Large-scale modelling of the phase transitions in KTa_1-xNb_xO₃ perovskite solid solutions

We use quantum chemical method of the intermediate neglect of the differential overlap (INDO) based on the Hartree-Fock formalism for a large-scale modelling of the atomic and electronic structure of KNb_xTa_1-xO₃ (KTN) perovskite solid solutions. Results for periodic defect models (large unit cell) of 40 and 320 atoms are compared with 135-atom INDO cluster calculations. Periodic Nb impurities in KTaO₃ reveal clear off-center displacement beginning with the smallest calculated concentrations, so does an isolated Nb impurity in a cluster INDO calculation. The magnitude of Nb off-center displacement is close to the X-ray-absorption fine-structure observation (0.27 a.u.). In contrast, Ta impurities in KNbO₃ always remain on-center, due to higher ionicity of Ta as compared to Nb atom. Using the calculated energy gain due to the off-center displacements of Nb atoms for several concentrations of Nb in KTN, we construct the non-empirical Ginzburg-Landau-type functional for the excess energy. The coefficients of this functional are concentration dependent. This dependence allows to define the type of the concentration-induced phase transition in KTaO₃ alloyed by Nb.