The theory of the local structure of solid solutions of oxides with Perovskite structure: Example of Pb 2 (FeNb)O 6
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STRUCTURE OF CRYSTALS
The Theory of the Local Structure of Solid Solutions of Oxides with Perovskite Structure: Example of Pb2(FeNb)O6 K. Yu. Gufana, R. V. Kolesovaa, M. Yu. Gurevicha, and Yu. M. Gufanb a
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Southern State University, Rostov-on-Don, 344006 Russia Institute of Physics, Southern State University, Rostov-on-Don, Russia e-mail: [email protected] Received February 20, 2008
Abstract—A method for constructing local-structure models for complex oxides with averaged perovskitetype structures has been developed. The constructed models take into account the probabilities of distributing different cations over sites belonging to the corresponding sublattices. The accepted approach to interpreting diffraction patterns is based on the same hypotheses as the commonly used one. As an example, a local-structure model is constructed for disordered PbFe1/2Nb1/2O3 and, on the basis of this model, the diffraction patterns of this single crystal, disordered with respect to Fe and Nb sites at T = 433 K, have been interpreted. PACS numbers: 61.50.Ah DOI: 10.1134/S1063774509010131
INTRODUCTION
important that different local structure models lead to approximately the same R factor (the discrepancy factor between experimental diffraction patterns of solid solutions and the results of model calculations). Generally, better agreement (a decrease in the R factor) is obtained by introducing additional fitting parameters of the theory. As an illustration, we can consider the result of [2, 3] and [6–9]. In [2, 3], the method for improving the R factor by increasing the number of theory parameters was illustrated by the example of PbFe1/2Nb1/2O3 and PbIn1/2Nb1/2O3. In [6–9], the local structure of PbMg1/3Nb1/3O3 was refined by introducing additional parameters. In [14–16], a general method for determining the local structure of OPS solid solutions was proposed. This method was justified in the form of simple but rigorous considerations within the Fermi statistics and an assumption about the leading role of effective pair interactions of the nearest cations in the formation of crystal field symmetry at each lattice site. The essence of the method is the construction of a sequence of models, where each subsequent model takes into account all configurations of the nearest cationic environment that were considered in the previous model and additionally takes into account the configurations with a lower probability of implementing at a given solution concentration. The use of the rigorous considerations of the probability theory made it possible to consider not only disordered but also partially ordered solid solutions [17, 18]. The method proposed is convenient for revealing the local structure of specific OPSs because this approach, based on the probability theory in combination with the approximation of effective pair interactions and the knowledge of the solid solution global symmetry,
Solid solutions of multication oxides with perovskite structure (OPSs) are widely applied in modern techniques as active media for piezoelectr
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