Semi-empirical calculations of the Nb-ion positions in doped KTaO₃ crystals

The atomic and electronic structures of Nb impurities in doped perovskite KTaO₃ crystals are calculated using the semi-empirical quantum chemical method of the intermediate neglect of the differential overlap (INDO) and a supercell model. When seven Ta ions are replaced by seven Nb ions, the latter clearly demonstrate self-ordering effects which are related to the experimentally observed impurity-induced phase transition. A single Nb impurity reveals an off-centre displacement which is very close to that found in XAFS experiments. The relevant energy gain is very small, approximately 0.0375 eV, which is much smaller than the Nb-clustering energy gain (0.12 eV). These results led us to the conclusion that such self-ordered high-symmetry seven-ion clusters are stable in a KTaO₃ matrix.