How Concerted Are Ionic Hops in Inorganic Solid-State Electrolytes?

Despite being fundamental to the understanding of solid-state electrolytes (SSEs), little is known on the degree of coordination between mobile ions in diffusive events, thus hindering a detailed comprehension and possible rational design of SSEs. Here, we introduce an unsupervised k-means clustering approach that is able to identify ion-hopping events and correlations between many mobile ions and apply it to a comprehensive ab initio MD database comprising several families of inorganic SSEs and millions of ionic configurations. It is found that despite two-body interactions between mobile ions being the largest, higher-order n-ion (2 < n) correlations are most frequent. Specifically, we prove a general exponential decaying law for the probability density function governing the number of concerted mobile ions. For the particular case of Li-based SSEs, it is shown that the average number of correlated mobile ions amounts to 10 +/- 5 and that this result is practically independent of the temperature. Interestingly, our data-driven analysis reveals that fast-ionic diffusion strongly and positively correlates with ample hopping lengths and long hopping spans but not with high hopping frequencies and short interstitial residence times. Finally, it is shown that neglection of many-ion correlations generally leads to a modest overestimation of the hopping frequency that roughly is proportional to the average number of correlated mobile ions.