Simulating Vapor Deposition of Nb₃Sn on SRF Cavities: Insights from Genetic Algorithms Surface Structure Search

Nb₃Sn-coated superconducting radiofrequency (SRF) particle accelerator cavities offer a promising route for developing next-generation accelerator cavities due to their high critical fields and ability to operate at relatively high temperatures. However, its widespread adoption is constrained by challenges in effectively coating Nb cavities with Nb₃Sn. The surface properties of Nb₃Sn, especially its outermost layers, play an important role in determining the superconducting behavior of the coated cavity. To gain insights into the surface structure of Nb₃Sn, we employ genetic algorithms coupled with density functional theory (DFT) calculations to simulate the vapor deposition methods typically used for Nb₃Sn coating. Using the generated data, we construct a surface phase diagram for Nb₃Sn(100), delineating stable surface configurations as a function of temperature and Sn partial vapor pressure. Interestingly, the optimal conditions for Nb₃Sn growth identified through our surface phase diagram align well with experimentally used parameters, underscoring the efficacy of our approach. Additionally, our findings indicate that Sn anti-site defects that are particularly detrimental to superconductivity are stable predominantly near the surface.