A method of separating functionals for extracting of a local atomic structure

A. L. Ageev ; T. V. Antonova ; T. Y. Reich ; C. Hennig

Matematičeskoe modelirovanie, Tome 16 (2004) no. 10, pp. 81-92.

Résumé

A determination of local atomic structure (partial distribution functions) by EXAFS experimental method are consedered. For finding partial distribution functions a system of integral equations of the first kind is solved. The situation is such that there is one experiment, but three functions are unknown. In this case the normal solution has no a physical sense. For wide class of materials additional for physical solution is presented: the solution is a sum of $\delta$-shaped peaks and number of this peaks is small. First, $\delta$-shaped peaks are replaced by the $\delta$-functions. The number of the $\delta$-functions, support and values by means of some heuristic methods and the new method of separating functionals are determined. Second, the extracted information is used for modified of Tihonov's method. For the compound of U, As and О the model and experimental data are processed.

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