Formation of vacancies and copper substitutionals in potassium sodium niobate under various processing conditions

In the lead-free perovskite potassium sodium niobate, the thermodynamically preferred lattice sites and charge states of vacancies and substitutional Cu atoms for different processing conditions are determined theoretically from first principles. For that purpose, defect-formation energies of vacancies and Cu substitutionals in different charge states are calculated with the density-functional theory in the local- density approximation using norm-conserving pseudopotentials and a mixed-basis supercell approach. The formation energy of vacancies and the relative stability of Cu substitutionals on alkali and Nb sites in potassium sodium niobate are determined for oxygen-rich and oxygen- poor processing conditions and as function of the Fermi energy, and the densities of states are analyzed in terms of free charge carriers.