A method for processing Mossbauer spectra of multicomponent single-phase disordered solid solutions using an extended mathematical model is proposed. The method can detect local distortions of a body-centered cubic lattice and the local symmetry of a resonant atom that arise from differences in the properties of the atoms of the mixed components. The significance of the extended mathematical model for obtaining reliable information and, accordingly, reliable interpretation of experimental spectroscopic results is demonstrated using processing of Mossbauer spectra of single-phase disordered solid solutions Fe75Si15Al10, Fe75Si15Ge10, and Fe75Sn15Ge10 as examples.

Research the properties of iron-based solid solutions by M & ouml;ssbauer spectroscopy has the problem of interpreting the results of processing experimental data within the traditional mathematical model. Since the disordered solid solutions, for example, as a result of mechanical activation, are consisted of a set of the different local atomic configurations, the corresponding M & ouml;ssbauer spectra contain a large number of the shifted relative to each other spectral components with close values of the hyperfine interaction parameters. The magnitude and sign of these shift are determined by many factors: the quantitative distribution of atoms of each type in the coordination spheres, the symmetry of their distribution relative to the quantization axis, the possible local shift relative to the average statistical position in the crystallographic structure, etc. In the mathematical model, as a rule, it's not possible to taken into account all these effects of the shift by analytically. The proposed extended mathematical model for describing the M & ouml;ssbauer spectra of solid solutions makes it possible to take into account the shifts in the spectral components by using Gaussian normal distribution function, as a function of statistical set of local distortions. The width of the Gaussian distribution makes it possible to estimate the degree of local distortions of the crystal lattice that arise due to differences in the sizes of atoms of the mixed components, local distortions of the structure and symmetry of the environment of the resonant atom. The inverse problem of nuclear gamma-resonance is formulated by the Fredholm integral equation of the first kind and is an ill-posed problem with a priori constraints on the desired solution. The introduction of two Gaussian functions with a priori unknown linewidths into the kernel of the integral equation leads to the problem of solving the equation by classical methods. Algorithm for obtaining a reliable solution based on the Tikhonov regularization method with correction of the parameters of the kernel of the integral equation is proposed in this paper. On the examples of the study of real objects, the reliability and informative application of the extended mathematical model of the inverse problem of nuclear gamma-resonance is proved.

При изучении свойств твердых растворов на основе железа методом мессбауэровской спектроскопии возникает проблема интерпретации результатов обработки экспериментальных данных в рамках традиционной математической модели. Поскольку для разупорядоченных, например в результате механоактивации, твердых растворов характерно наличие ансамбля различных локальных атомных конфигураций, соответствующие им мессбауэровские спектры содержат большое количество смещенных относительно друг друга спектральных составляющих с близкими значениями параметров сверхтонкого взаимодействия. При этом величина и знак смещения определяются многими факторами: количественным распределением атомов каждого сорта в координационных сферах, симметрией их распределения относительно оси квантования, возможным локальным смещением относительно среднестатистического положения в кристаллографической структуре и т.д. Аналитически учесть все эффекты смещения в математической модели, как правило, невозможно. Предложенная расширенная математическая модель описания мессбауэровских спектров твердых растворов дает возможность учесть смещения спектральных составляющих посредством введения в модель функции нормального распределения Гаусса, описывающей статистический набор локальных искажений. Ширина распределения Гаусса позволяет оценить степень локальных искажений кристаллической решетки, возникающих из-за различий в размерах атомов смешиваемых компонентов, локальных искажений структуры и симметрии окружения резонансного атома. Обратная задача ядерного гамма-резонанса выражается интегральным уравнением Фредгольма 1 рода и является некорректно поставленной задачей с априорными ограничениями на искомое решение. Введение в ядро интегрального уравнения двух функций Гаусса с неизвестными априори ширинами линий приводит к проблеме решения уравнения классическими методами. В работе предложен алгоритм получения достоверного решения, опирающийся на метод регуляризации Тихонова с коррекцией параметров ядра интегрального уравнения. Достоверность и информативность расширенной математической модели обратной задачи ядерного гамма-резонанса продемонстрирована на примерах исследования реальных объектов.

