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Regularization methods for the analysis of EXAFS spectra of chemical complexes

Regularization methods for the analysis of EXAFS spectra of chemical complexes The analysis of EXAFS data aimed at extracting information on the local atomic structure of materials is discussed. To identify the structure of interest, one has to solve a system of Fredholm integral equations of the first kind. The situation is considered in which three functions, that characterize the structure under study, are to be determined from one equation. In practice, in this case a nonuniqueness arises in the reconstruction of the unknown functions within a prescribed accuracy, so that additional information has to be used. For a broad range of materials, the functions that are reconstructed possess a rather specific form; namely, these functions appear to be a sum of several narrow peaks that can be approximated by δ functions. This qualitative information about the functions is non-classical. The proposed new analysis procedure is based on the classical theory of ill-posed problems and on using the available non-classical information. The efficiency of the algorithms proposed is illustrated by applying them to model and experimental data of a test compound consisting of uranium, silicon and oxygen, whose structure was previously identified by other authors. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and Ill-Posed Problems de Gruyter

Regularization methods for the analysis of EXAFS spectra of chemical complexes

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References (25)

Publisher
de Gruyter
Copyright
© de Gruyter
ISSN
0928-0219
eISSN
1569-3945
DOI
10.1515/jiip.2007.041
Publisher site
See Article on Publisher Site

Abstract

The analysis of EXAFS data aimed at extracting information on the local atomic structure of materials is discussed. To identify the structure of interest, one has to solve a system of Fredholm integral equations of the first kind. The situation is considered in which three functions, that characterize the structure under study, are to be determined from one equation. In practice, in this case a nonuniqueness arises in the reconstruction of the unknown functions within a prescribed accuracy, so that additional information has to be used. For a broad range of materials, the functions that are reconstructed possess a rather specific form; namely, these functions appear to be a sum of several narrow peaks that can be approximated by δ functions. This qualitative information about the functions is non-classical. The proposed new analysis procedure is based on the classical theory of ill-posed problems and on using the available non-classical information. The efficiency of the algorithms proposed is illustrated by applying them to model and experimental data of a test compound consisting of uranium, silicon and oxygen, whose structure was previously identified by other authors.

Journal

Journal of Inverse and Ill-Posed Problemsde Gruyter

Published: Dec 15, 2007

Keywords: Ill-posed problem; equation of the first kind; regularization; EXAFS spectra; local atomic structure; uranium complexes

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