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

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Abstract
The atomic and electronic structures of Nb impurities in doped perovskite 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 matrix.