Li jump process in $h$-Li$_{0.7}$TiS$_{2}$ studied by two-time $^{7}$Li spin-alignment echo NMR and comparison with results on two-dimensional diffusion from nuclear magnetic relaxation
M. Wilkening and P. Heitjans

$^7$Li spin-alignment NMR is used to trace ultra-slow diffusion of Li$^+$ in the layered Li conductor Li$_x$TiS$_2$ ($x = 0.7$). Two-time correlation functions were recorded for fixed evolution times as a function of mixing time at temperatures within the $^7$Li rigid-lattice regime. The corresponding decay rates were identified as Li jump rates $\tau^{-1}$ ranging from $10^{-1}$~s$^{-1}$ to 10$^3$~s$^{-1}$ between temperatures $T = 148$~K and 213~K. The jump rates obtained directly from spin-alignment echo NMR and those from diffusion induced maxima of spin-lattice relaxation peaks, monitored in the laboratory as well as in the rotating frame, are consistent with each other and follow an Arrhenius law with an activation energy of 0.41(1)~eV and a pre-exponential factor of $6.3(1) \cdot 10^{12}$~s$^{-1}$. Altogether a solitary Li diffusion process was found between 148~K and 510~K. Li diffusion was investigated in a dynamic range of about 10 orders of magnitude, i.\,e., 0.1~s$^{-1}\leq \tau^{-1} \leq 7.8 \cdot 10^{8}$~s$^{-1}$. Additionally, the analysis of final-state echo amplitudes of the two-time correlation functions revealed information about the Li diffusion pathway in Li$_{0.7}$TiS$_2$. Obviously, a two-site jump process is present, i.\,e., besides the regularly occupied octahedral sites also the vacant tetrahedral ones within the van-der-Waals gap are involved in the overall 2D diffusion process.

© 2008 The American Physical Society.