composition contains Tb which likely increases the total oxygen storage capacity of the material. The maximum oxygen content of both bulk samples decreases only subtly when increasing the heating and cooling rates even if the particles are much larger (Supp. Fig. ) with much longer diffusion distances. This is highly surprising when comparing with the difference in kinetics of oxidation of bulk vs nanocrystalline materials reported for perovskite La1-xSrxMnO3. To investigate the effect of Ti-doping, the HEO1-n and HEO2-n samples were studied further and their oxygen stoichiometry under different heating and cooling rates is shown in Figure . HEO1-n, without Ti 4+ , shows a small oxygen absorption at 500 °C during heating, highlighted in the inset of Figure (a), which may stem from oxidation of Tb 3+ to Tb 4+ . During heating, HEO1-n shows less oxygen absorption with increasing heating rates and shows a visible hysteresis in oxygen content during heating and cooling, with a width of ~20 °C. The width of the hysteresis does not change with heating rate, as observed for single R cation hexagonal manganites. The temperature of maximum oxygen content during heating is subtly shifted upwards for both samples with increasing heating rates. In contrast, the Ti-doped HEO1-n sample shows no thermal hysteresis in oxygen content, in accordance with previous findings for Ti 4+ doped RMnO3. The oxygen absorption of HEO2-n is less sensitive to faster heating rates than for HEO1-n. expansion. The relationship between lattice parameters and oxidation is further supported by XANES spectra revealing oxidation of Mn 3+ to Mn 4+ and of Tb 3+ to Tb 4+ (Supp. Fig. ). Lattice parameters a and c of HEO1n and HEO2-n from high-temperature XRD measurements are presented in Figure . The diffractograms for the HEO1-n sample were refined using the R3c space group, while P63cm was used for HEO2-n. Both samples show a large contraction along the c axis below 400 °C in O2, which is a signature of oxygen absorption. For HEO1-n, the largest changes in the a and c parameters occur between 325 °C and 350 °C, in accordance with the narrow temperature interval for oxygen absorption and release found from TGA (Figure ). A small hysteresis in the a parameter is visible at ~150 °C, which may indicate some oxidation below the bulk oxidation temperature ~300 °C. This could be due to oxidation of a fraction of Tb 3+ to Tb 4+ at ~150 °C. Only thermal expansion is observed upon heating and cooling HEO1-n in N2 atmosphere.