Scaling relation between renormalized discharge rate and capacity in Na_xCoO₂ films

Layered cobalt oxide, P2-Na_xCoO₂, is a prototypical cathode material for sodium-ion secondary battery. We systematically investigated the rate dependence of the discharge capacity (Q) in three thin films of Na_0.68CoO₂ with different film thickness (d) and in-plane grain radius (r). With subtracting conventional voltage drop effect on Q, we derived an intrinsic rate dependence of Q. We found a scaling relation between the renormalized discharge rate (γ ≡ r²/DT; D and T are the Na⁺ diffusion constant and discharge time, respectively) and relative capacity (=Q/Q₀; Q₀ is the value at a low rate limit). The observed scaling relation is interpreted in terms of the Na⁺ intercalation process at the electrolyte-Na_xCoO₂ interface and Na⁺ diffusion process within Na_xCoO₂.