Nucleation and Growth of Oxide Nanoparticles in Internally Oxidized APC Nb₃Sn and their influence on flux pinning

High Performance APC Nb₃Sn wires are made using an internal oxidation process to create ZrO₂ or HfO₂ nanoparticles during reactive-diffusional growth of Nb₃Sn. These nanoparticles both refine A15 grains (increasing GB flux pinning) and directly act as flux pinning centers themselves. The relative solubility of, e.g., Zr and oxygen in the A15 and Nb-alloy drives nucleation at the moving Nb-A15 boundary leading to a distribution of nano-oxides in the final A15. We present simple analytic nucleation and growth analysis which is consistent with the observed trends in nanoparticle size with Nb-alloying element and the trend in particle size as we move through the A15 layer. This latter effect is seen to be due to the growth during the heat treatment time via diffusion of the solutes through the Nb₃Sn. The size and size distribution of the nanoparticles has been characterized through image analysis of transmission electron micrographs, and a phase field model has been created which uses known thermodynamic and kinetic properties of the component materials to model the nucleation and growth process. Transport results are presented for ZrO₂ and HfO₂ APC variants, and the pinning is analyzed in terms of the size and density of the particles (and GB density). The change in pinning is observed as the mean particle size changes from much larger than the fluxon size to below it, and correlated to a modified model of pinning.