  Solid-state electrolytes with argyrodite structures, such as
$\mathrm{Li_6PS_5Cl}$, have attracted considerable attention due to their
superior safety compared to liquid electrolytes and higher ionic conductivity
than other solid electrolytes. Although experimental efforts have been made to
enhance conductivity by controlling the degree of disorder, the underlying
diffusion mechanism is not yet fully understood. Moreover, existing theoretical
analyses based on ab initio MD simulations have limitations in addressing
various types of disorder at room temperature. In this study, we directly
investigate Li-ion diffusion in $\mathrm{Li_6PS_5Cl}$ at 300 K using
large-scale, long-term MD simulations empowered by machine learning potentials
(MLPs). To ensure the convergence of conductivity values within an error range
of 10%, we employ a 25 ns simulation using a $5\times5\times5$ supercell
containing 6500 atoms. The computed Li-ion conductivity, activation energies,
and equilibrium site occupancies align well with experimental observations.
Notably, Li-ion conductivity peaks when Cl ions occupy 25% of the 4c sites,
rather than at 50% where the disorder is maximized. This phenomenon is
explained by the interplay between inter-cage and intra-cage jumps. By
elucidating the key factors affecting Li-ion diffusion in
$\mathrm{Li_6PS_5Cl}$, this work paves the way for optimizing ionic
conductivity in the argyrodite family.
