The scaling law for the strain dependence of the critical current density in Nb3Sn superconducting wires

Comprehensive measurements are reported of the critical current density (J(C)) of internal-tin and bronze-route Nb3Sn superconducting wires as a function of magnetic field (B 23 T), temperature (4.2 K <= T <= 12 K) and axial strain (-1.6% <= epsilon(I) <= 0.40%). Electric field-temperature characteristics are shown to be equivalent to the standard electric field-current density characteristics to within an experimental uncertainty of similar to 20 mK, implying that JC can be described using thermodynamic variables. We report a new universal relation between normalized effective upper critical field (B*(C2)(0)) and strain that is valid over a large strain range for Nb3Sn wires characterized by high upper critical fields. A power-law relation between B*(C2)(0, epsilon(I)) and T*(C)(epsilon(1)) (the effective critical temperature) is observed with an exponent of similar to 2.2 for high-upper-critical-field Nb3Sn compared to the value >= 3 for binary Nb3Sn. These data are consistent with microscopic theoretical predictions and suggest that uniaxial strain predominantly affects the phononic rather than the electronic properties of the material. The standard Summers scaling law predicts a weaker strain dependence than is observed. We propose a scaling law for J(C)(B, T, epsilon(I)) based on microscopic theory and phenomenological scaling that is sufficiently general to describe materials with different impurity scattering rates and electron-phonon coupling strengths. It parametrizes complete datasets with a typical accuracy of similar to 4%, and provides reasonable predictions for the JC (B, T, epsilon(I)) surface from partial datasets.