# Volume 24 № 4 2022

**1. Anna G. Knyazeva, Maria A. Anisimova. Diffusion and Stresses Interrelation in Transient Zone between Particle and Matrix during Composite Synthesis. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 421-435. **Download

Since the rates of many reactions involving solids are controlled by diffusion processes, in powder technologies changes in composition and properties are associated with diffusion and related phenomena. In the present work, the interaction of a solid particle with a metallic melt is described on the basis of the problems with moving interfaces. The model takes into account some possible mechanisms for the appearance of stresses in the transition zone formed between the particle and the matrix during the composite synthesis and the effect of stresses on diffusion. The mechanical stresses that accompany the phase formation follow from the solution of equilibrium problems in which time is a parameter. The solution of diffusion-kinetic problems is based on the quasi-stationary approximation. In two considered examples it is assumed, that only one new phase or only 2 new phases appear. The diffusion fluxes, the radial components of a displacement vector and the radial stresses are assumed to be continuous at the interfaces. Based on the solution of the coupled problem, the expressions for the coefficients at the degrees of concentration included in the expressions for diffusion coefficients are found for the first time. It is shown that for the growth of two phases, the law of motion of the boundaries remains parabolic, but the growth rate for each phase depends on the ratio of the mechanical properties of the phases. The results can be used not only for the analysis of the phase composition changes in the vicinity of the particle-matrix interfaces during the composite synthesis, but also for the development of two-level models of the composite synthesis.

* Keywords*: composite synthesis, transition zone, phase growth, diffusion, stresses, coupled problem.

**DOI:** https://doi.org/10.15350/17270529.2022.4.34

**2. Alexander V. Vakhrushev, Aleksey Yu. Fedotov, Olesya Yu. Severyukhina, Anatolie S. Sidorenko. Study of the Influence of the Cobalt Structure on the Magnetic Properties of Nanofilms. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 436-453. **Download

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The work is devoted to the study of the influence of the structure and local structural defects of a cobalt nanofilm on its magnetic properties. The results of the study were obtained using mathematical modeling based on a complex model. The model combines molecular dynamics and the dynamics of particle spin states. The results of modeling two variants of nanosystems are considered. The first nanosystem was cobalt with a structure close to an ideal hexagonal close-packed crystal lattice. In the second nanosystem, cobalt had structural defects and deviations from the ideal structure, since it was formed in an earlier computational experiment of the multilayer deposition of a niobium-cobalt nanocomposite. As the parameters under study, we considered such properties as the spin temperature, the total distribution of spins for atoms, and the magnetization modulus of the material. Significant differences in the behavior of these parameters were revealed for the considered variants of the cobalt structure. By the simulation tools it is shown that defects in the structure and local arrangement of atoms can cause deterioration in the magnetic characteristics of the material, for example, a decrease in the magnetization modulus and lead to jumps in the spin temperature.

* Keywords*: magnetic materials, nanofilms, nanocomposites, spintronics, molecular dynamics, LAMMPS.

**DOI:** https://doi.org/10.15350/17270529.2022.4.35

**3. Mikhail Yu. Alies, Aleksey I. Kalugin, Darya N. Kochurova, Еgor A. Antonov, Victor Yu. Trubitsin. Reflection of Laser Radiation with a Gaussian Intensity Distribution from a Rough Surface. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 454-462. **Download

The reflectivity of an object is important in many applications. It depends on the material and the condition of the surface of an object, including its roughness, and on the parameters of the incident radiation (polarization, spatial distribution of intensity). To describe the reflectivity of the surface of an object, a bidirectional reflectance distribution function (BRDF) is used. In the general case, the BRDF can be represented as the sum of diffuse and specular components. This work is aimed at establishing the regularities of the reflection of the laser radiation with a Gaussian intensity distribution from a rough surface. Rough surfaces reflect diffusely, evenly in all directions. In this case the bidirectional reflectance distribution function is constant. A theoretical model is presented for calculating the power of the laser radiation received after the reflection from an object with an arbitrary surface and optical characteristics. In particular, a model of the reflection of a laser beam with a Gaussian intensity distribution from a rough lambertian disk is considered. The calculations were carried out under the condition of the coincidence of the centers of the laser beam and the disk; the disk was oriented perpendicular to the laser radiation. The dependence of the reflected power on the ratio of the beam size and disk radius is shown. As the disk radius increases to the size of the beam, the power value increases; with further increase in the disk size, the power continues to grow more slowly and begins to tend to a constant value. When the disk radius is smaller than the beam size, the reflected power decreases inversely with the square of the distance to the object, and the fourth degree of the distance appears when the disk radius is larger than the size of the beam. Therefore, to achieve the maximum probing distances, a beam with low divergence should be used. However, if it is necessary to determine the structure and shape of an object from the reflected optical signal, the beam must completely cover the object. The power of the laser radiation reflected from plastic (polyvinylchloride) white disks of various radii was experimentally obtained depending on the distance from the photodetector to the object. A laser with a wavelength of 532 nm was chosen as the radiation source. A PVC disk can be considered a diffuse reflector because the roughness is one order of magnitude larger than the radiation wavelength. The correspondence of the theoretical model to the experimental dependences is established.

