Aplicação da teoria dinâmica na resolução de estruturas

Abstract

X-ray diffraction is a powerful technique, widely used for the study of materials. The kinematical theory was used initially to explain the diffraction results, however, some experiments have shown a flaw in this theory. The dynamical theory appeared as a more general theory, based on electromagnetism and the interaction between waves within matter, which are neglected by kinematical theory. In this work, at first, a careful analysis was made of the differences between the two theories, for this, the methodology of a perfect prototype crystal, developed by Miranda and Sasaki, was used. In this methodology, parameters such as structural factor, unit cell volume, Bragg angle, are varied to obtain the largest possible number of real structures. As a result, we arrive at an expression that determines the limit of application of the kinematical theory, based on the extinction length and the thickness of the crystal. Once an application limit has been found for the kinematical theory, we modify the conventional structure resolution methodology, where we replace the kinematical theory with the dynamical theory of X-ray diffraction. The developed methodology was compared with conventional structure resolution methodologies (SHELX). For this study, data obtained in the literature were used, such as the crystals of RbBrF4, simulated data, such as ZnFe2O4, KH2PO4 and Bi2Fe4O9 and data measured in the synchrotron, the crystals of SrTiO4 and Si. The results show that the structures solved by both methodologies are equivalent for small crystals, however, the greater the thickness of the crystal, it is necessary to use corrections of a dynamical nature (extinction corrections) in the kinematical methodology, to solve the structures. The use of this correction fails, when the crystals are thick, making it necessary to use the methodology based purely on dynamical theory. Another point that was observed, analyzed in this work, was the correction factor of the asymmetric reflections for the intensity. This parameter appears naturally in the development of dynamical theory, its effect becomes quite expressive the greater the thickness of the crystal. The result showed that if the crystal thickness is a few tens of micrometers, the kinematical theory is valid only if we take into account the corrections by dynamical theory. However for crystals of hundreds of micrometers, the kinematical theory completely loses its validity, even if it uses dynamical corrections. In this case, it is necessary to use completely dynamical structure refinement programs.