Thermodynamic relationships of the various phases, and enthalpies of formation, of the cubic (Pm\bar3m), tetragonal (P4mm), orthorhombic (Bmm2) and rhombohedral (R3m) phases of KNbO3 were calculated by 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. The formation energies of neutral vacancies in KNbO3 were quantitatively evaluated as functions of the atomic chemical potentials of the constituent elements by using the same procedure. Relaxation of the first- and second-nearest neighbor atoms around the vacancy was considered within a 40-atom super-cell.

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 O-rich and O-poor conditions. These results were in agreement with the empirical rule that B site defects in perovskite-type oxide did not exist. These results were explained in terms of the band structure of KNbO3.

Evaluations of Phases and Vacancy Formation Energies in KNbO3 by First-Principles Calculation. A.Shigemi, T.Wada: Japanese Journal of Applied Physics, 2005, 44[11], 8048-54