# Replacement of Cobalt in Lithium-Rich Layered Oxides by n-Doping: A DFT Study
## 3 Results
### Phase Stability of LRLO  
The thermodynamic stability of the LRLO supercells have been evaluated by calculating the energy of formation from the ternary ordered Li-metal oxides. Considering a generic LRLO material with stoichiometry Li\({}_{1,2}\)Ni\({}_{0,2-x/2}\)Mn\({}_{0,6-x/2}\)Co\({}_{x}\)O\({}_{2}\), we evaluated the thermodynamics of the following general reaction for the four supercells:  
\[\frac{2}{5}\text{Li}_{2}\text{MnO}_{3}+\left(\frac{1}{5}-\frac{x}{2}\right) \text{LiMnO}_{2}+\left(\frac{1}{5}-\frac{x}{2}\right)\text{LiNiO}_{2}+\text{ xLiCoO}_{2}\rightarrow\text{Li}_{1,2}\text{Ni}_{0,2-\frac{x}{2}}\text{Mo}_{0,6-\frac{x}{2}} \text{Co}_{x}\text{O}_{2} \tag{2}\]  
The corresponding equation for the formation energy at 0K, \(\Delta\)formE0K, of a an LRLO with fixed x and general formula Li\({}_{1,2}\)Ni\({}_{0,2-x/2}\)Mn\({}_{0,6-x/2}\)Co\({}_{x}\)O\({}_{2}\) (LNMCx) is given by Equation (3):  
\[\Delta_{\text{form}}\text{E}_{0K}(2)=\text{E}_{\text{tot,LNMCx}}-\left(0.4 \text{E}_{\text{tot,Li2 MnO3}}+0.2-\text{x}/2\text{E}_{\text{tot,LiMnO2}}+0.2- \text{x}/2\text{E}_{\text{tot,LiNiO2}}+\text{x}\text{E}_{\text{tot,LiCoO2}}\right) \tag{3}\]  
where x is the stoichiometric coefficient (0.12, 0.08, 0.04, and 0), and E\({}_{\text{tot}}\) values are the electronic total energies calculated at the DFT+U level of each species. The thermodynamic properties of Li\({}_{2}\)MnO\({}_{3}\), LiMnO\({}_{2}\), LiCoO\({}_{2}\), and LiNiO\({}_{2}\) have been evaluated by us in a previous work at the same level of theory [46]. We can approximate formation energy at 0K with the standard formation enthalpy at 0 K, i.e., \(\Delta_{\text{form}}\text{E}_{0K}\)\(\Delta_{\text{form}}\)\(\text{H}^{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\  
The calculated \(\Delta_{\rm form}\)H\({}^{\circ}\)0K, \(\Delta_{\rm form}\)S\({}^{\circ}\)0K and \(\Delta_{\rm form}\)G\({}^{\circ}\)298K for all stoichiometries are listed in Table 2: Gibbs free energy of formation of all LRLO are reported in the SI (Table S6) as a function of the temperature. The formation Gibbs energies of the LRLO phases are more negative while decreasing Co content, despite the parallel increase in the structural disorder, i.e., atomic displacement, and electronic disorder, i.e., large concentration of JT defects. This trend is driven by enthalpy and is likely due to the formation of stronger chemical bonds in the structure, whereas the stabilization from the configurational entropy unavoidably decreases while reducing the amount of cobalt. Thus, the p-doping of the LRLO lattice, induced by the simultaneous substitution of Co atoms with Mn and Ni, alters the stability of the disordered lattice. To shed further light on the LNMCx phase diagram, we evaluated the excess standard Gibbs energy of formation of the intermediate phases using the data in Table S6. The excess standard Gibbs energy of formation at temperature T for the phase j containing x moles of Co in the Li1.2 Ni0.2-x/2 Mn0.6-x/2 CoAO2 formula (\(\Delta_{excess}\)G\({}^{\circ}_{\rm T}(j_{x})\)) is defined by the Equation (6):  
\[\Delta_{excess}\)G\({}^{\circ}_{\rm T}(j_{x}) = \Delta_{f}G^{\circ}_{\rm T}(j_{x})-\frac{x}{0.12}\Delta_{f}G^{ \circ}_{\rm T}(LNMC12)-\frac{0.12-x}{0.12}\Delta_{f}G^{\circ}_{\rm T}(LNM) \tag{6}\]  
The \(\Delta_{excess}\)G\({}^{\circ}_{\rm T}(j_{x})\) represents the relative thermodynamic stability of the LNMC08 and LNMC04 phases, compared to mixtures of LNM and LNMC12. The values of the \(\Delta_{excess}\)G\({}^{\circ}_{\rm T}(j_{x})\) are shown in the form of a thermodynamic phase diagram in the Figure 6 for four different temperatures, namely 298.15, 500, 1000, and 1500 K.  
Remarkably, the \(\Delta_{excess}\)G\({}^{\circ}_{\rm T}(j_{x})\) is positive at all temperatures for both LNMC08 and LNMC04; this trend suggests that the formation of a single phase LRLO in this composition