Fig. 1: Local-structure dependence of cation vacancy formation in (Mg0.2Ni0.2Co0.2Cu0.2Zn0.2)O and comparison with binary oxides.

a, b The DFT-calculated formation energies of cation vacancies in (Mg0.2Ni0.2Co0.2Cu0.2Zn0.2)O as a function of a local strain relative to the average ESO bond length and b local strain relative to the bond length in corresponding binary oxide. The formation energies of cation vacancies decrease with increasing local strain relative to binary oxide. c The average formation energy of cation vacancy in ESO as a function of the average cation-oxygen bond length in corresponding binary oxides showing that the formation of cation vacancy is determined by the shift of the cation-oxygen bond distance from its equilibrium position in the binary oxides. d The comparison between the cation vacancy formation energy for binary oxides and the average cation vacancy formation energy for the ESO.