Ab initio study of sodium ordering in Na_0.75CoO₂ and its relation to Co³⁺∕Co⁴⁺ charge ordering

Charge ordering and Na-vacancy ordering in Na_0.75CoO₂ are investigated using first-principles electronic structure methods within the generalized gradient approximation (GGA) and GGA+U approximations. We find that Na ordering is determined not only by a competition between different Na site energies and Na⁺-Na⁺ repulsion, but also by the Co⁴⁺-Na⁺ repulsion when charge localization occurs. We predict a ground-state structure for Na_0.75CoO₂ in good agreement with experimental transmission electron microscopy and neutron-diffraction data and find that Co³⁺∕Co⁴⁺ charge ordering is strongly coupled to the Na-vacancy ordering.