Mismatch in cation size causes rapid anion dynamics in solid electrolytes: the role of the Arrhenius pre-factor

Crystalline ion conductors exhibiting fast ion dynamics are of utmost importance for the development of, e.g., sensors or rechargeable batteries. In some layer-structured or nanostructured compounds fluorine ions participate in remarkably fast self-diffusion processes. As has been shown earlier, F ion dynamics in nanocrystalline, defect-rich BaF₂ is much higher than that in the coarse-grained counterpart BaF₂. The thermally metastable fluoride (Ba,Ca)F₂, which can be prepared by joint high-energy ball milling of the binary fluorides, exhibits even better ion transport properties. While long-range ion dynamics has been studied recently, less information is known about local ion hopping processes to which ¹⁹F nuclear magnetic resonance (NMR) spin-lattice relaxation is sensitive. The present paper aims at understanding ion dynamics in metastable, nanocrystalline (Ba,Ca)F₂ by correlating short-range ion hopping with long-range transport properties. Variable-temperature NMR line shapes clearly indicate fast and slow F spin reservoirs. Surprisingly, from an atomic-scale point of view increased ion dynamics at intermediate values of composition is reflected by increased absolute spin-lattice relaxation rates rather than by a distinct minimum in activation energy. Hence, the pre-factor of the underlying Arrhenius relation, which is determined by the number of mobile spins, the attempt frequency and entropy effects, is identified as the parameter that directly enhances short-range ion dynamics in metastable (Ba,Ca)F₂. Concerted ion migration could also play an important role to explain the anomalies seen in NMR spin-lattice relaxation.