KEYWORDS honeycomb lattice, sodium ion batteries, Na 3 Ni 2 BiO 6 , Li 2 MnO 3 , stacking faults. 2 ABSTRACT: Ordered and disordered samples of honeycomb-lattice Na 3 Ni 2 BiO 6 were investigated as cathodes for Na-ion batteries and it was determined that the ordered sample exhibits better electrochemical performance with a specific capacity of 104 mAh/g delivered at plateaus of 3.5 and 3.2 V (vs. Na + /Na) with minimal capacity fade during extended cycling. Advanced imaging and diffraction

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... stigations showed that the primary difference between ordered and disordered samples is the amount of numbertype stacking faults associated with the three possible centering choices for each honeycomb layer. A labeling scheme for assigning the number position of honeycomb layers is described, and it is shown that the translational shift vectors between layers provide the simplest method for classifying different repeat patterns. It is demonstrated that the number position of honeycomb layers can be directly determined in STEM-HAADF imaging studies. Using fault models derived from STEM studies, it is shown that both the sharp, symmetric subcell peaks and the broad, asymmetric superstructure peaks in powder diffraction patterns can be quantitatively modeled. About 20% of the layers in the ordered monoclinic sample are faulted in a non-random manner, while the disordered sample stacking is not fully random but instead contains about 4% monoclinic order. Furthermore, it is shown that the ordered sample has a series of higher-order superstructure peaks associated with 6-, 9-, 12-, and 15-layer periods whose existence is transiently driven by the presence of long-range strain that is an inherent consequence of the synthesis mechanism revealed through the present diffraction and imaging studies. This strain is closely associated with a monoclinic shear that can be directly calculated from cell lattice parameters and which is strongly correlated with the degree of ordering in samples. The present results are broadly applicable to other honeycomb-lattice systems including Li 2 MnO 3 and related Li-excess cathode compositions.