Cation and vacancy ordering in Li x CoO 2

Using a combination of first-principles total energies, a cluster expansion technique, and Monte Carlo simulations, we have studied the Li/Co ordering in ${\mathrm{LiCoO}}_{2}$ and Li-vacancy/Co ordering in the $\ensuremath{\square}{\mathrm{CoO}}_{2}$. We find: (i) A ground-state search of the space of substitutional cation configurations yields the CuPt structure as the lowest-energy state in the octahedral system ${\mathrm{LiCoO}}_{2}$ (and $\ensuremath{\square}{\mathrm{CoO}}_{2})$, in agreement with the experimentally observed phase. (ii) Finite-temperature calculations predict that the solid-state order-disorder transitions for ${\mathrm{LiCoO}}_{2}$ and $\ensuremath{\square}{\mathrm{CoO}}_{2}$ occur at temperatures $(\ensuremath{\sim}5100 \mathrm{K}$ and $\ensuremath{\sim}4400 \mathrm{K}$, respectively) much higher than melting, thus making these transitions experimentally inaccessible. (iii) The energy of the reaction ${E}_{\mathrm{tot}}(\ensuremath{\sigma},\mathrm{Li}\mathrm{Co}{\mathrm{O}}_{2})\ensuremath{-}{E}_{\mathrm{tot}}(\ensuremath{\sigma},\ensuremath{\square}\mathrm{Co}{\mathrm{O}}_{2})\ensuremath{-}{E}_{\mathrm{tot}}(\mathrm{L}\mathrm{i},\mathrm{}\mathrm{bcc})$ gives the average battery voltage $\overline{V}$ of a ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}/\mathrm{Li}$ cell for the cathode in the structure $\ensuremath{\sigma}$. Searching the space of configurations $\ensuremath{\sigma}$ for large average voltages, we find that $\ensuremath{\sigma}=\mathrm{CuPt}$ [a monolayer $〈111〉$ superlattice] has a high voltage $(\overline{V}=3.78 \mathrm{V})$, but that this could be increased by cation randomization $(\overline{V}=3.99 \mathrm{V})$, by partial disordering $(\overline{V}=3.86 \mathrm{V})$, or by forming a two-layer ${\mathrm{Li}}_{2}{\mathrm{Co}}_{2}{\mathrm{O}}_{4}$ superlattice along $〈111〉$ $(\overline{V}=4.90 \mathrm{V})$.