We proposed an algorithm for separating the overlapping spectral components using the Tikhonov weighted regularization method is proposed. The use of the weighting function allows one to significantly reduce the regularization parameters and separate closely spaced spectral lines. The problem of the appearance of spurious oscillations in a sparse solution is solved by an iterative algorithm for correcting the main matrix. To determine the regularization parameter that provides the maximum resolution of the method, the posterior minimum threshold algorithm is used. The use of the algorithm fundamentally improves the quality of spectra processing and increases the information content of the spectroscopic methods. The efficiency of the proposed algorithm is shown on examples of processing the model and experimental Moss-bauer spectra.

The formation of phases in mechanically synthesized (Fe0.90−xMn0.10Nix)75C25 alloys, where х = 0.05 and 0.10, is studied via X-ray diffraction, Mössbauer spectroscopy, and magnetic measurements. It is shown that certain products form during the mechanosynthesis of the initial powders in a planetary ball mill: cementite doped mainly with manganese, ferrite, and an amorphous phase doped mainly with nickel. Annealing at 500°C and higher temperatures leads to the formation of a composite consisting of cementite and austenite doped mainly with nickel. Cementite regions with two different Curie temperatures form as the alloys cool after high-temperature (700°C) annealing, due to differences in the manganese doping of cementite in these regions.

An algorithm for separating overlapping spectral components using the Tikhonov weighted regularization method is proposed. Use of the weighting function allows one to significantly reduce the regularization parameters and separate closely spaced spectral lines. The problem of the appearance of spurious oscillations in a sparse solution is solved by an iterative algorithm for correcting the main matrix. An a posteriori minimum threshold algorithm is used to determine the regularization parameter that provides the maximum resolution of the method. Use of the algorithm fundamentally improves the quality of spectra processing and increases the information content of the spectroscopic methods. The efficiency of the proposed algorithm is shown using processing of model and experimental Mössbauer spectra as examples.

Nanocrystalline Fe–Cr alloys synthesized from pure components in a planetary ball mill with a chromium content of 20–48 at % were annealed for 4 h at temperatures of Tan = 400–700°C. Short-range order (SRO) evolution and phase separation dependent on Tan were studied using Mössbauer spectroscopy and X-ray diffraction. The precipitation of the σ-FeCr phase was observed only in the samples with 48 at % of Cr at Tan = 600 and 700°C. For all the samples, the grain growth began most intensively from 400°C, and the higher the Cr content in an alloy, the smaller the final size of grains after Tan = 700°C. The analysis of behavior of the mean hyperfine field on Fe nuclei and distribution of the hyperfine field width depending on Tan, as well as fitting of Mössbauer spectra with spectral components corresponding to the α (Cr depleted) and α' (Cr rich) phases, demonstrated that the mechanically alloyed Fe-Cr samples were characterized by weak short-range separation passing at Tan = 400°C to a nearly statistically uniform distribution of atoms. Heterogeneous short-range order with the α and α' regions was formed in the alloys with 30 at % of Cr and more after annealing at 500–700°C. An analysis with the material balance equation led to our conclusion about the existence of the grain boundary segregations of Cr atoms.

X-ray diffraction and Mössbauer spectroscopy are used to study solid-phase reactions that occur in Fe–Cr nanocrystalline alloys during heat treatment. Upon the isochronous annealing of mechanically alloyed Fe–Cr powders, the nanostructural state is retained for all samples up to a temperature of 700°C. Fe(80)Cr(20) alloy tends to separate throughout the range of annealing temperatures. The annealing of all samples in the temperature range of 400–500°C results in separation into iron-enriched and chromium-enriched regions. A change in the trend toward short range ordering is observed in the samples of Fe(70)Cr(30) and Fe(60)Cr(40) at annealing temperatures above 500°C. Annealing samples of Fe(52)Cr(48) at temperatures above 600°C results in the formation of the σ-phase.

An algorithm is proposed for mathematical processing of Mossbauer spectra of solid solutions by the Tikhonov regularization method using the Voigt function as an elementary line. For the cases of the spectra processing of Fe 100–x Ge x solid solutions (x = 5—25 at.%) and Fe 75 Si 15 Al 10 , we demonstrate that the algorithm permits to obtain a physically grounded solution, significantly improves the quality of spectra processing, and expands the possibilities of the Mossbauer spectroscopy method. It is shown that the Voigt function is a satisfactory approximation for taking into account the statistical ensemble of nonequivalent local atomic configurations of Fe atoms in disordered solid solutions.

Using Mössbauer spectroscopy on 57Fe nuclei and X-ray diffraction, the mechanism of mechanical alloying in a planetary ball mill of the Fe–Cr nanocrystalline system in a concentration range from 20 to 48 at % Cr has been studied in detail. It has been established that mechanical alloying occurs in one stage at a concentration of up to 30 at % Cr and in three stages at higher concentrations. The change in the mechanism of mechanical alloying occurs as iron is saturated with chromium and is caused by the inversion of the sign of the mixing energy from negative to positive.

