  $^{63}$Cu NMR measurements are reported for the Cu-rich phase of
\ch{Cu_{12+x}Sb4S13} ($x \lesssim 2$) and compared to \ch{Cu12Sb4S13}. We
identify the NMR signatures of the phase segregation into Cu-poor ($x \approx
0$) and Cu-rich ($x \lesssim 2$) phases, with the metal-insulator transition
observed in \ch{Cu12Sb4S13} suppressed in the Cu-rich phase. Based on NMR $T_1$
and $T_2$ measurements, the results demonstrate Cu-ion hopping below room
temperature with an activation energy of $\sim$150 meV for the Cu-rich phase,
consistent with superionic behavior. The NMR results also demonstrate the
effects of Cu-ion mobility in the \ch{Cu12Sb4S13} phase, but with a larger
activation barrier. We identify a small difference in NMR Knight shift for the
metallic phase of \ch{Cu12Sb4S13}, compared to the Cu-rich phase, and when
compared to DFT calculations the results indicate a mix of hyperfine
contributions to the metallic shift.

Materials Science