# Replacement of Cobalt in Lithium-Rich Layered Oxides by n-Doping: A DFT Study
## 1 Introduction  
Lithium-ion batteries are a power source widely used for numerous applications, including electric vehicles (EVs), computer and consumer electronic products, and energy storage devices for renewable and smart grids [1, 2, 3, 4]. Current cathode materials used in Li-ion batteries, as LiCoO\({}_{2}\) and LiM\({}_{2}\)O\({}_{4}\), suffer from lower-than-desired capacity and structural instability during cycling, which limits their lifetime [5, 6, 7, 8, 9]. Over-stoichiometric Li-rich nickel-manganese- cobalt layered oxides (LRLO, lithium-rich layered oxides) are a family of promising positive electrode materials with a general formula Li[Li\({}_{3}\)M\({}_{1-x}\)]O\({}_{2}\) (with M= transition metal blend) characterized by an over-stoichiometric lithium content, thus implying the simultaneous presence in the same crystallographic site of a mixture of transition metals and lithium atoms (TM atomic sites) [7, 10, 11, 12]. These materials have a sluggish and ambiguous crystal structure [5, 13, 14, 15], where two similar layered lattices are integrated [16]. The first structure crystallizes in a Li\({}_{2}\)MnO\({}_{3}\) monoclinic prototype (mC24, easily rewritten as Li[Li\({}_{1/3}\)Mn\({}_{2/3}\)]O\({}_{2}\); Li in 2c and 4 hwith y = 0.6606; O in 4i with x = 0.2189 and z = 0.2273, and 8j with x = 0.254 y = 0.32119 and z = 0.2233; TM in 2b and 4g with y = 0.16708) with a C2/m symmetry, whereas the second one crystallizes in a \(\alpha\)-NaFeO\({}_{2}\) -prototype and adopts an R3\({}^{-}\) m symmetry (hR12, Li in 3b, TM in 3a and O in 6c with x = 0.7458) [17; 18; 19]. Both lattices stack a repeated motif constituted by four parallel layers containing Li, O, TM, and O atomic species (where TM stands for a blend of transition metal ions and lithium ions), respectively, and differ by the local mutual arrangements of the TMO\({}_{6}\) and LiO\({}_{6}\) octahedra, as well as in the layers' stacking sequence. A full randomization among transition metals and lithium ions on the TM layers, and stacking faults along the layer-piling direction make the two hR12 and a mC24 structures indistinguishable [20], thus suggesting that local fluctuations in the defect concentrations can induce the coexistence of the two symmetries. Overall, the compresence of hexagonal and monoclinic symmetries in LRLO has been proved experimentally but an effective phase separation is debatable [17; 18; 19]. As an example, [PERSON] et al. proposed, based on experimental evidence, that Li[Li\({}_{0.2}\)Mn\({}_{0.6}\)Ni\({}_{0.2}\)]O\({}_{2}\) is a single-phase hR12 solid solution with a partial long range lithium ordering, leading to a mC24-like superlattice [21]. On the other hand, [PERSON] et al. proved that the same layered material with stoichiometry Li[Li\({}_{0.2}\)Mn\({}_{0.6}\)Ni\({}_{0.2}\)]O\({}_{2}\) is a nanoscale composite cathode where hR12 and mC24 domains coexist [22]. An interesting hypothesis has been proven by [PERSON] et al., who investigated the long range and local structure of Li\({}_{1.2}\)Co\({}_{0.4}\)Mn\({}_{0.4}\)O\({}_{2}\), suggesting that the LRLO material is constituted by a dendritic microstructure of hR12 and mC24 phases where Mn\({}^{4+}\) and Co\({}^{3+}\) are preferentially segregated in monoclinic and hexagonal lattices, respectively [16]. LRLO materials with a variety of compositions can exchange large specific capacity in lithium half cells (-250 mAh g\({}^{-1}\)) at high working potentials (3.5-3.9 V vs. Li) [7; 10; 11; 12], thanks to the combination of the redox reactions of transition metals, e.g., Mn\({}^{3+/4+}\), Ni\({}^{2+/3+/4+}\), Co\({}^{3+/4+}\), etc., and the anionic oxo/peroxo redox activity (i.e., (O\({}_{2}\)\({}^{4-}\))/(O\({}_{2}\)\({}^{(-)}\))) [23; 24]. Unfortunately, the oxygen-mediated lithium exchange mechanism promotes the inevitable release of gaseous O\({}_{2}\) at high potentials [25], and the formation of oxygen vacancies.