## Abstract

We show that NMR multi-time correlation functions provide interesting new insights into the nature of lithium and silver ion dynamics in solids. For solid ion conductors, they usually probe the elementary jumps of the long-range charge transport. NMR two-time correlation functions yield rates and activation energies of the ionic hopping motion. Moreover, they reveal that the ionic relaxation exhibits a strong nonexponentiality in the studied crystals and glasses. NMR three-time correlation functions enable quantitative determination of the origin of the nonexponentiality. For various solid-state electrolytes, the analysis shows that pronounced dynamical heterogeneities govern the ionic hopping motion. If dynamical heterogeneities exist, NMR four-time correlation functions allow one to measure the time scale of exchange processes within the rate distributions. For silver ion dynamics in a crystalline and a glassy material, the results indicate that initially slow ions exhibit random new rates from broad rate distributions after very few jump events.

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