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