Fig. 2. Examination of phase reconstruction behavior for Pr_0.5Ba_0.5−xSr_xFeO_3−δ material under reducing condition.

a–c Phase reconstruction tendency of Pr_0.5Ba_0.5−xSr_xFeO_3−δ material (x = 0, 0.1, 0.2, 0.25, 0.3, 0.4, and 0.5). a In-situ powder X-ray diffraction (XRD) patterns of Pr_0.5Ba_0.2Sr_0.3FeO_3−δ (A-PBSF30) under H₂ environment. b Proposed phase diagram of Pr_0.5Ba_0.5−xSr_xFeO_3−δ material (x = 0, 0.1, 0.2, 0.25, 0.3, 0.4, and 0.5) in H₂ environment as functions of reduction temperature and Sr²⁺ concentration from in-situ XRD measurements. The phases for region I (gray), II (green), III (blue), and IV (red) are simple perovskite, simple perovskite + Pr oxide + Fe metal, simple perovskite + Ruddlesden-Popper (R-P) perovskite + Fe metal, and R-P perovskite + Fe metal, respectively. c Schematic illustration of the above phase diagram. d, e Density functional theory (DFT) calculations. Calculated profiles of d the relative total energy required for the phase reconstruction from simple perovskite to R-P perovskite and e oxygen vacancy formation energies and co-segregation energies as a function of Sr²⁺ concentration in four models.