There is a central relationship between material structure and function. Using well-defined surfaces under ultra-high vacuum (UHV) conditions, representative systems interrogated with surface science techniques can elucidate the atomic-scale mechanisms for complex surface processes. Such studies have broadened the understanding of, and are integral to, developing accurate models for many interfacial phenomena. In this presentation, I will briefly highlight the complexity of the surface chemistry on oxidized transition metal surfaces before discussing recent materials growth studies of Nb and Nb3Sn for use in next-generation particle accelerator technologies. Although Nb is the current standard material for SRF cavities, Nb3Sn has been identified as a promising next-generation material for SRF cavities. It has been recently shown that hydrogen incorporated during Nb cavity fabrication results in the formation of Nb hydrides, which lower cavity quality factors at high fields and reduce cavity performance. Utilizing UHV surface science techniques and density functional theory calculations, the growth and suppression mechanisms of Nb nano-hydrides on (3×1)-O Nb(100) were determined; these results provide the first in situ, real-time nanoscale characterization of the effects of dopant incorporation on Nb nano-hydride growth and suppression. The latter part of this presentation will focus on the interaction of Sn with Nb substrates leading to the formation of Nb-Sn alloys. Through representative sample preparation and analysis, Sn adsorption and diffusion behavior on (3×1)-O Nb(100) was visualized at the nanometer scale. This spatially resolved mechanistic information of Sn adsorption and diffusion on an oxidized Nb surface guides the development of predictive Nb3Sn growth models needed for the further optimization of Nb3Sn growth procedures.