Sodium-ion diffusion and ordering in single-crystalP2-NaxCoO2

Sodium-ion self-diffusion in $P2(\ensuremath{\gamma}){\text{-Na}}_{x}{\text{CoO}}_{2}$ has been studied using a single crystal as an electrode. Mass transport and thermodynamic properties of Na ions were measured by the potentiostatic intermittent titration technique on a single-crystal electrode with greater accuracy under well-defined diffusion geometry. Excluding the significantly slower diffusion behavior near particular Na ordered phases, average diffusion coefficients ${D}_{\text{Na}}$ are extracted to be $1.2\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }{\text{cm}}^{2}/\text{s}$ for $x>0.5$ and $4.1\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }{\text{cm}}^{2}/\text{s}$ for $x<0.5$, respectively. The existence of stable phases with special Na ordering of $x\ensuremath{\sim}0.25$, 0.33, 0.43, 0.5, 0.55, and 0.71 are verified by either the maximum or diverging signature of the $x$-dependent self-diffusion coefficients.