Na Diffusion in Hard Carbon Studied with Positive Muon Spin Rotation and Relaxation

The diffusive natureof Na+ in Na-inserted hard carbon(C (x) Na), which is the most common anodematerial for a Na-ion battery, was studied with a positive muon spinrotation and relaxation (mu+SR) technique in transverse,zero, and longitudinal magnetic fields (TF, ZF, and LF) at temperaturesbetween 50 and 375 K, where TF (LF) denotes the applied magnetic fieldperpendicular (parallel) to the initial muon spin polarization. Attemperatures above 150 K, TF-mu+SR measurements showeda distinct motional narrowing behavior, implying that Na+ begins to diffuse above 150 K. The presence of two different muonsites in C (x) Na was confirmed with ZF- andLF-mu+SR measurements; one is in the Na-inserted graphenelayer, and the other is in the Na-vacant graphene layer adjacent tothe Na-inserted graphene layer. A systematic increase in the fieldfluctuation rate (nu) with increasing temperature also evidenceda thermally activated Na diffusion, particularly above 150 K. Assumingthe two-dimensional diffusion of Na+ in the graphene layers,the self-diffusion coefficient of Na+ (D Na J) at 300K was estimated to be 2.5 x 10(-11) cm(2)/s with a thermal activation energy of 39(7) meV.