X-ray and electron diffraction studies of superlattices and long-range three-dimensional Na ordering in γ-NaxCoO2 (x=0.71 and 0.84)

We have recently demonstrated that x = 0.71 and 0.84 are the two most stable single-phase compounds above x = 0.5 in gamma-NaxCoO2 [G. J. Shu et al., Phys. Rev. B 76, 184115 (2007); F. C. Chou et al., Phys. Rev. Lett. 101, 127404 (2008)], and this structural investigation was performed on the single crystals and pulverized samples elaborately synthesized therein. Using the complementary techniques of x-ray and electron diffractions, we unambiguously established the existence of superlattices in x = 0.71 and 0.84, root 12a(p) X root 12a(p) X 3c(p), and root 13a(p) X root 13a(p) X root 3c(p) (a(p) and c(p), the hexagonal primitive cell parameters), respectively. The exceptionally large superlattice for x = 0.71 arises from the long-range three-dimensional sodium ordering, consisting of the spiral-like sodium-trimer chain screwing along c axis and being decorated with alternating truncated-triangle and honeycomb sodium sublattices in ab plane. The trimers in the neighboring sodium planes show corner-shared-like characteristics along the chain direction. A larger interplane separation of the trimers that was expected to minimize the trimer interlayer Coulomb repulsion was, however, not observed, and all Co ions in the superlattice show similar charge characteristics. In x = 0.84, the large superlattice is rather a result of the long-range ordering of sodium monomers both in ab plane and along c axis. The differences in the superlattice structure and the corresponding long-range sodium ordering between x = 0.71 and 0.84 may provide the critical information in understanding their distinctly different physical properties from structural aspects.