In this work, the high-temperature diffusion doping method was used for introduction of active cobalt ions into calcium orthovanadate Ca₃(VO₄)₂crystals. Experimental samples were made from a nominally pure CVO single crystal obtained by the Czochralski method. The high-temperature diffusion conditions have been optimized to obtain doped crystals of optical quality during annealing in open and closed zones. Diffusion coefficients of cobalt ions (D) were calculated for various conditions: annealing time 24 - 48 hours; temperature range 1150-1300°C; diffusants - oxide compounds of calcium, cobalt and vanadium: Co₃O₄, Ca₁₀Co_0.5(VO₄)₇ and Ca₃(VO₄)2:2wt.%Co₃O₄; diffusion direction is parallel or perpendicular to the CVO crystal optical axis. The calculated values of the diffusion coefficient varied between 2.09·10^-8—1.58·10^-7 cm²/s. The activation energy of the diffusion process was determined to be 2.58±0.5 and 2.63±0.5 eV for the [001] and [100] directions, respectively. The maximum cobalt concentration in doped CVO crystals was 2·10²⁰ cm^–3. The absorption spectrum of diffusion-doped Ca₃(VO₄)₂:Co samples demonstrates the presence of absorption bands characteristic for Co²⁺ and Co³⁺ ions. It was shown that the intensity ratio of the characteristic absorption bands varies depending on the crystal doping method. The optical anisotropy of the crystal increases with dopant concentration increase.

Nominally pure lanthanum-gallium tantalate La₃Ga_5.5Ta_0.5O₁₄ crystals doped with aluminum, silicon and gallium oxide to above stoichiometric content have been grown by the Czochralski technique in iridium crucibles in argon and in agron with addition of oxygen atmospheres. The transmittance spectra of the crystals have been measured on a Cary-5000 UV-Vis-NIR spectrophotometer in the 200–800 nm range. Absorption spectra α(λ) have been plotted on the basis of the experimental data. The absorption spectra of the undoped crystals grown in an oxygen-free atmosphere have one weak absorption band at λ ~ 290 nm. The absorption spectra of the crystals grown in an agron with addition of oxygen have absorption bands at λ ~ 290, 360 and 480 nm. We show that for the crystals grown in an oxygen-free atmosphere, gallium doping to above stoichiometric content reduces the intensity of its only λ ~ 290 nm absorption band. Aluminum doping of the La₃Ga_5.5Ta_0.5O₁₄ crystals grown in an oxygen-free atmosphere significantly reduces the intensity of the λ ~ 290 nm absorption band and increases the intensity of the λ ~ 360 and 480 nm bands. Aluminum doping of the La₃Ga_5.5Ta_0.5O₁₄ crystals grown in an oxygen-containing atmosphere reduces the intensity of the λ ~ 360 and 480 nm bands and increases the intensity of the λ ~ 290 nm absorption band. Silicon doping of these crystals significantly reduces the intensity of the λ ~ 480 nm band and also reduces the intensity of the λ ~ 290 and 360 nm bands.

Magnetoelectric (ME) composites can be useful due to their wide range of possible applications, especially as sensors of weak magnetic fields at room temperature for magnetocardiography and magnetoencephalography techniques in medical diagnostic equipment. In most works on the topic of ME composites, structures are tested in uniform magnetic fields; however, for practical application, a detailed consideration of the interaction with inhomogeneous magnetic fields (IMF) is necessary. In this work we made measurements of IMF with radial symmetry of individual thin wire with AC voltage with different placements of ME sensor. A ME self-biased structure b-LN/Ni/Metglas with a sensitivity to magnetic field of 120 V/T was created for IMF detection. The necessity of external biasing magnetic field is avoided by a nickel layer and its remanent magnetization. ME composite shows a non-zero ME coefficient of 0.24 V/(cm·Oe) in absence of DC external magnetic field. It is shown that output voltage amplitude from ME composite, which is located in AC IMF, is dependent from relative position of investigated sample and magnetic field lines. Maximum ME signal is obtained when long side of ME sample is perpendicular to the wire, and symmetry plane which divides the long side in two similar pieces contains an axis of the wire. In frequency range from 400 Hz to 1000 Hz in absence of vibrational and other noises a limit of detection has value of (2 ± 0.4) nT/Hz^1/2.

In an Ag/SnSe/Ge₂Se₃/W ionic type memristor, the activation energy of two main processes responsible for its operation has been determined, namely: the activation energy for the formation of a conductive channel and the activation energy for memristor degradation. By measuring the current-voltage characteristics, the electrical conductivity of the memristor in low- and high-resistance operating modes was assessed. To determine the activation energy, the Arrhenius law and the provisions of the thermodynamics of irreversible processes were used, in particular the second postulate of Onsager, according to which the growth rate of the irreversible part of the entropy of a system tending to equilibrium is proportional to the sum of the products of the flows occurring in the system and the generalized thermodynamic force corresponding to each flow. The equilibrium state of the memristor was taken to be the state in which the memristor lost the ability to function as a resistive memory cell. The flow of Ag+ ions – electromigration was used as a substance flow. For the first process, the activation energy was 0.24 eV, and for the second, 1.16 eV. The different values of activation energy reflect the difference between the agglomeration mechanism of formation of a current-conducting channel, typical of an Ag/SnSe/Ge₂Se₃/W memristor, and the “standard” mechanism of substance transfer based on a group of point defects, which accompanies the process of memristor degradation.

