Effective energy landscapes for mobile ions in solid electrolytes
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Effective energy landscapes for mobile ions in solid electrolytes Stefan Adams GZG, Kristallographie, Universität Göttingen, Goldschmidtstr. 1, 37077 Göttingen, Germany ABSTRACT Bond valence mismatch landscapes may serve as simple models of the effective energy landscapes for mobile ions in solid electrolytes. Thereby they provide a tool to identify the ion transport mechanism and allow to predict the activation energy of the ionic conduction. Accounting for the mass dependence of the conversion from the BV mismatch into an activation energy scale yields a correlation that holds for different types of mobile cations. While in most cases the analysis of bond valence mismatch landscapes is consistent with the ion transport mechanism derived from experimental or other computational evidence, the presumed prototype of trivalent cation conductors Sc2(WO4)3 is discussed as an example, where the BV analysis of transport pathways suggests that the interpretation of previous experimental investigations has to be reconsidered. Both bond valence calculations and molecular dynamics simulations suggests that the most probable mobile species in stoichiometric Sc2(WO4)3 is neither Sc3+ nor individual O2- but the complex divalent anion WO42-. THE BOND VALENCE METHOD The bond valence (BV) concept is commonly used in chemistry, e.g. to judge the plausibility of atom positions in crystal structures from empirical relationships between the length RA-X and the valence sA-X = exp[(R 0 -RA-X) / b] of a bond as sites where the "bond valence sum" (1) V( A) sA X X
for interactions of A with all adjacent counterions X equals the oxidation state Vid(A) (c.f. [1,2]). In contrast to conventional BV parameters that usually treat b as a universal constant and use only R0 as an empirical parameter, our softBV parameters [2,3] are designed to account for differences in the softness of bonds between different atom pairs by an appropriate choice of b. Moreover, they include the weak contributions from higher coordination shells up to a cut-off distance Rcut-off in the range 5 to 8 Å , while conventional BV parameters are generally based on the assumption that only the first coordination shell contributes to V. Besides the classical range of applications for BV parameters in crystal chemistry the modified BV approach proved to be a useful tool for the prediction of various properties of inorganic solids from their structure. As an example from our recent work [4], Fig. 1 displays predictions of static solid-state NMR quantities such as the chemical shift cs. For a wide range of alkali oxyacid salts cs rises with increasing shift parameter A:
A
O
The effect of a particular oxide ion on
s Na O
M
bM1 O
V Na CN Na cs(Na)
CN O
(2)
is weighted by the individual bond valence sNa-O.
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Figure 1. Correlation between the experimental 23Na-NMR chemical shift cs (with respect to 1M NaCl solutions) and the shift parameter A as defined in equation 2. (silicates: , phosphates: , other inorganic oxyacid salts: ). Redrawn after [4]. Similarly,
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