Variation of $T_c$, lattice parameter and atomic ordering in $Nb_3Sn$ platelets irradiated with 12 MeV protons: correlation with the number of induced Frenkel defects

$Nb_3Sn$ platelets with thicknesses between 0.12 and 0.20 mm produced by a high isostatic pressure process at 1250 °C were irradiated at 300 K with 12 MeV protons. The effects of irradiation on the lattice parameter a, the atomic order parameter S and the transition temperature $T_c$ were measured as a function of proton fluence. In view of the presence of multiple energy radiation sources in future accelerators, the present proton data are compared with neutron irradiation data from the literature. The fluences for both types of radiation were replaced by the dpa number, the 'displacements per atom', calculated using the FLUKA code, which is proportional to the number of radiation induced Frenkel defects. It was found that the variation of both a and S for $Nb_3Sn$ after proton and neutron irradiation as a function of dpa fall almost on the same curve, in analogy to the recently reported correlation between T c and the dpa number. By a simultaneous irradiation of two adjacent thin $Nb_3Sn$ platelets, we have shown that this correlation is not only valid for the state of 'steady energy loss' (protons traveling through the first platelet) but also for the state of higher damage at the Bragg peak (second platelet). It follows that the number of radiation induced Frenkel defects in the A15 grains, calculated via the dpa number, can be considered as a 'universal' parameter, allowing the calculation of the variation of $T_c$, a and S of $Nb_3Sn$ under the effect of multiple high energy radiation sources, as in future superconducting accelerators.