Relationship between Li diffusion and ion conduction for single-crystal and powder garnet-type electrolytes studied by Li PGSE NMR spectroscopy.

Ion-conducting garnets are important candidates for use in all-solid Li batteries and numerous materials have been synthesized with high ionic conductivities. For understanding ion conduction mechanisms, knowledge on Li diffusion behaviour is essential. The proposed nano-scale lithium pathways are composed of tortuous and narrow Li channels. The pulsed gradient spin-echo (PGSE) NMR method provides time-dependent Li diffusion on the micrometre space. For powder samples, collision-diffraction echo-attenuation plots were observed in a short observation time, which had not been fully explained. The diffraction patterns were reduced or disappeared for single-crystal garnet samples of LiLaZrTaO (LLZO-Ta) and LiLaZrNbO (LLZO-Nb). The inner morphology and grain boundaries affect importantly the collision-diffraction behaviours which is inherent to powder samples. The Li diffusion observed by PGSE-NMR depends on the observation time (Δ) and the pulsed field gradient (PFG) strength (g) in both powder and single-crystal samples, and the anomalous effects were reduced in the single-crystal samples. The scattered Li diffusion constants converged to a unique value (D) with a long Δ and a large g, which is eventually the smallest value. The D activation energy was close to that of the ionic conductivity (σ). The D values are plotted versus the σ values measured for four powder and two single-crystal garnet samples. Assuming the Nernst-Einstein (NE) relation which was derived for isolated ions in solution, the carrier numbers (N) were estimated from the experimental values of D and σ. The N values of metal-containing garnets were large (<10 cm) and insensitive to temperature. They were larger than Li atomic numbers in cm calculated from the density, molecular formula and Avogadro number for LLZOs except for cubic LLZO (LiLaZrO, N∼ 10 cm).