  Depth-controlled $\beta$-NMR was used to study highly spin-polarized $^8$Li
in a Cu film of thickness 100 nm deposited onto a MgO substrate. The positive
Knight Shifts and spin relaxation data show that $^8$Li occupies two sites at
low temperatures, assigned to be the substitutional ($S$) and octahedral ($O$)
interstitial sites. Between 50 to 100 K, there is a site change from $O$ to
$S$. The temperature dependence of the Knight shifts and spin-lattice
relaxation rates at high temperatures, i.e. when all the Li are in the $S$
site, is consistent with the Korringa Law for a simple metal.
