Copper ion dynamics and phase segregation in Cu-rich tetrahedrite: an NMR study

$^{63}$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.