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Nb$_3$Sn is a promising advanced material under development forsuperconducting radiofrequency (SRF) cavities. Past efforts have been focusedprimarily on small development-scale cavities, but large, often multi-celledcavities, are needed for particle accelerator applications. In this work, wereport on successful Nb$_3$Sn coatings on Nb in a 1 m-long 9-cell Nbsample-host cavity at Fermilab. The geometry of the first coating with only oneSn source made it possible to study the influence of Sn flux on themicrostructure. Based on these results, we postulate a connection betweenrecently observed anomalously large thin grains and uncovered niobium spotsobserved in the past by other authors [Trenikhina 2018]. A phenomenologicalmodel to explain how these anomalously large grains could form is proposed.This model is invoked to provide possible explanations for literature resultsfrom several groups and to guide key process parameters to achieve uniformvapor-diffusion coatings, when applied to complex structures as the multi-cellcavity under study.

Development and Understanding of Nb$_3$Sn films for radiofrequency applications through a sample-host 9-cell cavity