  Whispering Gallery (WG) mode resonators have been machined from a boule of
single-crystal isotopically pure silicon-28. Before machining, the as-grown rod
was measured in a cavity, with the best Bragg confined modes exhibiting
microwave $Q$-factors on the order of a million for frequencies between 10 and
15 GHz. After machining the rod into smaller cylindrical WG mode resonators,
the frequencies of the fundamental mode families were used to determine the
relative permittivity of the material to be $11.488\pm0.024$ near 4 K, with the
precision limited only by the dimensional accuracy of the resonator. However,
the Q-factors were degraded by the machining to below $4\times10^4$. Raman
spectroscopy was used to optimize post-machining surface treatments to restore
high $Q$-factors. This is an enabling step for the use of such resonators for
hybrid quantum systems and frequency conversion applications, as silicon-28
also has very low phonon losses, can host very narrow linewidth spin ensembles
and is a material commonly used in optical applications.
