# NMR-investigations on the lithium solid state electrolyte Li10GeP2S12 (LGPS)

• NMR-spektroskopische Untersuchungen am Lithium-Festkörperelektrolyten Li10GeP2S12 (LGPS)

This work includes the introduction and analysis of a new 2D spin-lattice relaxation ($T_\text{1}$)/spin alignment echo (SAE) correlation experiment to study Li ion diffusion in Li\textsubscript{10}GeP\textsubscript{2}S\textsubscript{12} (LGPS) material. LGPS is one of the fastest known solid state electrolytes with an ionic conductivity in the range of liquid electrolytes used today in battery technology. The samples investigated in this thesis consist of a mixture of tetragonal and orthorhombic LGPS. The 2D-experiment correlates the \textsuperscript{7}Li spin lattice relaxation time constants $T_\text{1}$ with the SAE decay time constants ${{\tau }_{c}}$ to distinguish between hopping time constants and signal decay limited by relaxation. For the analysis, the 2D data set measured at a temperature of 298~K and at an external magnetic field of $B_0=9.4~\text{T}$ was inverted together with the spectral dimension, whereby an algorithm for inverse Laplace transformation (ILT) without a non-negativity constraint was used. The resulting ${{T}_{\text{1}}}$- ${{\tau }_{c}}$ correlation map showed several distinguishable regions. By the additional inversion of the spectral component, the corresponding spectrum could be mapped for each point in the ${{T}_{\text{1}}}$- ${{\tau }_{c}}$ map, which enabled the assignment of the regions to different motion processes. Based on the regions, it was possible to distinguish between tetragonal and orthorhombic LGPS, and for the first time in tetragonal LGPS between fast short-range diffusion within crystallites and long-range diffusion between crystallites over grain boundaries.\\Evidence for the theoretically predicted coupling of all longitudinal orders due to a symmetry breaking during relaxation of the spin alignment states is presented for the first time in this work at the LGPS system. Analysis of the relaxation spectra showed systematically occurring asymmetries and central dispersive components and it has been shown by multiquantum filter (MQF) experiments that all longitudinal orders in the tetragonal LGPS are coupled effective by a longitudinal relaxation process. Since the strength of the observed coupling and the asymmetries in the spectra cannot be explained by quadrupolar relaxation alone, Cross-relaxation by heteronuclear dipole-dipole interaction between \textsuperscript{7}Li and \textsuperscript{31}P seems to be responsible for the symmetry breaking of the longitudinal orders. Plausible indications were provided by the application of an Independent Component Analysis (ICA) to the multidimensional raw data, that proved to be easily feasible and was effective in determining independent processes, driven either mainly by dipolar or quadrupolare interactions. Furthermore the application of an asymmetry parameter for all spectra reflected the division of the ${{T}_{\text{1}}}$- ${{\tau }_{c}}$ distribution into different regions in large parts and thus underlines the direct correlation of relaxation coupling and lithium dynamics in the LGPS.\\Temperature-dependent $T_\text{1}$/SAE measurements from 233~K to 413~K at $B_0=14.1~\text{T}$ were performed, from which activation energies for ${{\tau }_{c}}$ and $T_\text{1}$ were determined. For $T_\text{1}$ these values are lower for the tetragonal LGPS than previously determined from NMR data, but almost identical to activation energies determined from neutron data. This finding underlines the importance of ILT analysis for relaxation measurements on complex solids. Furthermore, it was shown that the activation energies obtained from tetragonal LGPS are smaller than those from the orthorhombic phase. The results also showed a significant exchange of Li spins between the two LGPS phases and a significantly weaker relaxation asymmetry within the orthorhombic LGPS.