LiNi1-yCoyO2 (NC) was studied first. Atom-spin coupled cluster expansion (CE) based on the density functional theory (DFT) calculations was performed to find stable atom-spin configurations of NC. The cationic mixing was accounted for by assuming that each cationic lattice site can be occupied by any of Li, Co, or Ni. The result predicted three stable configurations at zero temperature: LiNi0.8Co0.2O2, LiNi0.67Co0.33O2, and LiNi0.5Co0.5O2, as well as several more configurations at finite temperature, especially at y < 1/3, which agreed to the experimental observation on the range of solid-solution phase NC. Interestingly, the configurations of solid-solution phase NC had Ni ions in Li-layer (Ni-defects). We also found that that the solid-solution phase NC became less dominant when the Co content increased, which suggested that Co substitution might have suppressed the formation of Ni-defects.
DFT calculations with HSE06 functional were additionally performed to investigate the mechanism of Co substitution associated with the suppression of Ni-defects formation. The oxidation state of each ion was obtained by analyzing the magnetic moment and agreed well with experimental observations. We found that a Ni-defect tended to be Ni2+ by oxidizing one Ni ion in TM layer to Ni4+ when they formed the nearest neighbor pair. In this case, the antiferromagnetic spin distribution was possible for all pairs of paramagnetic Ni ions (Ni2+ and Ni3+), which implies the configurations with Ni-defects (Ni ions in Li layer) are thermodynamically more favorable than non-defective configurations where such the antiferromagnetic spin distribution is not possible due to magnetic frustration. When Co is substitued for Ni, the oxidation state of Co is Co3+, which is diamagnetic like Ni4+. Then the antiferromagnetic spin distribution for all paramagnetic ions is also possible even without creating Ni-defects and we will demonstrate that the most ideal case is when y=1/3.
We performed further calculations to find stable NCA configurations by replacing a portion of Co in NC with Al. By comparing NC and NCA, the effect of Al-doping to the structural stability will be also discussed.