# Ion transport in solid-state electrolytes

Transport of ions in solids is of enormous interest from the viewpoints of both fundamental and applied sciences. Most technological applications, e.g., use in solid-state batteries or fuel cells, require sufficiently fast ion transport. In general, the charge transport in solid-state electrolytes results from a thermally activated ionic jump motion between defined sites in a solid matrix. However, the ion dynamics is a very complex dynamical process, which is not completely understood. Our goal is a comprehensive characterization of the ionic jump dynamics so as to improve our understanding of this motion and to identify factors that limit the rate of the charge transport and, thus, applications. For this purpose, we employ NMR experiments and MD simulations.

# NMR experiments on solid-state electrolytes

NMR experiments enable measurement of multi-time correlation functions, which provide valuable insights into ion dynamics in solid-state electrolytes. Two-time correlation functions map out the probability to find an ion at the initial site at a later time. Thus, they yield detailed information about the repopulation of the ionic sites, e.g., about jump rates and energy barriers. Results for crystalline, glassy, and ceramic electrolytes consistently show that the above probability decays in a pronounced non-exponential manner. The origin of this non-exponentiality can be determined on the basis of three-time correlation functions. Our findings demonstrate that an existence of a broad distribution of jump rates leads to the non-exponentiality and, hence, pronounced dynamical heterogeneities exist. Four-time correlation functions measure the life time of these dynamical heterogeneities, i.e., the time scale of exchange between fast and slow ions from the distribution. We find that fast and slow jumps frequently alternate during the migration of an ion. We compare these results for ion dynamics on microscopic scales with diffusion coefficients on larger scales, which are available from field-gradient approaches. In this way, we ascertain how the net charge transports develops from individual ionic jumps.

# MD simulation on lithium phosphate glass

MD simulations enable complete identification of all relevant lithium ionic sites in a glassy matrix. The results show that the number of sites hardly outnumbers the number of ions. Hence, competition between the ions for vacant sites is an important aspect of charge transport in solids, which is not considered in single-particle approaches. Moreover, we find that the existence of a broad rate distribution for the ionic jumps can be traced back, at least in large part, to the existence “fast” and “slow” sites in the glassy matrix. During their migration through the glassy matrix, the ions visit fast and slow sites in rapid alternation. Finally, the simulations reveal that ionic back-and-forth jumps between neighboring lithium sites can occur, leading to a delay of the macroscopic charge transport. All these phenomena demonstrate the high complexity of the ionic jump dynamics in disordered solids. Moreover, they are detailed demands for a successful theoretical description of charge transport in solid-state electrolytes.