[en] The problems of the regularization parameter and estimation of the error of the hyperfine interaction (HFI) parameter distribution restored in processing Moessbauer spectra are discussed. The Tikhonov's regularization method is used as a method for solving the inverse problem. We consider the case when errors in the experimental data are due to statistics only. A procedure for estimating the distribution error, based on singular value decomposition (SVD) - decomposition with some additional information on the exact solution, is proposed. A direct simulation of the error is carried out for some model with the known HFI parameter distribution. The results obtained agree well with the error estimation calculated using SVD. As an example, the proposed procedure is applied to the Moessbauer spectrum of the non-ordered Fe-Si alloy

[en] Generalizing the regular solution algorithm the inverse problem of Moessbauer spectroscopy is proposed for obtaining the distribution function of the hyperfine interaction parameters from the spectrum. By model calculations it is shown that the algorithm is stable with respect to statistical noise and errors in the spectrum parameters. It is noticed that the algorithm is applicable strictly only to objects which properties can be described by a continuous distribution of one of the hyperfine interaction parameters. The condition of the normalization is introduced as an additional criterion of the correctness of the solution. There is a possibility of investigating the spectra with paramagnetic components. The algorithm may be applied to an analysis of both, poorly resolved and well resolved spectra. (author)

[en] It is shown that the radial atomic distribution function for disordered systems can, in priciple, be determined from the oscillating extended fine structure of X-ray absorption spectra using the regular algorithms of solution of incorrect problems. The radial atomic distribution function for Fe⁸⁰B²⁰, obtained from experimental EXAFS data and corresponding to the results of diffraction studies, is presented. (author)

[en] The capabilities of the regularization method in the problem of extracting the radial atomic distribution function from X-ray scattering data for amorphous and liquid metals are studied. The results are compared to the data obtained by the conventional Fourier transformation procedure, with reference to the examples of liquid Ga and Fe₈₀B₂₀ metallic glass. (author)

[en] The capabilities of the regularization method in the problem of the determination of partial structure factors and partial radial distribution functions using anomalous X-ray scattering data are discussed. The results are compared to the data obtained by conventional procedures (Keating approach, Fourier transformation method). (orig.)

No abstract available

[en] An algorithm for correcting parameters in the kernel of an integral equation is proposed. This problem appears in particular in the estimation of the distribution of a hyperfine parameter from Moessbauer spectra. The problem is solved within the framework of Tikhonov variational method. The computational scheme and an experimental example are presented. (author). 1 tab., 1 fig., 7 refs

[en] Highlights: •A depth-resolved method for investigation of the local atomic structure is proposed. •We combined data of X-ray reflectivity and angle-depended EXAFS. •The regularization method and Levenberg–Marquardt (L–M) algorithm are used. •Mathematical algorithm comprises three process steps. •This general mathematical scheme cannot be interrupted. - Abstract: A depth-resolved method for the investigation of the local atomic structure by combining data of X-ray reflectivity and angle-resolved EXAFS is proposed. The solution of the problem can be divided into three stages: 1) determination of the element concentration profile with the depth z from X-ray reflectivity data, 2) determination of the X-ray fluorescence emission spectrum of the element i absorption coefficient ${\mu }_i^a$(z,E) as a function of depth and photon energy E using the angle-resolved EXAFS data $I_i^f\left(E,{\vartheta }_l\right),$ 3) determination of partial correlation functions $g_{\mathit{ij}}\left(z,r\right)$as a function of depth from ${\mu }_i\left(z,E\right)$. All stages of the proposed method are demonstrated on a model example of a multilayer nanoheterostructure Cr/Fe/Cr/Al₂O₃. Three partial pair correlation functions are obtained. A modified Levenberg-Marquardt algorithm and a regularization method are applied.

[en] The uptake mechanism of plutonium by kaolinite was investigated by applying X-ray absorption spectroscopy to batch sorption samples (total Pu concentrations 1 and 10 μM; 4 g kaolinite/L in 0.1 M NaClO₄; 1 ≤ pH ≤ 9; presence and absence of ambient CO₂). For XAFS measurements, one sample was prepared from a Pu(III) solution at pH 6 under argon atmosphere. Three samples were obtained by sorption of Pu(IV) at pH I, 4, and 9 in an air-equilibrated system. The Pu L_III-edge XANES spectra indicated that in all samples, including the Pu(III) sample, plutonium is sorbed at the kaolinite surface as Pu(IV). The Pu L_III-edge k³-weighted EXAFS spectra showed eight oxygen atoms at an average Pu-O distance of 2.3 angstrom. Two Pu atoms were detected at ∼ 3.7 angstrom in all spectra, indicating the formation of polynuclear Pu(IV) species at the kaolinite surface. For the sample prepared from Pu(III) solution, an additional Pu-O shell at 3.2 angstrom was observed. The spectra of samples prepared from Pu(IV) included a Pu-Al/Si co-ordination shell at approximately 3.6 angstrom, indicating formation of inner-sphere sorption complexes. The structural models used in the least-squares fits were confirmed by an alternative EXAFS data analysis approach based on a modified Tikhonov regularization method. (authors)

[en] Photoluminescence (PL) quenching, which usually obeys empirical Street law for glassy solids, is analyzed taking into account the fact that the quenching of each particular emission center is statistically described by the known Mott law. A numerical technique for retrieving energy distributions of luminescent centers from PL quenching measurements is proposed. Mathematical treatment procedure is established and tested for reliability. Calculation results for chalcogenide, quartz and lead-silicate glasses demonstrate the possibility for obtaining both ordinary and polymodal energy distributions of centers and also a good promise for application in PL spectroscopy of disordered solids.