An algorithm for mathematical processing of the Mössbauer spectra of supersaturated disordered solid solutions by the Tikhonov regularization method using a double convolution of the Lorentz function and two Gaussians is proposed. By the examples of spectra of supersaturated disordered solid solutions Fe100–xGex (x = 10—25 at.%) and Fe75Si15Al10, it is shown that the algorithm allows more correct processing, which provides a reliable distribution function of the hyperfine magnetic field. It is shown that to take into account the statistical ensemble of nonequivalent local atomic configurations of Fe atoms in disordered supersaturated solid solutions, it is necessary to use not only the convolution of two Gaussian functions, but also the projection scaling factor of the hyperfine magnetic field onto the velocity scale.

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.

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.

A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.

Surface modification of iron powder was carried out via wet ball milling in siloxane block copolymer and surfactant (sodium dodecyl sulfate) solutions. The produced materials were characterized by means of SEM, XRD and Mössbauer spectroscopy. The structure of the modified surface layers was studied by XPS and FT-IR spectroscopy.

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.

Fe75Si15Al10 alloy was produced by ball milling the elemental powder mixture under argon atmosphere. Surface modification of the powder particles was carried out via wet ball milling in organosilicon block copolymer (“Lestosil SM”) and surfactant (sodium dodecyl sulfate) solutions. The produced materials were characterized by means of scanning electron microscopy, X-ray diffraction and Mossbauer spectroscopy. The interaction of modifying agents with particles surface was evaluated by the analysis of the modified surface layers of the particles by X-ray photoelectron spectroscopy.

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.

Complex study using direct structural and spectroscopic methods allowed to obtain the data on polymorphous transformations, taking place during mechanical activation of CaGlu. It was revealed the formation of two-dimensional structures (i.e., plane 2-D structures, nanotubes) in the process of mechanical treatment of calcium gluconate monohydrate

The double electromagnetoacoustic transformation method is used to study the dynamic magnetoelastic properties of the Fe81Si7B12 amorphous alloy depending on the temperature of crystallization annealing. Changes found in the velocity of sound, its damping, and differential magnetostriction are related to the relaxation of quenching stresses and the surface crystallization.

An iterative algorithm for narrowing the definition domain of the distribution function of the hyperfine interaction parameter is proposed. The use of this algorithm increases the resolving power of the Tikhonov regularization method for solving the inverse problem of Mössbauer spectroscopy.

Mechanical activation of titanium in petroleum ether with subsequent heat treatment produced titanium carbohydrides with hexagonal close-packed and face-centered cubic lattices. The effect of iron and copper additions on the structural and phase composition of the titanium-based powders after the mechanical activation and heat treatment was studied. In these systems, both titanium carbohydrides, and the intermetallics Ti–Cu, Ti–Fe, and Ti–Fe–Cu formed. All the obtained powders contained ~1 wt % hydrogen. The release of hydrogen by heating the powders was investigated, and the lowest release temperatures (220–500°C) were detected for the phase Ti–Fe–Cu.

Fe-Si alloys are known for excellent soft magnetic properties and are widely used as fillers of composites for microwave applications. A change in the size and morphology of powder particles has a significant effect on the microwave properties of composites filled with such powders. In this paper, Fe75Si25 powders were produced by high-energy wet ball milling in organic media. A solution of stearic acid in petroleum ether (a surfactant solution) and acetone were used as milling media. The effect of wet ball milling conditions on the morphology and structure of the produced powders was studied by electron microscopy, X-ray diffraction, Mossbauer spectroscopy and X-ray photoelectron spectroscopy. The use of a surfactant solution and acetone as milling media promotes the plasticization of the brittle alloy Fe75Si25 and the formation of flat particles. The wet ball milling of the alloy in acetone leads to the formation of particles of a much larger thickness and smaller size in comparison to the particles produced by wet ball milling in a surfactant solution. In both cases, after milling the alloy is disordered. During the milling process the Si concentration in the alloy decreases due to the formation of surface oxide layers enriched with silicon. The frequency dependence of microwave permittivity and permeability of composites filled with produced powders was studied. The depolarization factor, percolation threshold and intrinsic permeability of produced powder particles were determined. The frequency dependence of intrinsic permeability of the particles was shown to depend strongly on the milling conditions. A change in the milling conditions makes it possible to produce Fe75Si25 powders with the required microwave properties.