Relationship between Li⁺ diffusion and ion conduction for single-crystal and powder garnet-type electrolytes studied...

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 ⁷Li 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 Li_6.5La₃Zr_1.5Ta_0.5O₁₂ (LLZO-Ta) and Li_6.5La₃Zr_1.5Nb_0.5O₁₂ (LLZO-Nb). The inner morphology and grain boundaries affect importantly the collision-diffraction behaviours which is inherent to powder samples. The ⁷Li 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_Li) with a long Δ and a large g, which is eventually the smallest value. The D_Li activation energy was close to that of the ionic conductivity (σ). The D_Li 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_NE) were estimated from the experimental values of D_Li and σ. The N_NE values of metal-containing garnets were large (<10²³ cm^-3) and insensitive to temperature. They were larger than Li atomic numbers in cm³ calculated from the density, molecular formula and Avogadro number for LLZOs except for cubic LLZO (Li₇La₃Zr₂O₁₂, N_NE∼ 10²⁰ cm^-3).