Relation of short-range and long-range lithium ion dynamics in glass-ceramics: Insights fromLi7NMR field-cycling and field-gradient studies

We use various $^{7}\mathrm{Li}$ NMR methods to investigate lithium ion dynamics in ${70\mathrm{Li}}_{2}{\mathrm{S}\ensuremath{-}30\mathrm{P}}_{2}{\mathrm{S}}_{5}$ glass and glass-ceramic obtained from this glass after heat treatment. We employ $^{7}\mathrm{Li}$ spin-lattice relaxometry, including field-cycling measurements, and line-shape analysis to investigate short-range ion jumps as well as $^{7}\mathrm{Li}$ field-gradient approaches to characterize long-range ion diffusion. The results show that ceramization substantially enhances the lithium ion mobility on all length scales. For the ${70\mathrm{Li}}_{2}{\mathrm{S}\ensuremath{-}30\mathrm{P}}_{2}{\mathrm{S}}_{5}$ glass-ceramic, no evidence is found that bimodal dynamics result from different ion mobilities in glassy and crystalline regions of this sample. Rather, $^{7}\mathrm{Li}$ field-cycling relaxometry shows that dynamic susceptibilities in broad frequency and temperature ranges can be described by thermally activated jumps governed by a Gaussian distribution of activation energies $g({E}_{\mathrm{a}})$ with temperature-independent mean value ${E}_{\mathrm{m}}=0.43\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ and standard deviation $\ensuremath{\sigma}=0.07\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$. Moreover, use of this distribution allows us to rationalize $^{7}\mathrm{Li}$ line-shape results for the local ion jumps. In addition, this information about short-range ion dynamics further explains $^{7}\mathrm{Li}$ field-gradient results for long-range ion diffusion. In particular, we quantitatively show that, consistent with our experimental results, the temperature dependence of the self-diffusion coefficient $D$ is not described by the mean activation energy ${E}_{\mathrm{m}}$ of the local ion jumps, but by a significantly smaller apparent value whenever the distribution of correlation times $G(log\ensuremath{\tau})$ of the jump motion derives from an invariant distribution of activation energies and, hence, continuously broadens upon cooling. This effect occurs because the harmonic mean, which determines the results of diffusivity or also conductivity studies, continuously separates from the peak position of $G(log\ensuremath{\tau})$ when the width of this distribution increases.