GLAG theory for superconducting property variations with A15 composition in Nb₃Sn wires

We present a model for the variation of the upper critical field H _c2 with Sn content in A15-type Nb-Sn wires, within the Ginzburg-Landau-Abrikosov-Gor'kov (GLAG) theory frame. H _c2 at the vicinity of the critical temperature T _c is related quantitatively to the electrical resistivity ρ, specific heat capacity coefficient γ and T _c. H _c2 versus tin content is theoretically formulated within the GLAG theory, and generally reproduces the experiment results. As Sn content gradually approaches the stoichiometry, A15-type Nb-Sn undergoes a transition from the dirty limit to clean limit, split by the phase transformation boundary. The H-T phase boundary and pinning force show different behaviors in the cubic and tetragonal phase. We dipict the dependence of the composition gradient on the superconducting properties variation in the A15 layer, as well as the curved tail at vicinity of H _c2 in the Kramer plot of the Nb₃Sn wire. This helps understanding of the inhomogeneous-composition inducing discrepancy between the results by the state-of-art scaling laws and experiments.