Evaluations of phases and vacancy formation energies in KNbO3 by first-principles calculation

In order to clarify thermodynamic relationships of the various phases of KNbO3, enthalpies of formation for cubic (Pm3m), tetragonal (p4mm), orthorhombic (Bmm2) and rhombohedral (R3m) phases of KNbO3 were calculated using a plane-wave pseudopotential method within a density functional formalism. The KNbO3 phase with the lowest symmetry was found to have the lowest enthalpy of formation. Moreover, we quantitatively evaluated the formation energies of neutral vacancies in KNbO3 as functions of the atomic chemical potentials of the constituent elements by the use of the same procedure. Relaxation of the first- and the second-neighbor atoms around the vacancy was considered in a 40-atom supercell. The formation energy of a K vacancy was found to be the lowest under an oxidizing atmosphere and that of an O vacancy was found to be the lowest under a reducing atmosphere. The formation energy of a Nb vacancy was the highest under both oxygen-rich and -poor conditions. These results are in agreement with the empirical rule that B site-defects in perovskite-type oxide do not exist. These results are discussed on the basis of the band structure of KNbO3.