Diffusion coefficient of lithium ions in garnet-type Li_6.5La₃Zr_1.5Ta_0.5O₁₂ single crystal probed by ⁷Li pulsed field gradient-NMR spectroscopy

Diffusion coefficient of lithium ions in Li_6.5La₃Zr_1.5Ta_0.5O₁₂ (LLZTO) single crystal is measured using ⁷Li pulsed field gradient nuclear magnetic resonance (PFG-NMR) spectroscopy in the temperature range from 298 K to 353 K. The Li diffusion coefficient in LLZTO is evaluated to be 1.9 × 10⁻¹³ m² s⁻¹ at 298 K with the activation energy of 0.43 eV. The ionic conductivity of LLZTO single crystal is measured by impedance spectroscopy, which gives 7 × 10⁻⁴ S cm⁻¹ at 298 K with the activation energy of 0.43 eV. The diffusion coefficient obtained by PFG-NMR is lesser than the diffusion coefficient calculated from ionic conductivity using Nernst-Einstein relation. The small discrepancy gives the Haven ratio of 0.4, which suggests a correlated migration of the lithium ions in the tetrahedral and octahedral sites in LLZTO. To compare the present result with previous reports, the diffusion time (Δ) dependence is carefully checked in PFG-NMR not only for the single crystal but also the crushed powdered samples, which revealed no significant dependence in the single crystal but small dependence in the crushed samples which may be due to the restricted diffusion in the powder grains.