## 5 Discussion and Conclusions
Concerning the Mn-based system with Cu addition, compositions ranging from x(Cu) = 0.4 to x(Cu) = 0.8 show a good reversibility, higher OSC and similar reaction enthalpy than pure Mn\({}_{2}\)O\({}_{3}\). The gap in temperature between the charge and discharge steps is especially reduced for x(Cu) = 0.4. When compared with literature data, the compositions with x(Cu) = 0.5 and x(Cu) = 0.8 also demonstrate suitable properties. Because higher Cu amounts imply increased effect of sintering and higher cost, the composition at x(Cu) = 0.8 should be thus avoided. From x(Cu) = 0.3, a good reaction reversibility is observed but a low OSC, whereas compositions with lower Cu content show low reaction reversibility due to the presence of the hausmannite phase. Similarly, the Fe addition shows a positive impact on Mn\({}_{2}\)O\({}_{3}\) cycling activity. Reversibility and stability over redox cycles are achieved with Fe addition above x(Fe) = 0.15, while the OSC remains stable. The enthalpy also remains unchanged (around 190 kJ/kg for x(Fe) between 0.15 and 0.50). Besides, the temperature gap betweenthe reduction and oxidation is decreased with the addition of iron above x(Fe) = 0.15. The low material re-oxidation at low Fe content (x(Fe) < 0.15) comes from the formation of the tetragonal spinel phase (hausmannite). The hausmannite phase is no more stable when increasing the Fe content, and heating leads to a transition into a cubic spinel phase with enhanced re-oxidation capabilities. In conclusion, the addition of iron to Co\({}_{3}\)O\({}_{4}\) and Mn\({}_{2}\)O\({}_{3}\) demonstrates the possible tuning of the systems temperatures to higher temperatures, while also reducing the hysteresis gap for both materials depending on the composition. The addition of Cu to Co\({}_{3}\)O\({}_{4}\) also shifts the transition temperature to lower temperature. The Mn\({}_{2}\)O\({}_{3}\) performance is greatly improved with the addition of a secondary metal in sufficient amounts to avoid the hausmannite phase formation during the heating. Although some compositions within Mn-Cu and Mn-Co systems are performant, Mn-Fe mixed oxides can exhibit high performance and be cost-effective due to the high availability of iron. Significant performance improvements can thus be achieved when considering mixed metal oxides and the limitations associated to both Co and Mn oxides (low re-oxidation yield, poor reversibility, large temperature gap between redox reactions, scarce availability and high cost) can be alleviated with secondary metal additives. The oxygen storage capacity and energy storage density stand out from a linear correlation that was unraveled for each type of binary oxide system, paving the way for the possible optimization of the heat storage capacity via the improvement of the oxygen exchange rates. In addition, thermodynamic modelling and equilibrium calculations were shown to be a relevant support for predicting reliably the behavior of mixed oxide systems and phase transitions. The results provided consistent transition temperatures, oxygen storage capacities and enthalpies. The application of suitable models provided new physical insights into the role of secondary metal addition on the redox properties' improvement of Co and Mn-based oxides. The calculations also highlighted that the CuFeO\({}_{2}\) stoichiometric compound might be a relevant candidate material. The identification of new suitable mixed oxides could become possible with the development of new thermodynamic models encompassing large multi-component systems, which then would allow the selection of different transition metals for tuning the redox properties of mixed metal oxides for TCES applications. Data curation, S.A. and L.C. ; Investigation, L.A., S.A. and L.C. ; Supervision, S.A.; Writing--original draft, L.A.; Writing--review and editing, S.A. and L.C. This research received no external funding. The authors declare no conflict of interest.