** Keywords**: reflectivity, bidirectional reflectance distribution function, lambertian reflectance, rough surface.

**DOI:** https://doi.org/10.15350/17270529.2022.4.36

**4. Gabriela Morar, Alexander I. Karpov, Artem A. Shaklein. Numerical Study of the Thermal Structure of Turbulent Diffusion Flame on the Horizontal Surface of PMMA. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 463-472. **Download

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The numerical study of turbulent diffusion flame behavior on the surface of solid combustible material has been carried out. The predictions have been performed by employing the open-source software Fire Dynamic Simulator (FDS) employing LES technique for turbulent transfer modeling. Methylmethacrylate (product of PMMA pyrolysis) is assigned as the gaseous fuel component of gas-phase combustion reaction with corresponding values of molar weight and heat release. The height from the burning surface of solid combustible material on which the turbulent eddies are formed has been determined based on the distribution of instant values of temperature. In the vicinity of burning surface where turbulent fluctuations do not occur, the temperature profile agrees with the one obtained through the prediction in laminar assumption. The algorithm for the coupled problem of flame spread over the surface of solid fuel is proposed. Entire computation domain is divided into two regions: one, relatively thin near-wall zone, where laminar flow occurs and other, the outer area, which includes the flame plume where turbulent regime is dominant. Thus, in near-wall zone the assumptions of laminar flow and two-dimensional formulation (if any) are accepted, which allow to use high resolution numerical grid. This results in accurate prediction of temperature gradient and correspondingly the heat flux from the flame to the solid fuel's burning surface. As LES approach demands, the conservation equations in the outer area are to be three-dimensional and the size this area is much larger to cover whole flame and surroundings. These factors strongly restrict the number of grid nodes due to affordable computational resources, which resulting in rather coarse grid resolution allowed. The solutions in both regions are coupled by mutual boundary conditions at some surface, the position of which must ensure that laminar flow assumption is valid here.

** Keywords**: diffusion flame, turbulent combustion, numerical simulation, Fire Dynamic Simulator, methylmethacrylate burning.

**DOI:** https://doi.org/10.15350/17270529.2022.4.37

**5. Tatyana S. Kartapova, Faat Z. Gil’mutdinov, Marina A. Eryomina, Andrey A. Kolotov, Konstantin G. Mikheev, Vladimir F. Kobziev, Gennady M. Mikheev. Effect of the Pulse Repetition Frequency of Ion Current on the Characteristics and Properties of Carbon Films Obtained by Magnetron Sputtering. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 473-486. **Download

Thin carbon films 36 nm thick were obtained by magnetron sputtering on glass substrates. The synthesized films were subjected to the pulsed irradiation with argon ions with a variation in the frequency f of the repetition of ion pulses at the fixed values of the ion energy Е_{i} = 30 keV and the irradiation dose D = 10^{17}
ion/cm^{2}. It has been experimentally established that the electrical resistivity of the carbon films depends nonmonotonically on f. In order to explain the obtained dependences ρ(f), the carbon films were studied by Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). Raman spectroscopy and XPS showed that the obtained films before and after the ion irradiation have an amorphous (disordered) carbon structure that differs from those of graphite and diamond. In this case, the Raman and XPS spectra of the carbon films significantly depend on f. The analysis of the measured spectra indicates a complex dependence of the sizes of the carbon structure clusters in the film on f, which can explain the nonmonotonic dependence of the electrical resistance of the films on f. Under irradiation with high repetition rates of the ion implantation pulses (100 and 200 Hz), a radiation-thermal effect appears leading to the coagulation of fine particles into larger formations, and this is accompanied by a decrease in the electrical resistivity of the films.

