Temperature-concentration phase diagram of P2-NaxCoO2 from first-principles calculations

Temperature-concentration phase diagrams for NaxCoO2 (0.5 <= x <= 1) are obtained by combining density functional theory (DFT) in the generalized gradient approximation (GGA) and in the GGA with Hubbard U correction (GGA+U) with the cluster expansion and Monte Carlo simulation technique. In the GGA, holes are delocalized over the Co layer, while in GGA+U the charges on the Co layer completely localize, forming distinct Co3+ and Co4+ cations. The leading interactions in GGA are long-range in-plane electrostatics and relaxation effects, whereas in GGA+U Co-Co interactions dominate. Comparison of ground states, c-lattice parameter, and Na1/Na2 ratio with experimental results consistently suggests that GGA is a better approximation for 0.5 <= x <= 0.8.