Regularization methods for the analysis of EXAFS spectra of chemical complexes

Journal of Inverse and Ill-Posed Problems

Volumn 15, Issue 8, 2007, Pages 767-783

  Ageev, A L ^a   Korshunov, M E ^a   Reich, T Ye ^b   Reich, T ^b   Moll, H ^c  

^a INSTITUTE OF MATHEMATICS AND MECHANICS   (Russian Federation)

^b JOHANNES GUTENBERG UNIVERSITY   (Germany)

^c INSTITUTE OF ION BEAM PHYSICS AND MATERIALS RESEARCH   (Germany)

Author keywords

Equation of the first kind; EXAFS spectra; Ill posed problem; Local atomic structure; Regularization; Uranium complexes

Indexed keywords

EID: 38649107057     PISSN: 09280219     EISSN: None     Source Type: Journal    
DOI: 10.1515/JIIP.2007.041     Document Type: Article

References (25)

1. A. N. Tikhonov and V. Ya. Arsenin, Solution Methods for Ill-Posed Problems (in Russian). Nauka, Moscow, 1974.
2. V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Linear Ill-Posed Problems and its Applications (in Russian). Nauka, Moscow, 1978.
3. V. P. Beskachko, N. A. Vatolin, V. F. Ukhov, and B. R. Gel'chinskii, Calculation of radial distribution function for a liquid from diffraction data using a regularization method. Dokl. Akad. Nauk SSSR 245 (1979), 863-865.
4. R. James, Optical Principles of X-Ray Diffraction (in Russian). Inostr. Liter., Moscow, 1950.
5. Yu. A. Babanov, R. Sh. Sadykova, V. R Shvetsov, et al., Anomalous X-ray scattering study of amorphous alloys. Nucl. Instrum. Meth. A282 (1989), 646-650.
6. D. E. Sayers, E. A. Stern, and F. W. Lytle, New technique for investigating noncrystalline structures: Fourier analysis of the extended X-ray absorption fine structure. Phys. Rev. Let. 27 (1971), 1204-1207.
7. E. A. Stern, Theory of the extended x-ray absorption fine structure. Phys. Rev. B10 (1974), 3027-3037.
8. V. V. Vasin and A. L. Ageev, Ill-Posed Problems with A Priori Information. VSP, Utrecht, 1995.
9. Yu. A. Babanov, N. V. Ershov, V. R. Shvetsov, et al., A new method of determining partial radial distribution functions for amorphous alloys. 1. The quasibinary problem. J. Cryst. Sol. 79, (1986), 1-17.
10. 2Zr amorphous alloy. Z. Naturforsch. 47A, (1992), 1191-1196.
11. V. R. Shvetsov, A. L. Ageev, Yu. A. Babanov, et al., A method for examining the structure of binary amorphous alloys from x-ray scattering and absorption data. USSR Acad. Sci. Ural Scientific Center. Inst. of Mathematics and Mechanics. Sverdlovsk, 33 (1989). (Dep. in VINITI 13.01.89, N 661-B89).
12. Yu. A. Babanov, V. V. Vasin, A. L. Ageev, and N. V. Ershov, A new interpretation of EXAFS spectra in real space. 1. General formalism. Phys. Stat. Sol. (B) 105 (1981), 747-754.
13. N. V. Ershov, A. L. Ageev, V. V. Vasin, and Yu. A. Babanov, A new interpretation of EXAFS spectra in real space. 2. A comparison of the regularization technique with the Fourier transformation method. Phys. Stat. Sol. (B) 108 (1981), 103-111.
14. G. Khelashvili and G. Bunker, Practical regularization methods for analysis of EXAFS spectra. J. Synchrotron Rad. 6 (1999), 271-273. (Pubitemid 129488938)
15. K. Yamaguchi, Y. Ito, T. Mukoyama, et al., The regularization of the basic X-ray absorption spectrum fine structure equation via the wavelet-Galerkin method. J. Phys. B: At. Mol. Opt. Phys. 32 (1999), 1393-1408.
16. A. L. Ageev, T. V. Antonova, T. Ye. Reich, et al., Method of separating functionals for the determination of local atomic structure. Mathematical modeling 16 (2004), 81-92.
17. Yu. A. Babanov, T. Ye. Zayarnaya, T. Reich, and H. Funke, EXAFS study of U(VI) compounds: A new approach to data analysis. In: Workshop Proceedings "Speciation, Techniques and Facilities for Radioactive Materials at Synchrotron Light Sources", Grenoble, France, Sept., 2000. OECD Publications, Paris, 2002, 105-116.
18. 2O. In: Workshop Proceedings "Speciation, Techniques and Facilities for Radioactive Materials at Synchrotron Light Sources", Grenoble, France, Sept. 2000. OECD Publications, Paris, 2002, 359-366.
19. 2O. J. Nucl. Mater. 227 (1995), 40-49.
20. W. Matz, N. Schell, G. Bernhard, et al., ROBL - a CRG beamline for radiochemistry and materials research at the ESRF. J. Synchrotron Rad. 6 (1999), 1076-1085. (Pubitemid 129489146)
21. M. Newville, P. Livins, Y. Yacoby, et al., Near-edge X-ray absorption fine structure of Pb: A comparison of theory and experiment. Phys. Rev. B47 (1993), 14126-14131.
22. A. L. Ankudinov, C. E. Bouldin, J. J. Rehr, et al., Parallel calculation of electron multiple scattering using Lanczos algorithms. Phys. Rev. B65 (2002), 104107/1-104107/11.
23. D. E. Sayers and B. A. Bunker, Data analysis. X-ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and XANES. (D. C. Koningsberger and R. Prins, eds.), 211-253. John Wiley & Sons, New York, 1988.
24. 2O. Acta Cryst. C48 (1992), 1-4.
25. 2. Dokl. Akad. Nauk SSSR 246 (1979), 93-96.