* Keywords*: magnetron sputtering, carbon films, electrical resistivity, Raman spectroscopy, X-ray photoelectron spectroscopy.

**DOI:** https://doi.org/10.15350/17270529.2022.4.38

**6. Sergey A. Karskanov. Analysis of Viscous Gas Flows Pulsation Characteristics in Expanding Conical Nozzles. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 487-496. **Download

A numerical experiment was carried out based on direct numerical simulation. The problem of the viscous gas flow through expanding conical nozzles was solved by integrating the Navier-Stokes equations without involving additional models and empirical constants. The integration of the Navier-Stokes equations was carried out using high-order approximation algorithms on a multiprocessor cluster. The distribution fields of the fluctuations of the velocity components are given. Longitudinal and radial pulsations have the same range of change. The maximum of the longitudinal fluctuations is located in the flow core, while the maximum values of the fluctuations of the radial velocity component are located in the vicinity of the line emanating from the separation point. The acoustic parameters of the studied flows are considered. The Lighthill stress tensor was used to describe acoustic interactions in a pulsating medium. Two components of the tensor were considered and compared. The tensor component, which describes the stresses in the flow caused by the interaction of turbulent fluctuations, is responsible for the intrinsic noise. The tensor that describes the shear-turbulence interaction is responsible for the shear noise. Graphs of the change in the components of the Lighthill tensor in time for various nozzles are plotted. In all cases, it can be seen that the amplitudes of the values of the tensor components are comparable in absolute value, i.e. they are within the same order. With an increase in the expansion angle, the amplitude of the fluctuations in the values of the components increases too. On the basis of the discrete Fourier transform, the frequency spectra are plotted, at which the components of the Lighthill tensor oscillate in nozzles with different constriction angles. It is shown that at a point on the axis the frequency distribution does not depend on the taper angle. The oscillation amplitudes at a point close to the expansion zone grow with an increase in the taper angle.

** Keywords**: direct numerical simulation, expanding conical nozzle, viscous flow, high order approximation, discrete Fourier transform.

**DOI:** https://doi.org/10.15350/17270529.2022.4.39

**7. Alexey M. Lipanov, Dmitriy K. Zhirov. Device for the Destruction of Materials by Pressure Release. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 497-502. **Download

To grind most of the existing materials, it is sufficient to use traditional methods of destruction: impact, abrasion, cutting, sawing, splitting, and crushing. However, not all materials can be effectively ground by the methods indicated above in terms of the energy consumption and the quality of a final product of grinding. For example, for grinding fibrous materials, from the standpoint of the energy cost it is more preferable to use a different method - destruction by "explosion" or pressure relief. This method is most effective for the destruction of porous materials that can easily absorb moisture changing the requirements for destruction at the same time. Another method of destruction can be successfully used based on the compression of the crystal lattices of particles followed by abrupt unloading of the particles and their rupture under the action of internal stresses. The design of a device for the destruction of natural and technogenic materials by pressure relief presented in the paper can be successfully applied to the destruction of porous materials absorbing moisture. When the humidity of the environment changes, colloid capillary-porous materials may require a significant increase in the energy for their destruction to the required size due to an increase in their damping properties; thus, it becomes completely impossible to destroy them by such methods as constrained impact, free impact or compression. In this case, using the device for destruction by pressure release makes it possible to destruct such materials without preliminary drying.

** Keywords**: destruction, pressure release, explosion, grinding, particle, contamination.

**DOI:** https://doi.org/10.15350/17270529.2022.4.40

**8. Victor Yu. Trubitsin, Konstantin A. Shlyakhtin, Tatyana E. Shelkovnikova. Model of Artificial Neural Network of Biological Type and Simulation of the Network Operation. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 503-510. **Download

