  Cu2Se and Cu2S are excellent model systems of superionic conductors with
large diffusion coefficients that have been reported to exhibit different
solid-liquid-like 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 (INS) 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-Cu2Se at 500 K, we find solid-like diffusion with
Cu-jump lengths matching well the first-neighbour Cu-Cu distance of ~3 {\AA} in
the crystal, and clearly defined optic phonons involving Cu-vibrations. Above
700 K, the jump-length distribution becomes a broad maximum cantered around 4
{\AA}, spanning the first and second neighbour lattice distances, and a
concurrent broadening of the Cu-phonon density of states. Further, above 900 K,
the Cu-diffusion becomes close to liquid-like, with distributions of Cu-atoms
continuously connecting crystal sites, while the vibrational modes involving Cu
motions are highly damped, though still not fully over-damped as in a liquid.
At low temperatures, the solid-like diffusion is consistent with previous X-ray
diffraction and quasielastic neutron scattering experiments, while the
higher-temperature observation of the liquid-like diffusion is in agreement
with previous AIMD simulations. We also report AIMD simulations in Cu2S in the
hexagonal and cubic superionic phases, and observe similar solid and
liquid-like diffusion at low- and high-temperatures, respectively. The
calculated ionic-conductivity is in fair agreement with reported experimental
values.
