Quantification of Honeycomb Number-Type Stacking Faults: Application to Na3Ni2BiO6 Cathodes for Na-Ion Batteries.

Ordered and disordered samples of honeycomb-lattice Na3Ni2BiO6 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 mA h/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 investigations showed that the primary difference between the ordered and disordered samples is the amount of number-type 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 high-angle annular dark-field scanning transmission electron microscopy (STEM-HAADF) imaging studies. By the use of 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 nonrandom 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 is strongly correlated with the degree of ordering in the samples. The present results are broadly applicable to other honeycomb-lattice systems, including Li2MnO3 and related Li-excess cathode compositions.