Solidlike to liquidlike behavior of Cu diffusion in superionic Cu 2 X ( X = S , Se ) : An inelastic neutron scattering and ab initio molecular dynamics investigation

${\mathrm{Cu}}_{2}\mathrm{Se}$ and ${\mathrm{Cu}}_{2}\mathrm{S}$ are excellent model systems of superionic conductors with large diffusion coefficients that have been reported to exhibit different solidlike and liquidlike Cu-ion diffusion. In this paper, we clarify the atomic dynamics of these compounds with temperature-dependent ab initio molecular dynamics (AIMD) simulations and inelastic neutron scattering experiments. Using the dynamical structure factor and Van Hove correlation function, we interrogate the jump time, hopping length distribution, and associated diffusion coefficients. In cubic ${\mathrm{Cu}}_{2}\mathrm{Se}$ at 500 K, we find solidlike diffusion with Cu jump lengths matching well the first-neighbor Cu-Cu distance of \ensuremath{\sim}3 \AA{} in the crystal, and clearly defined optic phonons involving Cu vibrations. Above 700 K, the jump-length distribution becomes a broad maximum centered around 4 \AA{}, spanning the first and second neighbor lattice distances, and a concurrent broadening of the Cu-phonon density of states. Further, above 900 K, the Cu diffusion becomes close to liquidlike, with distributions of Cu atoms continuously connecting crystal sites, while the vibrational modes involving Cu motions are highly damped, though still not fully overdamped as in a liquid. At low temperatures, the solidlike diffusion is consistent with previous x-ray diffraction and quasielastic neutron scattering experiments, while the higher-temperature observation of the liquidlike diffusion is in agreement with previous AIMD simulations. We also report AIMD simulations in ${\mathrm{Cu}}_{2}\mathrm{S}$ in the hexagonal and cubic superionic phases, and observe nearly liquidlike diffusion above \ensuremath{\sim}500 K. The calculated ionic conductivity is in fair agreement with reported experimental values.