Ab initiostudy of sodium ordering inNa0.75CoO2and its relation toCo3+∕Co4+charge ordering

Abstract

Charge ordering and Na-vacancy ordering in ${\mathrm{Na}}_{0.75}\mathrm{Co}{\mathrm{O}}_{2}$ are investigated using first-principles electronic structure methods within the generalized gradient approximation (GGA) and $\mathrm{GGA}+U$ approximations. We find that Na ordering is determined not only by a competition between different Na site energies and ${\mathrm{Na}}^{+}\ensuremath{-}{\mathrm{Na}}^{+}$ repulsion, but also by the ${\mathrm{Co}}^{4+}\ensuremath{-}{\mathrm{Na}}^{+}$ repulsion when charge localization occurs. We predict a ground-state structure for ${\mathrm{Na}}_{0.75}\mathrm{Co}{\mathrm{O}}_{2}$ in good agreement with experimental transmission electron microscopy and neutron-diffraction data and find that ${\mathrm{Co}}^{3+}∕{\mathrm{Co}}^{4+}$ charge ordering is strongly coupled to the Na-vacancy ordering.