57Fe Mössbauer spectroscopy and X-ray diffraction are used to study in detail the mechanism of mechanical alloying in a planetary ball mill of the Fe-Cr nanocrystalline system in the concentration range from 20 to 48 at.% Cr. It is established that mechanical alloying proceeds in one stage at a concentration of up to 30 at.% Cr and in three stages at higher concentrations. The change in the mechanical alloying mechanism occurs as iron is saturated with chromium and is caused by the inversion of the mixing energy sign from negative to positive.

The electronic structure of 16 complex compounds of RE (Y, La–Tb) with the same ligand – nitrilotris(methylenephosphonic acid) [NTP, N(CH2PO3)3H6] and with different coordination symmetries of the RE atom is investigated. The structure of XP‐spectra of a valence band in this area significantly differs for structures with non‐octahedral O‐coordination of the RE atom, on the one hand, and those with pseudo‐octahedral O‐coordination of the RE atom, on the other hand. In the XP‐spectra of non‐octahedral O‐coordination complexes the O2s‐states have a maximum at EB = 24–26 eV and are poorly overlapped with Ln5p‐states. For pseudo‐octahedral O‐coordination structures a wide strip is observed in the field of EB = 20–28 eV corresponding to an overlap M5p‐ and O2s‐states with formation of internal valence molecular orbitals (IVMO). Apparently, in pseudo‐octahedral O‐coordination structures the arrangement of O atoms agrees with the octahedral symmetry of RE p‐orbitals and leads to the formation of IVMO M5p+O2s.

Evolution of the structure and atomic distribution in Fe 1− x Cr x ( x = 0.2, 0.3, 0.4 and 0.48) samples in the course of Fe and Cr elemental powder mechanical alloying (MA), as well as during the subsequent isochronous (4 hours) annealing in the 400 °C to 700 °C temperature range, has been studied using 57 Fe Mössbauer spectrometry and X-ray diffraction with a focus on the short-range order (SRO). It was established that MA proceeds in one stage for x ≤ 0.3 or three consecutive stages for x > 0.3. The single-stage process is characterized by preferential penetration of Cr into the Fe matrix, while the three-stage process comprises diffusion of Cr into Fe as in the previous case, formation of Cr- and Fe-rich areas, and formation of homogeneous α-Fe(Cr) solid solution. The change in the MA mechanism occurs as Fe is saturated with Cr and is caused by the inversion of the mixing energy sign from negative to positive. For all samples with x ≤ 0.3 annealed at all temperatures and for x > 0.3 annealed at 400 °C, only a small trend toward SRO was observed (SRO parameter < 0). The samples with x > 0.3 annealed at temperatures > 400 °C are subjected to thermally induced decomposition, which is accompanied by chromium segregations to the grain boundaries.

An algorithm is proposed for mathematical processing of Mössbauer spectra of solid solutions by the Tikhonov regularization method using the Voigt function as an elementary line. Spectra of solid solutions Fe100–xGex (x = 5–25 at.%) and Fe75Si15Al10 were processed as examples to show that the algorithm can produce a physically reasonable solution, improve significantly the quality of the processed spectra, and expand the possibilities of Mössbauer spectroscopy. The Voigt function was shown to be a satisfactory approximation for describing the statistical ensemble of nonequivalent local Fe configurations in disordered solid solutions.

The kinetics of the mechanical alloying of Fe and Cr powder mixtures with Cr contents of 20–48 at % has been studied by Mössbauer spectroscopy, X-ray diffraction analysis, and temperature measurements of dynamic magnetic susceptibility. It has been found for the first time that the processes of mechanical alloying differ for initial mixtures with chromium contents of 30 at % or more and contents of less than 30 at %. For the first case, the unidirectional dissolution of Cr in Fe is observed through the whole process of mechanical alloying of the mixture in a planetary ball mill. For the second case, the dissolution of Cr in Fe is observed at the beginning stage of milling; however, after milling for 2 h (tmil), the reverse process, namely, the dissolution of Fe in Cr is likely to dominate. The mechanically alloyed samples are characterized by inhomogeneous Cr and Fe concentration distribution in powder particles, in particular at a Cr concentration in the initial mixture of more than 30 at %.

Mössbauer spectroscopy and X-ray diffraction are used to investigate the kinetics of the mechanical alloying (MA) of Fe and Cr powdered mixtures with Cr contents of 20 to 48 at % in the initial mixtures. Variations during mechanical alloying in specimens with Cr contents of ≤30% and >30% in the initial mixtures are observed for the first time. After MA, specimens are characterized by heterogeneous concentration distributions of Cr and Fe atoms in particles, especially at Cr concentrations of >30% in the initial mixture.

The kinetics of solid Fe–Cr solution formation has been studied during mechanical alloying of Fe and Cr powders taken in an atomic ratio of 80: 20. X-ray diffraction and Mössbauer spectroscopy data have been analyzed within the framework of the energetic approach. It has been established that, in this system, reaction product yield N is related to mechanical energy dose D and specific surface area S of Fe nanograin boundaries in an ideal manner: N ~ D 2 at S ~ D and N ~ D at S = const.