Sodium Ion Ordering in double-layered and triple-layered Na$_{x}$CoO$_{2}$

The layered sodium cobalt oxide Na$_{x}$CoO$_{2}$ is studied by electron diffraction for a wide range of sodium contents, 0.15$<$x$<$0.75. This range in compositions is obtained by removal of Na by various methods for the starting materials Na$_{0.7}$CoO$_{2}$, and Na$_{1.0}$CoO$_{2 }$ The structure of Na$_{x}$CoO$_{2}$ is based the stacking of triangular O-Co-O layers with Na planes. The Co atoms are in edge-sharing CoO$_{6}$ octahedra. For the starting compound Na$_{0.7}$CoO$_{2}$, the Na$^{+}$ ions are in a trigonal prismatic coordination whereas for Na$_{1.0}$CoO$_{2 }$ the Na$^{+}$ coordination is octahedral. Prismatic coordination occurs when the close packed oxygen planes directly adjacent to the Na plane have the same projection into the basal plane (A-Na-A), whereas octahedral coordination of Na occurs when the directly adjacent oxygen planes have different projections (A-Na-B) into the basal plane. Due to this difference in stacking the a axis is about 1.08 nm and 1.65 nm for Na$_{0.7}$CoO$_{2}$ and Na$_{1.0}$CoO$_{2 }$respectively. For Na$_{0.7}$CoO$_{2}$ as well as Na$_{1.0}$CoO$_{2 }$a series of superstructures are observed, which can be explained with ordered Na ion-Na vacancy superlattices. The structural principle for some of the observed ordering schemes, particularly near x=0.5, is, surprisingly, the presence of lines of Na ions and vacancies rather than simply maximized Na-Na separations. With Na$_{0.7}$CoO$_{2}$ as starting material, the most strongly developed superlattice is found for the composition Na$_{0.5}$CoO$_{2}$. With Na$_{1,0}$CoO$_{2}$ as starting material, the most strongly developed superlattice is found for the compositions Na$_{0.75}$CoO$_{2 }$and Na$_{0.5}$CoO$_{2}$. In particular the superstructure Na$_{0.75}$CoO$_{2 }$of is very complicated. \newline \newline In collaboration with M.L. Foo, Department of Chemistry and Princeton Materials Institute, Princeton University, Princeton, NJ 08544 USA; Q. Xu and V. Kumar, National Centre for HREM, Department of Nanoscience, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands ; L. Viciu, Department of Chemistry and Princeton Materials Institute, Princeton University; Q. Huang, NIST Center for Neutron Research, NIST, Gaithersburg, MD 20899; and R.J. Cava, Department of Chemistry and Princeton Materials Institute, Princeton University.