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

Abstract

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 BaF 2 is much higher than that in the coarse-grained counterpart BaF 2 . The thermally metastable fluoride (Ba,Ca)F 2 , 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 19 F nuclear magnetic resonance (NMR) spin-lattice relaxation is sensitive. The present paper aims at understanding ion dynamics in metastable, nanocrystalline (Ba,Ca)F 2 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 compo-sition 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)F 2 . Concerted ion migration could also play an important role to explain the anomalies seen in NMR spin-lattice relaxation.

Substitutional disorder: structure and ion dynamics of the argyrodites Li6PS5Cl, Li6PS5Br and Li6PS5I

“…Without any strong site preference of the Li ions they are expected to jump quickly between the local minima of such a heterogeneous, i.e., non-uniformly shaped, potential landscape. Such a situation, sometimes also connected to geometric frustration, is very similar to F diffusion in the recently investigated system (Ba,Ca)F 2 , 41,42 Li diffusion in Li 7 La 3 Zr 2 O 12 oxides 43 and Na diffusion in some closo-borates. 44 While this situation might be the origin for the high conductivity in Li 6 PS 5 Br and Li 6 PS 5 Cl, for the I analogue it seems to incompletely describe the real situation as for Li 6 PS 5 I relatively low ion conductivities are reported.…”

“…The pre-factor is proportional to the attempt frequencies n a , the number of effective charge carriers n Li and an entropy term. 42 Besides the effect of n a , trapping effects in Li 6 PS 5 I, because of a very low intercage jump rate, might reduce N for this sample. If we assume similar n a values for Li 6 PS 5 Cl and Li 6 PS 5 Br, entropy effects could serve as an explanation for the change in s 0 .…”

F anion dynamics in cation-mixed nanocrystalline LaF3: SrF2

“…This increase tells us that, while E a remains almost constant for compositions above x ¼ 0:03, the further enhancement of r DC is driven by r 0 rather than by E a . A similar observation has been quite recently reported for mechanosynthesized samples of Ba 1Àx Ca x F 2 [32].…”

“…The activation energy of tysonite-type La 0:9 Ba 0:1 F 2:9 , which has been studied in detail in [10,37], is comparable to that of the Sr analogue. Just for comparison, ion transport in La 0:9 Ba 0:1 F 2:9 [31] turned out to be clearly higher than that in metastable and nanocrystalline Ba 0:5 Ca 0:5 F 2 [32], which crystallizes with cubic symmetry and which has been studied earlier by some of us [15,32]. For the sake of clarity, for most of the samples only the values referring to P1 have been included in Fig.…”

Fluorine Translational Anion Dynamics in Nanocrystalline Ceramics: SrF2-YF3 Solid Solutions

“…The change in E a from 0.88 eV to 0.81 eV is accompanied by a significant increase of the pre-exponential factor σ 0 in σ DC T = σ 0 exp(−E a /(k B T)), see also [50]. While log(σ 0 /(S cm −1 K)) of SrF 2 amounts to 4.1, it increases to 5.3 for Sr 0.9 Y 0.1 F 2.1 .…”