Cluster Expansion Framework for the Sr(Ti_1–xFe_x)O_3–x/2 (0 < x < 1) Mixed Ionic Electronic Conductor: Properties Based on Realistic Configurations

Several mixed ionic/electronic conductors (MIECs) used as fuel or electrolysis cell electrodes may be thought of as solid solutions of perovskite oxides and ordered oxygen vacancy compounds. For example, the model MIEC SrTi_1–xFe_xO_3–x/2+δ (STF) can be described as a mixture of the perovskite SrTiO₃ and the brownmillerite Sr₂Fe₂O₅ that can accommodate some degree of oxygen off-stoichiometry δ. The large configurational space for these nondilute, disordered mixtures has hindered atomic scale modeling, limiting in-depth understanding and predictive analysis. We present a cluster expansion framework to describe the energetics of the disordered STF system within the full solid solution composition space Sr­(Ti_1–xFe_x)­O_3–x/2, 0 < x < 1, δ = 0. Cluster expansion Monte Carlo (CEMC) simulations are performed to identify low-energy configurations and to investigate the origin and degree of lattice disorder. Using realistic configurations obtained from CEMC, the electronic structure, band gap, and optical properties of STF and their sensitivity to the stoichiometry are examined and compared to those of hypothetical ordered structures and special quasirandom structures. The predicted evolution of the band gap and optical absorption with composition is consistent with the experiment. Analysis of the electronic structure elucidates that electronic transport within the mixture benefits from the simultaneous presence of Fe/Ti disorder on the B cation sublattice and a tendency for oxygen vacancies to cluster around Fe atoms. The modeling framework adopted here for the SrTiO₃/Sr₂Fe₂O₅ mixture can be extended to other MIEC materials.