Sodium-Ion Diffusion in Alluaudite-Type Na2+dFe2-d/2(SO4)3 Cathodes
Here we analyze pathways for the mobile Na+ from literature structure and from our MD simulations using our bond valence pathway method.[2,3] This modelling of pathways for mobile alkali ions as regions of low site energy E(A) has been demonstrated to be a simple and reliable way of identifying transport pathways in local structure models, provided that the local structure model captures the essential structural features. Bond valence parameters are taken from our softBV database as published in . In accordance to the suggestions in  the material is essentially a one-dimensional conductor with the lowest activation energy of ca 0.3 eV for transport in the ca. half-occupied Na(3) channels. The same empirical BV parameters bA-X, R0(A-X) used in this pathway analysis are also used as force-field parameters for the generation of disordered local structure models by MD simulation of a 918 atoms 2x2x3 supercell of composition Na108Fe90(SO4)144, which corresponds to the fully discharged state factoring in the experimentally observed sodium excess and iron deficiency. The MD simulations yield a low activation energy of 0.26 eV for 1-dimensional transport along the c-direction in partially occupied Na(3) channels. With increasing temperature Na(1) can act as a source for an increased number of mobile ions in the Na(3) channels and Na(2) become mobile in separate partially occupied channels leading to a high temperature activation energy of 0.68 eV (see Fig. 1).
For the favourable experimental performance of the material it is however important that the Fe-deficiency considerable lowers the activation energy for cross-linking in-between the fast-ion conducting channels to below 1 eV, which will be crucial to prevent the vulnerability to blocking of the one dimensional sodium transport channel by defects.
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