## 2 Materials and Methods  
The reaction kinetics of the iron oxide samples were determined by the setup, depicted schematically in Figure 2, in which a hydrogen conform thermo-gravimetric analyzer device (STA 449-F3, Netzsch) builds the main component. The accuracy of the TGA device in weighting the samples amounts to \(\pm\)0.1 ug, while the accuracy in adjusting the sample temperature is better than \(\pm\)0.3 \({}^{\circ}\)C. For the reduction reaction, a gas mixture of N\({}_{2}\) and H\({}_{2}\) in different concentrations can be prepared by the applied mass flow controllers (MFCs) and fed into the TGA device, where the iron oxide pellets are placed. By means of the MFC, the concentrations can be adjusted by the flow of the reacting gas to \(\pm\)0.5% in the range of 0 to 250 mL/min. The oxidation of the previously reduced samples takes place with a H\({}_{2}\)O-N\({}_{2}\) mixture. Steam is produced in a dedicated steam generator (DV2 MK, ADROP). With a resolution of 0.1 g/h, a maximum steam flow rate of 25 g/h with an accuracy of 1% of the final value can be achieved. A vacuum pump is applied to evacuate the experimental setup after each experiment as a safety precaution. The measured values of the TGA system are stored locally on the measuring PC with a sampling rate of 200 points/min. To investigate the structure of the samples, a tomographic examination before and after the TGA experiments is performed using a \(\upmu\)CT (v\(|\)tome\(|\)x s 240/180, GE Sensing & Inspection Technologies GmbH). The investigated samples, based on the recipe of [38], were acquired from the German company, Nacompex GmbH, Karl-Marx-Damm 85, 15526 Bad Saarow, Germany. The almost spherical sample consists of a mixture of 90% hematite (Fe\({}_{2}\)O\({}_{3}\)) and 10% support material of high-alumina cement [40]. After mixing and shaping processes, the pellets were dried for 28 days under ambient conditions, before they were sintered at 950 \({}^{\circ}\)C for 3 h.  
During the test campaign (see Figure 2), the reaction kinetics were measured at the gas mixture flow rates of 250 mL/min. The molar concentration of the reducing and oxidizing gas mixtures was changed according to Table 2 for the different redox runs (ro\({}_{1}\)-ro\({}_{4}\)). Figure 1: Schematic of a renewable energy storage and supply system based on the redox concept. (**a**) Charging phase and (**b**) discharging phase (inspired by [39]). The redox reactions can take place between 500 \({}^{\circ}\)C and 900 \({}^{\circ}\)C, with the risk of sintering the iron composites at higher temperatures and the associated damage of the redox performance. Accordingly, the upper temperature limit at which sintering can take place was tested here. The reduction/oxidation processes were carried out at isothermal conditions of 700 \({}^{\circ}\)C, 800 \({}^{\circ}\)C, or 900 \({}^{\circ}\)C. Additionally, two sizes of the iron oxide pellets were investigated, the first sample (S1) with \(d_{\rm s1}\approx 12.7\) mm and a mass of \(m_{\rm s1}=3658.5\) mg, as well as the second sample (S2) with \(d_{\rm s2}\approx 9.8\) mm and a mass of \(m_{\rm s2}=1388.4\) mg. The oxidation atmosphere of 80/20 vol.% results from the maximum allowed steam concentration in the TGA reactor. At higher concentrations, undesired condensation may take place inside the weighing section of the TGA. In order to evaluate the redox reaction kinetics, the instantaneous reduction/oxidation fraction \(\gamma(t)\) is defined by Equation (4) as the instantaneous mass change of the sample relative to its initial mass, divided by the final (or maximum) mass change reached after the given reaction time. \[\gamma(t)=\frac{m(t)-m_{\rm min}}{m_{\rm max}-m_{\rm min}} \tag{4}\]  
with \(m(t)\) as the sample weight at time \(t\), \(m_{\rm min}\) as the starting or smallest weight, and \(m_{\rm max}\) as the highest or final weight during the respective reduction/oxidation phase.