattice spacing is approximately 1000 Å or nearly one flux line per grain. Kramer has proposed a model to account for flux pinning in such hard type‐II superconductors, and while the pinning‐site density in the present samples is near the upper limit to which Kramer’s model was meant to apply, it is possible to interpret the present data using his model. The dynamic pinning force fs (h) calculated by Kramer for flux‐lattice shear around pinning sites too strong to be broken by the Lorentz force has the magnetic field dependence h1/2 (1−h)2. In the high pinning‐density limit where √ρ=1/2a0, ρ being the pinning density and a0 the flux‐line lattice spacing, the magnetic field dependence of fs (h) must be changed to h3/2 (1−h)2/(h1/2−n)2, where n equals (φ0ρ/Hc2)1/2, by incorporating the field dependence of a0. Using this new field dependence enables a prediction of Fpmax, and associated hp values, which fit the present data for bronze‐processed Nb3Sn. It is concluded that near the upper limit of pinning density to which the theory applies a sharp increase in Fpmax may occur without significant shifts in hp to lower values. This result is added to the model’s prediction for lower pinning‐density materials, i.e., when lower values of Fpmax increase there is a shift in hp to smaller values.