Crystal structure ofLixNi2−xO2and a lattice-gas model for the order-disorder transition

The crystal structure of ${\mathrm{Li}}_{\mathit{x}}$${\mathrm{Ni}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{O}}_{2}$ for 0\ensuremath{\le}x\ensuremath{\le}1 is reported. For x0.62, ${\mathrm{Li}}_{\mathit{x}}$${\mathrm{Ni}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{O}}_{2}$ has a disordered rocksalt structure. For 0.62\ensuremath{\le}x\ensuremath{\le}1.0, Li and Ni atoms segregate into Li-rich and Ni-rich layers normal to one of the four 〈111〉 directions in the cubic lattice. This breaks the cubic symmetry and an apparently continuous transition to a hexagonal phase occurs. At x=1, alternate cation layers are nearly pure Li and pure Ni. The degree of order is quantified by defining an order parameter \ensuremath{\eta}, which we take to be the difference in the Li composition of neighboring metal atom layers. Using x-ray diffraction and Rietveld profile refinement, we have measured \ensuremath{\eta} versus x. We model ${\mathrm{Li}}_{\mathit{x}}$${\mathrm{Ni}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{O}}_{2}$ as a lattice of oxygen atoms into which cations (either Li or Ni) can be inserted, subject to the constraint that the number of cations equals the number of oxygen atoms. Interactions between cations on nearest- and on next-nearest-neighbor sites are included, and the lattice-gas model is solved with use of mean-field and Monte Carlo methods. We find that the nearest-neighbor interaction is not sensitive to the observed ordering and that we can describe the experimental variation of \ensuremath{\eta} versus x for an appropriate choice of the next-nearest-neighbor interaction.