Currently, the electromagnetic characteristics of various materials, including polymers, are being widely studied with the aim of using them as radio-absorbing coatings in electronics products. One such material is pyrolyzed polyacrylonitrile (PPAN). A model of electromagnetic wave absorption by PPAN layers with electrical conductivity of 72 and 180 S/m and a layer width of 0.15 to 2 mm, including those containing a metal filler (the so-called PPAN-based metal composite), in the frequency range of 3–50 GHz is considered. The simulation was performed in the COMSOL Multiphysics software package.

A comparison of the experimental results with the data obtained during the simulation was carried out for such parameters as reflection, transmission and absorption. The conclusions obtained from the analysis of simulation data coincide with the results of practical experiments. Analysis of the model showed the convergence of modeling results with experimental data at a qualitative level.

At the end of the 20th century, the demand for more efficient methods for solving large sparse unstructured linear systems of equations increased dramatically. Classical single-level methods had already reached their limits, and new hierarchical algorithms had to be developed to provide efficient solutions to even larger problems. Efficient numerical solution of large systems of discrete elliptic PDEs requires hierarchical algorithms that provide a fast reduction of both shortwave and longwave components in the error vector expansion. The breakthrough, and certainly one of the most important advances of the last three decades, was due to the multigrid principle. Any appropriate method works with a grid hierarchy specified a priori by coarsening a given sampling grid in a geometrically natural way (a "geometric" multigrid method). However, defining a natural hierarchy can become very difficult for very complex, unstructured meshes, if possible at all. The article proposes an algorithm for calculating the deformation that occurs under the action of a thermal expansion force in three-dimensional solid models based on a grid approximation of the problem by hexagonal 8-node cells. The operation of the algorithm is illustrated by solving three problems.

The effect of high-temperature treatment in different media on the phase composition, microhardness and fracture toughness of (ZrO₂)_1-х(Sm₂O₃)_х crystals with x = 0.02÷0.06 has been studied. The crystals have been grown using direction melt crystallization in a cold skull. The crystals have been heat treated at 1600 °C for 2 h in air and in vacuum. The phase composition of the crystals has been studied using X-ray diffraction and Raman scattering. We show that samarium cations enter the ZrO₂ lattice mainly in a trivalent charge state and do not change their charge after air or vacuum annealing. The as-annealed phase composition has changed in all the test crystals except for the (ZrO₂)_0.94(Sm₂O₃)_0.06 composition. After air or vacuum annealing the (ZrO₂)_1-x(Sm₂O₃)_x crystals with 0.002 ≤ x ≤ 0.05 contain a monoclinic phase. The (ZrO₂)_0.94(Sm₂O₃)_0.06 crystals contain two tetragonal phases (t and t´) with different tetragonality degrees. After air or vacuum annealing of the (ZrO₂)_0.94(Sm₂O₃)_0.06 crystals the lattice parameters of the t and t´ phases change in opposite manners, suggesting that the tetragonality degree of the t phase increases whereas the tetragonality degree of the t´ phase decreases. The microhardness and fracture toughness of the as-annealed crystals depend on the Sm₂O₃ concentration in the solid solutions. The formation of the monoclinic phase in the (ZrO₂)_1-х(Sm₂O₃)_х crystals with 0.037 ≤ x ≤ 0.05 significantly reduces the microhardness and fracture toughness of the crystals. Annealing of the (ZrO₂)_0.94(Sm₂O₃)_0.06 crystals triggers more efficient hardening mechanisms and thus increases the fracture toughness of the crystals. We show that air or vacuum annealing of the (ZrO₂)_0.94(Sm₂O₃)_0.06 crystals increases the fracture toughness of the crystals by 1.5 times as compared with that of the as-grown crystals.

Solid solutions 0.65BiFeO₃–0.35Ba_1-xSr_xTiO₃ (0 ≤ x ≤ 1) with the compositions in the vicinity of the morphotropic phase boundary “rhombohedral-cubic” were synthesized by the Solid-state reaction method. The crystal structure and morphology of the ceramics 0.65BiFeO₃–0.35Ba_1-xSr_xTiO₃ were studied based on the data obtained by X-ray diffraction, scanning electron microscopy, Raman spectroscopy, as well as energy-dispersive X-ray spectroscopy methods. It was determined that the chemical substitution of barium ions with strontium ions leads to a decrease in the magnitude of rhombohedral distortions, while the unit cell parameters decrease in the whole substitution concentration range. The solid solutions with x ≥ 0.25 are characterized by a single-phase structural state with a cubic unit cell; the average crystallite size decreases with increase of the dopant ions. The results of the structural studies carried out using Raman spectroscopy indicate the presence of rhombohedral distortions in the structure of all studied compounds, which is caused by the presence of nanosized clusters with rhombohedral symmetry. The obtained results made it possible to determine the sequence of the changes occurred in the phase state and the unit cell parameters in the region of the morphotropic phase boundary “rhombohedral -pseudocubic”; the concentration intervals corresponding to the single-phase and two-phase structural states of the compounds were determined. The region of concentration stability of the polar rhombohedral phase was clarified using the structural data obtained by local and microscopic research methods.

The article discusses current problems of the synthesis of new materials in modern conditions. It is noted that today this is the most important strategic task of innovative development of Russian industry. The factors determining the relevance of this task are formulated. A brief analysis of the state of Russian microelectronics is given. The importance of mathematical modeling methods and the need to develop innovative approaches in the field of synthesis of new materials are shown. The main directions of scientific research related to the development of new model concepts, methods and algorithms used in the field of mathematical modeling of the structures and properties of nanomaterials, as well as systems based on them, discussed at the IV International Conference “Mathematical Modeling in Materials Science of Electronic Components” (ICM3SEC-2022). The paper shows that for the further development of methods and means of mathematical modeling, a domestic high-performance environment for scientific research is required, with a comfortable user interface, flexibility in setting up resources, high performance and reliability.

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