Cation- and vacancy-ordering in Li_xCoO_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 LiCoO_2 and Li-vacancy/Co ordering in CoO_2. We find: (i) A ground state search of the space of substitutional cation configurations yields the (layered) CuPt structure as the lowest-energy state in the octahedral system LiCoO_2 (and CoO_2), in agreement with the experimentally observed phase. (ii) Finite temperature calculations predict that the solid-state order- disorder transitions for LiCoO_2 and CoO_2 occur at temperatures (~5100 K and ~4400 K, respectively) much higher than melting, thus making these transitions experimentally inaccessible. (iii) The energy of the reaction E(LiCoO_2) - E(CoO_2) - E(Li) gives the average battery voltage V of a Li_xCoO_2/Li cell. Searching the space of configurations for large average voltages, we find that CuPt (a monolayer <111> superlattice) has a high voltage (V=3.78 V), but that this could be increased by cation randomization (V=3.99 V), partial disordering (V=3.86 V), or by forming a 2-layer Li_2Co_2O_4 superlattice along <111> (V=4.90 V).