Diffusion of Li + ions in solids is a basic principle behind the operation of Li-ion batteries. Such diffusive behavior is represented by the diffusion equation (Fick's law), J = -D × ∂φ/∂x, where J is the diffusion flux, D is the self diffusion coefficient, φ is the concentration, and x is the position. Although D of Li + ions (D Li ) in solids is usually evaluated by 7 Li-NMR, difficulties arise for materials that contain magnetic ions. This is because the magnetic ions contribute additional spin-lattice relaxation processes that is considerably larger than the 1/T 1 expected from only Li diffusion [1,2,3]. This implies that 7 Li-NMR provides a rough estimate of D Li for the positive electrode materials of Li-ion batteries, which include transition metal ions in order to compensate charge neutrality during a Li + intercalation/deintercalation reaction. This is an unsatisfactory situation since D Li is one of the primary parameters that govern the charge/discharge rate of a Li-ion battery.
We have, therefore, attempted to measure D Li for lithium-transition-metal-oxides with muon-spin relaxation (μ + SR) since 2005 [4, 5, 6]. Muons do not feel fluctuating magnetic moments at high T , but instead sense the change in nuclear dipole field due to Li diffusion. Even if magnetic moments still affect the muon-spin depolarization rate, such an effect is, in principle, distinguishable from that of nuclear dipole fields. In particular, a weak longitudinal field can be applied that decouples the magnetic and nuclear dipole interactions [7,8]. Here, we wish to summarize our μ + SR study on the lithium-transition-metal-oxides, Li x CoO 2 , LiNiO 2 , and LiCrO 2 .