  In this work we address Li-ion diffusion in thio-LISICON materials and in
their oxide counterparts, exploring both the orthorhombic and tetragonal phases
of Li10GeP2S12(LGPS) and Li10GeP2O12(LGPO) through extended Car-Parrinello
molecular dynamics in the canonical and isobaric-isothermal ensemble. The
(quasi-)orthorhombic and tetragonal phases are studied both for the oxide and
for the sulfide, with the aim of comparing their conductivity with the same
approach; out of these four case studies, tetragonal LGPO has not been reported
and, while dynamically stable, it sits (0.04 Ha/formula unit) above
orthorhombic LGPO. We calculate activation energies for diffusion of 0.18 eV
and 0.23 eV for tetragonal and orthorhombic LGPS, and of 0.22 eV and 0.34eV for
tetragonal and orthorhombic LGPO. In line with experiments, we find
orthorhombic LGPO orders of magnitude less conductive, at room temperature,
than the two sulfide systems. However, this is not the case for tetragonal
LGPO, which, although less stable than its orthorhombic allotrope, shows at
room temperature a conductivity comparable to orthorhombic and tetragonal LGPS,
and, if synthesized, could make a very attractive Li-ion conductor.
