Lattice-gas-model approach to understanding the structures of lithium transition-metal oxides LiMO2

Many lithium transition-metal oxides (LiM${\mathrm{O}}_2$, M=Ti, V, Cr, Mn, Fe, Co, Ni) have structures made up of oxygen atoms occupying a cubic close-packed fcc or distorted fcc lattice, with cations occupying all octahedral interstices. The cation lattice is therefore also fcc and the arrangements of the cations on that lattice can be studied with a lattice-gas model. The ${\mathrm{LiNiO}}_2$, layered ${\mathrm{LiCoO}}_2$, spinel ${\mathrm{LiCoO}}_2$, ${\mathrm{Li}}_2$ ${\mathrm{Ti}}_2$ ${\mathrm{O}}_4$, and γ-${\mathrm{LiFeO}}_2$ structures are predicted for appropriate values of first- (${\mathit{J}}_1$) and second- (${\mathit{J}}_2$) neighbor interactions within such a model by analogy with binary-alloy materials having similar structures. We are able to assign allowable ranges for the interactions for each of the oxides above based on their position in the ${\mathit{J}}_{1\mathrm{-}}$ ${\mathit{J}}_{2\mathrm{-}}$T phase diagram. A surprising result is that the layered and spinel ${\mathrm{LiCoO}}_2$ structures are equally stable over the same wide range of ${\mathit{J}}_1$ and ${\mathit{J}}_2$, as predicted by mean-field and Monte Carlo results. Although ${\mathrm{LiMnO}}_2$ is structurally related to the above materials, the ${\mathrm{LiMnO}}_2$ structure is not stable for any choice of ${\mathit{J}}_1$, ${\mathit{J}}_2$, or T. Further neighbor interactions or anisotropies in the near-neighbor interactions are needed to stabilize the ${\mathrm{LiMnO}}_2$ structure.