Cation- and vacancy-ordering in LiₓCoO₂

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Using a combination of first-principles total energies, a cluster expansion technique, and Monte Carlo simulations, we have studied the Li/Co ordering in LiCoO₂ and Li-vacancy/Co ordering in CoO₂. 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 LiCoO₂ (and CoO₂), in agreement with the experimentally observed phase. (ii) Finite temperature calculations predict that the solid-state order- disorder transitions for LiCoO₂ and CoO₂ 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(LiCoO₂) - E(CoO₂) - E(Li) gives the average battery voltage V of a LiₓCoO₂/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 Li₂Co₂O₄ superlattice along <111> (V=4.90 V).