Currently, research in almost all fields of science and technology involves methods of machine learning and data processing. The existing principles of artificial neural networks implementation require a large dataset, significant training time as well as the choice of neural network architecture and tuning for each specific purpose. A review of different models of spiking neural networks has been conducted. A biological type of neural network is developed in the present article. The article simulates the formation of neural connections for a system of three areas of neurons. The article describes the basic concepts of functioning of the developed biological type network. The mathematical model of the exchange of neurotransmitters between neurons is proposed and two methods for the realization of the dendrite growth in the network are considered. The first method is based on the piecewise increment of the dendrite outgrowths; the second method is based on changing the length and direction of the dendrite growth. The algorithm of the network operation and neuron interaction using the developed mathematical models is proposed. The model of the neural network was created in Python using the developed algorithm and the method of piecewise dendrite regrowth. To speed up the calculations, they were parallelized using the Numba library. The library Matplotlib was used to visualize the model and plot the number of neurotransmitters on neurons. Experimental studies of the developed model of the biological type of the network were carried out. It was shown that the developed network after training responds faster to the signals that were applied to it in the process of training.

** Keywords**: biological neural network, neuron, axon, dendrite, neurotransmitter.

**DOI:** https://doi.org/10.15350/17270529.2022.4.41

**9. Aigul I. Bazhenova, Vladimir A. Shirokov, Vladimir N. Milich. Verification of the Sensors Spatial Position in the Multistatic Underwater Vision System Development. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 511-522. **Download

The issues of increasing the accuracy of determining the spatial position of the illuminating and receiving sensors of a hydroacoustic system of underwater vision are considered in the present article. This is necessary for the correct coordination of detected objects in the underwater environment. The pre-calibration system is needed to ensure an accurate determination of the spatial position of sensors for which satellite positioning methods are not applicable. The proposed method of the verification of the sensors location consists of two main stages of processing: the preliminary localization of objects and the subsequent adjustment of the coordinates of the receiving sensors based on the results of the localized coordinates of objects. At the first stage, the threshold processing of signals allows identifying many pulses, which includes both the pulses reflected from objects and the pulses from the signals of noise. The use of an excessive number of sensors (channels of the reflected signal) makes it possible to choose the true positions of objects from the total number of calculated positions. At the second stage, the coordinates of the sensors are adjusted using the iteration process of gradient descent. At each iteration the displacement of the sensors coordinates is selected so as to increase the degree of the coincidence using the proposed measure of the closeness of the coordinate values of objects calculated by different pairs of sensors. The described method was tested when verifying the coordinates of the sensors in the experimental pool. In the process of localizing the objects positions the set of all possible positions of objects was formed; two of all the positions were confidently identified as true. At the stage of the iterative adjustment of the coordinates of the sensors, the accuracy of determining the coordinates of their acoustic centers was increased. Thus, the application of the proposed method made it possible to obtain more accurate data on the location of the elements of the multistatic underwater vision system. At the same time, the method has certain limitations associated with the arrangement of objects when the reflected pulses from different objects merge.

** Keywords**: hydroacoustics, multistatic system, redundancy of the number of sensors, variation of arbitrary constants, gradient descent, trilateration.

**DOI:** https://doi.org/10.15350/17270529.2022.4.42

**10. Oleg B. Baryshev, Oleg Yu. Goncharov, Alexander V. Stepanov, Sergey V. Rybin, Sergey P. Starostin, Vasiliy A. Volkov. Relationship of the Mechanical Properties of Porous Anode Bodies with the Electrical and Reliability Characteristics of Tantalum Capacitors. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 523-532. **Download

The data on the manufacture of tantalum capacitors made from 2 types of tantalum capacitor grade powders (low CV and high CV) have been analyzed. Additional studies of the mechanical characteristics of anodes after sintering and electrochemical oxidation selected from serial batches have been carried out. Capacitors containing the studied anodes have been tested for reliability characteristics. Based on the analysis of the data obtained, a method has been developed for assessing the quality (reliability margin) of tantalum capacitors without carrying out a full cycle of manufacturing and testing of products. The method is based on the analysis of the data on the yield strength of the porous body of anodes before and after electrochemical oxidation. It allows a) to estimate the limiting voltage for electrochemical oxidation during the formation of the dielectric by determining the yield strength of the sintered anode, b) to detect an unacceptable level of defectiveness of the dielectric layer on the surface of the anode by the relation of the yield strength of the porous body of the anode after electrochemical oxidation to the yield strength after sintering. The performance of these mechanical tests allows a) to identify defects at the early stages of the capacitor manufacturing (to prevent defective capacitors from entering the further technological process), b) to assess the reliability margin and technological reserve of capacitors without conducting long-term reliability tests for 1000 hours or longer. Based on the results obtained, for each group of the tantalum powder of a certain manufacturer and a certain specific charge it is recommended to determine the permissible (pass-through) values of the yield strength of the porous anode body after sintering and the ratio of the yield strength of the porous anode body after electrochemical oxidation to the yield strength after sintering.

