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RESEARCH PRODUCT

Quantum chemical modelling of perovskite solid solutions

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In line with our previous study (Eglitis R I et al 1998 J. Phys.: Condens. Matter 10 6271) for a single Nb impurity and Nb clusters in KTaO3 we present here the results of calculations for a series of perovskite KNbx Ta 1−x O3 (KTN) solid solutions (x = 0, 0.125, 0.25, 0.75, and 1). The quantum chemical method of the intermediate neglect of the differential overlap (INDO) combined with the large unit cell (LUC) periodic model is used. According to the INDO calculations, Nb impurity becomes off-centre in KTaO3 already at the lowest studied Nb concentration. Its off-centre displacement is in a good agreement with XAFS measurements. We compare our results with previous FP-LMTO calculations. Perovskite-type oxides such as KNbO3 ,K TaO3 and their solid solutions KNbxTa 1−xO3 (KTN) have numerous technological applications (2). As the temperature decreases, KNbO3 goes through three ferroelectric phase transitions, whereas KTaO3 remains in a non-polar phase down to low temperatures. However, the introduction of several percent of Nb or Li impurities brings KTaO3 to the ferroelectric state (3-5). This raises a question about the nature of the phase transition in KTN. X-ray photoelectron spectroscopy (XPS) has shown (6) that Ta ions are replaced in KTN by the Nb ions, whereas XAFS measurements (5) have additionally demonstrated that the Nb sits in an off-centre position. Its (111) displacement is 0.145 A at 70 K, and changes by less than 20% as the temperature increases to room temperature. We are aware of the only theoretical calculation of the KTN solid solution made using an ab initio full-potential LMTO method (7). In this study, the critical Nb concentration found for the off- centre Nb displacement in KTaO3, responsible for the ferroelectric phase transition, was too high (x = 0.25), and was in contradiction with the experiment (5). The purpose of this Letter is the calculation of the Nb off-centre (111) and (100) displacements in KTN solid solutions at a series of Nb impurity concentrations (x = 0, 0.125, 0.25, 0.75 and 1). We have used the semi-empirical, quantum chemical method of the intermediate neglect of the differential overlap (INDO) (8). The modification of the standard INDO method for ionic solids is described in detail in (9-11). This method is based on the Hartree-Fock formalism and allows self-consistent calculations of the atomic and electronic structure of pure and defective crystals. Recently the INDO method has been used in the study of bulk solids and defects in many oxide (9-14) and semiconductor (15,16) materials. In particular, this method has been applied to the study of phase transitions and frozen phonons in pure KNbO3 (17), pure and Li-doped KTaO3 (18) and point defects—F-centres and hole polarons—in KNbO3 (19- 21). More details about the INDO method and the relevant program CLUSTERD are given in references (8-11). With the help of this code it is possible to perform both cluster and periodic-system calculations, as well as to carry out automated geometry optimization. In our KTN solid solution calculations we used a periodic model, the so-called large unit cell (LUC) model (22). Its idea is to perform the electronic structure calculations for an extended unit cell