From Ultraslow to Fast Lithium Diffusion in the 2D Ion Conductor ${\mathrm{Li}}_{0.7}{\mathrm{TiS}}_2$ Probed Directly by Stimulated-Echo NMR and Nuclear Magnetic Relaxation

${}^7\mathrm{Li}$ stimulated-echo NMR and classical relaxation NMR techniques are jointly used for the first time for a comprehensive investigation of Li diffusion in layer-structured ${\mathrm{Li}}_{0.7}{\mathrm{TiS}}_2$. One single 2D Li diffusion process was probed over a dynamic range of almost 10 orders of magnitude. So far, this is the largest dynamic range being measured by ${}^7\mathrm{Li}$ NMR spectroscopy directly, i.e., without the help of a specific theoretical model. The jump rates obey a strict Arrhenius law, determined by an activation energy of $0.41(1)\mathrm{eV}$ and a preexponential factor of $6.3(1)\times {10}^{12}{\mathrm{s}}^{-1}$, and range between $1\times {10}^{-1}{\mathrm{s}}^{-1}$ and $7.8\times {10}^8{\mathrm{s}}^{-1}$ (148–510 K). Ultraslow Li jumps in the kHz to sub-Hz range were measured directly by recording ${}^7\mathrm{Li}$ spin-alignment correlation functions. The temperature and, in particular, the frequency dependence of the relaxation rates fully agree with results expected for 2D diffusion.

Figure 1

Semilog plot of normalized ${}^7\mathrm{Li}$ SAE amplitudes of ${\mathrm{Li}}_{0.7}{\mathrm{TiS}}_2$ vs $t_m$ ($t=t_p=15\mu \mathrm{s}$) at 193 K. The first decay step directly yields the Li residence time $\tau =1.01(1)\times {10}^{-2}\mathrm{s}$, whereas the second decay step simply reflects $T_1$ relaxation, $T_1\approx 1.1\times {10}^1\mathrm{s}$. The solid line represents a fit according to the sum of a stretched $(\tau )$ and a single exponential ($T_1$).

Figure 2

Li jumps rates ${\tau }^{-1}$ (●) vs $1/T$ directly measured by SAE NMR in comparison with the $T_{1\mathrm{diff}}^{-1}$ (▿ 9.97 MHz) and $T_{1\varrho \mathrm{diff}}^{-1}$ (○ 5.2 kHz) data. The dashed and solid lines are fits according to the Richards expression (see text). Constant $T_2^{-1}$ rates ($◑$) below 220 K mark the rigid-lattice regime.

Figure 3

Li jump rates for ${\mathrm{Li}}_{0.7}{\mathrm{TiS}}_2$ vs $1/T$. Model-independent jump rates were obtained from the diffusion induced NMR relaxation maxima at different resonance (▿: 9.97, 19.2, 27.9, and 77.7 MHz) and locking frequencies (○: 2.1, 5.2, and 10 kHz) and directly via ${}^7\mathrm{Li}$ SAE NMR correlation functions (●: 155 MHz and $t_p=15\mu \mathrm{s}$). Furthermore, at 240 K the jump rate ${\tau }^{-1}$ ($◑$) can be estimated from $T_2^{-1}$ (${\omega }_0/2\pi =155\mathrm{MHz}$). The solid line corresponds to ${\tau }^{-1}=6.3(1)\times {10}^{12}{\mathrm{s}}^{-1}\exp \mathbf{(}-0.41(1)\mathrm{eV}/k_{B}T\mathbf{)}$.