** Keywords**: tantalum, porous body, anode, dielectric, mechanical characteristics.

**DOI:** https://doi.org/10.15350/17270529.2022.4.43

**11. Evgenii Yu. Prosviryakov, Alexsey S. Sokolov. Numerical Construction of a Set of Zero Values of Velocities and Countercurrents for Steady Dynamic Equilibria. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 533-543. **Download

The article considers a steady shear convective flow of a fluid moving between two rotating infinite planes (disks). The angular velocities of the boundaries of an infinite horizontal layer are described by various quantities. In other words, the article studies the differential rotation of the medium (dynamic equilibria), instead of the solid-body rotation of the fluid (Ekman convective flow). The exact solution of the Oberbeck-Boussinesq equations is considered. The system of equations is overdetermined, because to determine the four unknown functions for the shear convective flow, it is necessary to integrate a nonlinear system of partial differential equations from five equations. The velocity field is determined by linear forms. The temperature field and the pressure field are described by quadratic forms. Shapes depend on two coordinates (horizontal or longitudinal). The shape factor is determined by the connection from the vertical (third, transverse) coordinate. The exact solution used in the article allows satisfying the "extra" equation (the incompressibility equation) and constructing a nonlinear system of ordinary differential equations. The numerical integration of the equations for determining the hydrodynamic fields has been carried out. The structure of countercurrents arising at the steady convection of liquid is investigated. Using numerical algorithms for the systems of ordinary equations, the regions of the existence of countercurrents are constructed depending on the fluid parameters and boundary conditions for an infinite horizontal layer.

* Keywords*: exact solution, Navier-Stokes equation, incompressible fluid, heat transfer equation, counterflows, bifurcation, dynamic equilibria.

**DOI:** https://doi.org/10.15350/17270529.2022.4.44

**12. Nikolai M. Barbin, Marina A. Shumilova, Oleg Yu. Goncharov. Thermal Stability of Arsenates and Arsenites of Alkali Metals. Chemical Physics and Mesoscopy, 2022, vol. 24, no. 4, pp. 544-553. **Download

The study of the physico-chemical features of the behavior of arsenates creates the basis for optimizing technological processes associated with the removal of arsenic in various industries. The high-temperature behavior of Na_{3}AsO_{4}, K_{3}AsO_{4}, Na_{3}AsO_{4}+NaF, K_{3}AsO_{4}+KF was analyzed by thermodynamic modeling and compared with that of arsenite systems. The equilibrium compositions of the condensed phase at temperatures up to 1900 K in the argon atmosphere were calculated. The results of thermodynamic modeling of the pyrolysis of К_{3}AsО_{4 }и Na_{3}AsO_{4} show that at high temperatures this system is a melt-solution of potassium and sodium arsenates and arsenites, respectively. Despite the close nature of the changes occurring during the pyrolysis of arsenate and arsenite ions as the main components, it is obvious that potassium arsenates are more thermally stable compounds compared to arsenites. Depending on the temperature the K_{2}O content for potassium arsenates and arsenites has the same values, confirming that all the features of the pyrolysis of arsenic salts are due to the difference in the stability of its heterovalent compounds. The comparison of the concentration of the main components in the condensed phase of sodium arsenate and arsenic oxide with that in sodium arsenite and the corresponding arsenic oxide with increasing temperature shows its almost double excess in the arsenate system, which indicates its greater stability. The changes in the Na_{2}O concentration with temperature in both systems are equivalent; the potassium oxides in the arsenate system have the same quantitative characteristics; therefore, all differences in the thermal properties of arsenate and arsenite systems are associated only with the features of the electronic structure of arsenic. The introduction of potassium fluoride into the arsenate system leads to a decrease in the thermal stability of the salt. A similar pattern of a significant drop in thermal stability with the introduction of potassium fluoride is also observed in the arsenite system.

** Keywords**: sodium arsenates, potassium arsenates, sodium fluorides, potassium fluorides, thermodynamic modeling.

**DOI:** https://doi.org/10.15350/17270529.2022.4.45