Ceria (CeO
2) has a fluorite structure, which is favorable for the diffusion of lattice O atoms and oxygen vacancy formation. Yang et al.
[17] investigated the structural modifications induced by the oxygen vacancy formation on CeO
2 using the spin-polarized PW91 functional, and found that the structural modifications followed a pattern in which cerium (Ce) atoms near to vacancy sites migrated away from the defect sites, while the next-nearest vacancy sites of the lattice O atoms contracted in the region. Vanadium oxide (V
2O
5), which was considered to be most effective oxygen carrier for the selective oxidation of CH
4 to formaldehyde (HCHO), was widely studied recently
[18]. Sauer and Dobler
[19] investigated the oxygen vacancies on V
2O
5 surface using the 2L cluster model and the B3LYP functional, and reported an oxygen vacancy formation energy of 1.17 eV. This indicated that the lattice O atoms on V
2O
5 surface are easy to release due to the low oxygen vacancy formation energy. In addition to ceria and vanadium oxide, iron oxide is an important oxygen carrier for CH
4 CLR, in which it converts CH
4 to syngas via partial oxidation
. In this process, the adsorbed CH
x radicals on the surface bind to lattice O atoms transferred from the bulk of the iron oxide, resulting in the formation of oxygen vacancies. The CH
4 partial oxidation reaction on the iron oxide oxygen carrier is a complex process due to the stepwise reduction: Fe
2O
3 → Fe
3O
4 → FeO → Fe. Fan et al. [
20,
21] investigated the characteristics of the multiple oxidation states of iron, and developed a countercurrent moving bed reactor system for their application in chemical looping system. Fe
2O
3, Fe
3O
4, and FeO have similar close-packed oxygen structures, thus the redox transitions between each phase are faster than that between FeO and Fe [
22,
23]. Cheng et al.
[24] studied oxygen vacancies in these oxidation phases using the atomistic thermodynamics appraoch and DFT calculations, and found that the formation energies of oxygen vacancies on the surface are lower than that of oxygen vacancies in the subsurface (Table 2 and Fig. 3), which significantly affects the phase transition of iron oxide oxygen carriers.