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We study mechanisms of vortex nucleation in Nb$_3$Sn Superconducting RF (SRF) cavities using a combination of experimental, theoretical, and computational methods. Scanning transmission electron microscopy (STEM) image and energy dispersive spectroscopy (EDS) of some Nb$_3$Sn cavities show Sn segregation at grain boundaries in Nb$_3$Sn with Sn concentration as high as $\sim$35 at.\% and widths $\sim$3 nm in chemical composition. Using ab initio calculations, we estimate the effect excess tin has on the local superconducting properties of the material. We model Sn segregation as a lowering of the local critical temperature. We then use time-dependent Ginzburg-Landau theory to understand the role of segregation on magnetic vortex nucleation. Our simulations indicate that the grain boundaries act as both nucleation sites for vortex penetration and pinning sites for vortices after nucleation. Depending on the magnitude of the applied field, vortices may remain pinned in the grain boundary or penetrate the grain itself. We estimate the superconducting losses due to vortices filling grain boundaries and compare with observed performance degradation with higher magnetic fields. We estimate that the quality factor may decrease by an order of magnitude ($10^{10}$ to $10^9$) at typical operating fields if 0.03\% of the grain boundaries actively nucleate vortices. We additionally estimate the volume that would need to be filled with vortices to match experimental observations of cavity heating.

Antisite defects play a critical role in Nb$_3$Sn superconducting radio frequency (SRF) cavity physics. Such defects are the primary form of disorder in Nb$_3$Sn, and are responsible for stoichiometry variations, including experimentally observed tin-depleted regions within grains and tin-rich regions around grain boundaries. But why they cluster to form regions of different stoichiometries and how they affect the SRF properties of Nb$_3$Sn cavities are not fully understood. Using $\textit{ab initio}$ techniques, we calculate the A15 region of the Nb-Sn phase diagram, discuss a possible modification to the phase diagram near grain boundaries, and calculate $T_c$ as a function of stoichiometry, including experimentally inaccessible tin-rich stoichiometry. We find that the impact of antisite defects on the density of states near the Fermi-level of Nb$_3$Sn plays a key role in determining many of their properties. These results improve our understanding of the obstacles facing Nb$_3$Sn SRF systems, and how modified growth processes might overcome them., 8 pages, 11 figures

We use Time-Dependent Ginzburg-Landau theory to study the nucleation of vortices in type II superconductors in the presence of both geometric and material inhomogeneities. The superconducting Meissner state is meta-stable up to a critical magnetic field, known as the superheating field. For a uniform surface and homogenous material, the superheating transition is driven by a non-local critical mode in which an array of vortices simultaneously penetrate the surface. In contrast, we show that even a small amount of disorder localizes the critical mode and can have a significant reduction in the effective superheating field for a particular sample. Vortices can be nucleated by either surface roughness or local variations in material parameters, such as Tc. Our approach uses a finite element method to simulate a cylindrical geometry in 2 dimensions and a film geometry in 2 and 3 dimensions. We combine saddle node bifurcation analysis along with a novel fitting procedure to evaluate the superheating field and identify the unstable mode. We demonstrate agreement with previous results for homogenous geometries and surface roughness and extend the analysis to include variations in material properties. Finally, we show that in three dimensions, suface divots not aligned with the applied field can increase the super heating field. We discuss implications for fabrication and performance of superconducting resonant frequency cavities in particle accelerators., 11 pages, 20 figures

In this work, we employ theoretical ab initio techniques to solve mysteries and gain new insights in Nb₃Sn SRF physics. We determine the temperature dependence of Nb₃Sn antisite defect formation energies, and discuss the implications of these results for defect segregation. We calculate the phonon spectral function for Nb₃Sn cells with different combinations of antisite defects and use these results to determine Tc as a function of stoichiometry. These results allow for the first-ever determination of Tc in the tin-rich regime, where experimental measurements are unavailable and which is critical to understanding the impact of tin-rich grain boundaries on superconducting cavity performance. Finally, we propose a theory for the growth mechanism of Nb₃Sn growth on a thick oxide, explaining the puzzling disappearing droplet behavior of Sn on Nb oxide and suggesting how in general an oxide layer reacts with Sn to produce a uniform Nb₃Sn layer., Proceedings of the 19th International Conference on RF Superconductivity, SRF2019, Dresden, Germany