# Replacement of Cobalt in Lithium-Rich Layered Oxides by n-Doping: A DFT Study
## 3 Results  
### Crystal Structures of Cobalt Doped LRLO  
Despite the absence of constraints during structural relaxations, all supercells keep the hexagonal symmetry without any distortion and the layered structure, in line with the experimental evidence [54; 55; 56; 57]. Thus, starting from each optimized supercell, we evaluated the hexagonal hR12-apparent lattice parameters for all cobalt concentrations, using the \([5\times 2\times 5/3]^{-1}\) inverse supercell transformation. In the Table 1, we compare the calculated values with those available in the literature (reported in parentheses) [54]. The cell parameters agree within 1.5%, with respect to experiments for both LNM and LNMC4 stoichiometries, thus confirming the accuracy of our modeling. Overall, the substitution of cobalt in the supercell leads to an isotropic expansion of both a and c cell parameters, and, therefore, of the cell volume: this trend is in excellent quantitative agreement with the available experimental literature [55; 56]. Remarkably, the volume increase observed passing from LNMC12 to LNMC8 and LNMC4 does not occur in passing from LNMC4 to the Co-free LNM supercell, where a slight cell volume shrinking of \(-0.06\%\) is observed. Despite the LNMC4 stoichiometry having been studied for application in Li-ion batteries [57], we lack an experimental confirmation of this last structural peculiarity. Figure 1: Optimized geometry and volume structures supercell \(5\times 2\times 5/3\) containing 200 atoms. On the left, Li\({}_{1.2}\)Ni\({}_{0.14}\)Mn\({}_{0.54}\)Co\({}_{0.12}\)O\({}_{2}\) (LNMC12). In the middle, Li\({}_{1.2}\)Ni\({}_{0.16}\)Mn\({}_{0.56}\)Co\({}_{0.08}\)O\({}_{2}\) (LNMC08), and Li\({}_{1.2}\)Ni\({}_{0.18}\)Mn\({}_{0.58}\)Co\({}_{0.04}\)O\({}_{2}\) (LNMC04). On the right Li\({}_{1.2}\)Ni\({}_{0.2}\)Mn\({}_{0.6}\)O\({}_{2}\) (LNM). Color code: Li light green; LiTM orange; Ni grey; Mn purple; Co light blue; and O red. Focusing on the alteration of the layers stacking with the cobalt content, we evaluated the changes in the O-(Li)-O and O-(TM)-O, oxygen-oxygen interlayer average distance, and the out-of-plane corrugations of the various atomic planes. The O-(TM)-O distances are 2.142, 2.147, 2.151, and 2.151 A for the LNMC12, LNMC8, LNMC4, and LNM compositions, respectively, whereas the corresponding O-(Li)-O are 2.671, 2.678, 2.685, and 2.682 A. Thus, both O-(Li)-O and O-(TM)-O interlayer mean distances increase in parallel with the substitution of Co and p-doping of the lattice. The O-(TM)-O expansion can be an indirect clue to the increase of the Ni\({}^{2+}\)/Ni\({}^{3+}\)/Mn\({}^{3+}\) concentrations originating from the larger Ni content, and a possible presence of Jahn-Teller defects (see below for more details); in fact, all these ions are larger than Mn\({}^{4+}\) and Co\({}^{3+}\)[59]. On the other hand, the origin of the expansion of the O-(Li)-O distance is less clear. Overall, this effect is expected to be beneficial for the transport of Li\({}^{+}\) ions across the layer, thanks to the less effective coordination originating from the longer (and weaker) Li-O bonds, while removing Co from the lattice. Turning to the buckling of the atomic layers, these inevitable corrugations are due to the heterogeneity and fluctuation of the local composition. To evaluate the structural disorder emerging at atomic level in the LRLO structures, we calculated the displacement factors, \(\sigma^{2}\) for all fractional atomic position, with respect to a \(5\times 2\times 5/3\) supercell built from the ordered LiCoO2 hR12 lattice.