Incommensurately modulated crystal structure of a⁰ (O⁰3)-type sodium cobalt oxide Na_xCoO₂ (x ~ 0.78)

A single-phase sample of α⁰ (O⁰3)-type layered sodium cobalt oxide Na_xCoO₂ (x ~ 0.78) was prepared and its incommensurately modulated crystal structure was analyzed using the (3+1)-dimensional superspace approach to the powder neutron diffraction data. The crystal structure of the cobaltate is accurately described based on the superspace group C2/m(α0γ)00, wherein the positions of Na atoms are most significantly modulated in the monoclinic a direction to form an ordered arrangement. Such a displacive modulation causes a quasi-periodic shift of Na atoms from the centers of the NaO₆ polyhedra between undulated CoO₂ sheets, changing the form of the NaO₆ polyhedron from an octahedral coordination (O) to a trigonal prismatic (P) one, via an intermediate capped trigonal prismatic NaO₇ coordination (C). At the positions where the Na atoms are most significantly shifted, the neighboring Na atoms are located at almost touching distances. However, the occupation factor of Na atoms becomes zero at such positions, yielding Na-deficient sites V_Na, sandwiched either between C and P, or C and C-type polyhedra.