Formation energy of Cr/Al vacancies in spinel MgCr2O4 and MgAl2O4 by first-principles calculations -: art. no. 153103

First-principles pseudopotential calculations using plane-wave basis functions have been made to quantitatively evaluate the formation energy of Cr/Al vacancies in MgCr2O4 and MgAl2O4. Relaxation of atoms within the second nearest neighbor shell of the vacancy was taken into account in a 56-atom supercell. The formation energy was calculated as a function of the atomic chemical potential of Cr/Al. It shows negative values in the case of the oxidation limit of MgCr2O4, which is in good agreement with experimental results showing abundance of Cr vacancies when annealed in air. On the other hand, the formation energy of the Al vacancy in MgAl2O4 under the same condition is as large as 4.76 eV. This also well corresponds to the experimental fact that MgAl2O4 does not form the Al vacancy alone in air.