1. Thermodynamic assessment mapThe combination of ΔS_solid and ΔH_solid of redox material candidates should fall in the shaded triangular region. The experimental data points (open scatters) of (ΔS_solid, ΔH_solid) were plotted for pure CeO₂/CeO_2-δ and 10% Samaria-doped Ce_0.9Sm_0.1O_1.95/Ce_0.9Sm_0.1O_1.95-δ redox pairs (δ=0.01-0.05)^[28,29]. The calculation results (solid scatters) in Section 2 were also plotted for these redox pairs (δ=0.03). Error bars represent standard deviations. Colourful figure is available on website

2. Variations of the favorable regions with operating conditions of the thermal reduction step (Reaction (2)) (a) Temperature. T_H=2000 and 1773 K; (b) Pressure. P_O2=0.101, 1.01 and 101 kPa. Other conditions in (a, b) are the same with those in Fig. 1; Colourful figure is available on website

3. Supercells for DFT+U calculations (a) Bulk CeO₂ supercell; (b) CeO₂ supercell with a single oxygen- vacancy defect; (c) CeO₂ supercell with a single polaron defect(The charge density of the polaron is also shown); (d) Sm-doped CeO₂ supercell (Methods in Supporting Materials)

4. Variations of $\Delta {{S}_{\text{V}_{\text{O}}^{\centerdot \centerdot }}}$, $2\Delta {{S}_{\text{C}{{{\text{{e}'}}}_{\text{Ce}}}}}$, ΔS_vib, and ΔS_solid with temperature Solid and dash curves are for CeO₂/CeO_2-δ and Ce_0.9Sm_0.1O_1.95/Ce_0.9Sm_0.1O_1.95-δ redox pairs (δ=0.03), respectively; Colourful figure is available on website

5. Illustration of a viable screening approach

S1. Phonon dispersion of a 10% samaria-doped ceria supercell comprising an oxygen vacancy

S2. Calculated variations of (a) α_V, (b) K_T and (c) α_V×K_T with temperatures