Fig. 2: Dependence of the oxygen-vacancy formation energy on the local configuration and structural distortion in (Mg_0.2Ni_0.2Co_0.2Cu_0.2Zn_0.2)O.

a DFT-calculated formation energy of oxygen vacancy (V_O) as a function of first-nearest-neighbor (1NN) shell composition. Each column represents a different oxygen atom in the cell and the cation combination for each 1NN shell is illustrated by the colored bars in the background. The data is ordered along the horizontal axis according to E^f from our linear regression analysis. b The contribution of each 1NN cation to the oxygen vacancy formation, obtained by fitting the DFT-calculated V_O formation energies to the number of each 1NN cation with the linear-regression scheme. The formation energy of V_O strongly depends on the local atomic configuration: it increases with an increasing number of Mg and Ni 1NN cations, and it decreases with more Cu 1NN cations. c Schematic of the octahedral arrangement of O in ESO, where the six 1NN cation sites are determined by the combination of the five cation species. Different combinations of cations lead to different local bond-angle deviations, Δθ (°) d The values of the average M₁-O-M₂ bond-angle deviation from 90°, where M₁ and M₂ indicate metal cations in the ESO. Cu (Mg) contributes the most (least) to the distortion of bond angle. e The formation energy of V_O as a function of average bond-angle deviation and average bond strain. The local structural distortion, determined by local bond strain and bond-angle deviation, decreases the formation energy of V_O’s and increases their formation probability.