A formalism was developed for the first-principles calculation of the diffusion coefficient in solids which exhibited configurational disorder. The formalism involved the use of a local cluster expansion to describe the configurational dependence of activation barriers. The local cluster expansion served as a link between accurate first-principles calculations of the activation barriers and kinetic Monte Carlo simulations. By introducing a kinetically resolved activation barrier, it was shown that a cluster expansion for the thermodynamics of ionic disorder could be combined with a local cluster expansion in order to obtain the activation barrier for migration in any configuration. This ensured that, in kinetic Monte Carlo simulations, detailed balancing was maintained at all times and that kinetic quantities could be calculated in a properly equilibrated thermodynamic state. This formalism was applied to an investigation of Li diffusion in LixCoO2. A study of the activation barriers, within the local density approximation, showed that the migration mechanism and activation barriers depended strongly upon the local Li-vacancy arrangement around the migrating Li ion. By parametrizing the activation barriers using a local cluster expansion, and applying it to kinetic Monte Carlo simulations, it was predicted that Li diffusion in layered LixCoO2 was mediated by divacancies at all Li concentrations. Due to a strong concentration dependence of the activation barrier, the predicted diffusion coefficient varied by several orders of magnitude as a function of x.

First-Principles Theory of Ionic Diffusion with Non-Dilute Carriers. A.Van der Ven, G.Ceder, M.Asta, P.D.Tepesch: Physical Review B, 2001, 64[18], 184307 (17pp)