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We present studies on crystal structure and ionic diffusion behaviors ofsuperionic Cu$_{2-\delta}$Se ($\delta$=0, 0.04, and 0.2) by utilizing neutronpowder diffraction and quasi-elastic neutron scattering. In the superionicphase, the structural model with Cu ions occupying the Wyckoff sites of 8$c$and 32$f$ provides the best description of the structure. As the content of Cuincreasing in Cu$_{2-\delta}$Se, the Cu occupancy increases on the 32$f$ site,but decreases on the 8$c$ site . Fitting to the quasi-elastic neutronscattering spectra reveals two diffusion modes, the localized diffusion betweenthe 8$c$ and 32$f$ sites and the long-range diffusion between the adjacent 8$c$sites using the 32$f$ site as a bypass, respectively. Between 430 and 650 K, wemeasured that the compound with more Cu content exhibits a larger long-rangediffusion coefficient. Temperature in this range does not affect the long-rangediffusion process obviously. Our results suggest the two diffusion modescooperative and thus provide a microscopic understanding of the ionic diffusionof the Cu ions in superionic Cu$_{2-\delta}$Se.

Neutron scattering studies on ionic diffusion behaviors of superionic $\alpha$-Cu$_{2-\delta}$Se