Persons

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The self-consistent approach and the rotating group representation theory have been used to calculate the effective conductive sensor of the polycrystalline textured medium, consisting of anisotropic spherical crystallites oriented in space according to a certain probability law, that implies the uniaxial texture existence. The analytical solution for two cases - if the crystallites are slightly anisotropic and if the angle between one of the crystallites axes and the texture axis is small - has been obtained.

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Using the effective medium approximation the analytical decision of the calculation problem of the effective conductivity tensor of a polycrystalline medium with the uniaxial weakly depressed texture has been obtained. The polycrystalline medium is considered to consist of one-type spherical crystallites. To take into consideration the crystallites' orientations the rotation group representations theory has been used. The generalization of the decision for a case of triaxial textures has been obtained.

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Two methods of the accounting of randomness of inclusions’ form for calculation of effective permittivity tensor of the textured heterogeneous medium of matrix type with inclusions of a casual ellipsoidal form have been offered: an analytical method and a method of modeling of the medium with several types of inclusions. Both methods are constructed on the basis of the generalized Maxwell-Garnett's model, representations of the rotation group are applied to the accounting of inclusions’ orientations’ distribution. The results of calculation of effective dielectric characteristics of porous silicon models in the frequency range of 10-10 Hz produced by these two methods have been compared.

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Isolated small particles with a dielectric nucleus and metal shell are characterized by more complex behavior under effect of electromagnetic radiation upon them, than solid metal particles. Therefore, the composite medium, containing a big number of such particles, will have more interesting optical properties compared to a composite with solid metal inclusions. On condition of small sizes of the inclusions compared to the electromagnetic radiation wave length the optical characteristics of non-homogeneous medium can be estimated using the effective dielectric permeability of the given medium. Based on the generalized approach of the effective field the formula for calculating the effective dielectric characteristics of the matrix composite with the spherical inclusions with the shell has been derived. The given formula can be considered as a generalization of the classical Maxwell-Garnet formula for a case of the matrix medium with non-homogeneous spherical inclusions, consisting of an anisotropic nucleus and an isotropic shell. Using this formula in the range of wave length 0.282-0.855 μm the frequency dependencies of real and imaginary parts of effective dielectric permeability of the composite, consisting of alpha-quartz as a matrix and spherical nanoinclusions with a nucleus from alpha-quartz and silver shell, at various relative volume parts in the composite have been calculated. In the indicated range of the wave lengths, also, the frequency dependencies of the refraction coefficients and extinction of the given composite and the transmission and refraction coefficients of the composite film have been calculated. It has been shown that presence in the composite of the inclusions with a metal shell results in appearance of an additional plasmon resonance compared to the composite with the whole metal inclusions. For the given composite an additional plasmon resonance becomes apparent in the ultra-violet region at the wave length of 0.33-0.34 μm and from the point of intensity is much weaker than the main plasmon resonance. The availability of an additional plasmon resonance leads to appearance of a narrow band of very weak transmission of the composite film in the ultra-violet region. At the fixed volume part of inclusions in the composite and increase of the nuclei volume parts in the inclusions results in the shift of the main Plasmon resonance to the side of big lengths of waves and in its intensity decrease.

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In real polycrystals the crystallites are separated from each other by an intergranular space, affecting the effective conductivity of the polycrystal. This influence is higher when the less are the dimensions of crystallites. In the work the method of predicting the effective conductivity of polycrystalline media, which takes into account the presence of the intergranular space, has been developed. To construct the method, a polycrystal model has been adopted, in which the crystallites are considered to be non-uniform, consisting of a uniform crystalline anisotropic core and a uniform isotropic shell. To calculate the effective conductivity of the polycrystal, a generalized effective-field approximation is used, and the effective conductivity of the medium is used as a parameter of the comparison medium, i.e. a method of the self-consistent solution is used. On the basis of the developed method for a case of spherical crystallites with spherical shell the formula for polycrystal effective conductivity depending on the tensor of the crystalline cores, the conductivity of the shell and the volume fraction of the cores in the crystallines, has been obtained. This formula is applied in particular cases of polycrystalline medium, precisely for a polycrystal with single-type crystallites with isotropic core, in which case the expression for effective conductivity coincides with the classical Maxwell - Garnet formula; for polycrystal with the single-type with anisotropic cores with the same orientation of their crystallographic axes in space; for polycrystal with single-type crystallites with anisotropic cores with uniform distribution of orientations of their crystallographic axes in space; for polycrystal with conducting cores of crystallites and absolutely non-conducting shells. In the latter case the effective conductivity of the polycrystal turns to zero conductivity, which is fully consistent with the physical meaning. Funding: the work has been supported by the Russian Foundation for Basic Research (project no. 19-08-00111-a).

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Porous plastics are used in various fields of industry, including radio- and electrotechnical fields. They are characterized by good heat- and sound isolating, dielectric and mechanical properties as well as by resistance to effect of various external factors during operation. The problem of estimation of effective permittivity of foam-polymer materials with a large volume fraction of pores, in particular, polyepoxide foam materials, has been considered. Two methods for solving it, both based on the matrix have been proposed. In the first method the matrix is considered as a polyepoxide binder, and the cavities filled with gas are taken as inclusions. In the second method the polyepoxide walls, separating cavities, are taken as inclusions, and gas filling cavities is considered as a matrix. To obtain the formulas for calculation, both methods use a generalized singular approximation of the theory of random fields. Based on the obtained expressions, the model calculations of the effective permittivity of a macroscopically isotropic foam material with a polymer binder based on E-20 and the cavities filled with freon, depending on the apparent density of the material, have been made. The calculations in the generalized singular approximations have been carried out for two of its variants: when the matrix was considered as a comparison medium; and, also by the self-consistent method. In the calculations using the second method two variants of the shape of the cells of the material have been considered: a weakly leaked or heavily leaked polyhedron. The calculated dependences obtained by all methods have shown the qualitative compliance with the experimental data.

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Syntactic materials (spheroplastics) having low density due to structural features, depending on the material of the microsphere walls can have a sufficiently high strength and low thermal conductivity, which makes them promising for use as heat insulation materials. By selecting the material of the microsphere walls and the concentration of the components of the spheroplastics, their dielectric characteristics can be significantly changed. In this work, the task of modeling the effective dielectric characteristics of a syntactic material with a polymer binder and filler in the form of hollow glass microspheres is considered, taking into account the presence of technological impurities in the material. A model for calculating the effective permittivity of a sample of a syntactic material was proposed, based on a model of a matrix composite with several types of inhomogeneous or homogeneous inclusions. To calculate, a generalized effective-field approximation for a heterogeneous medium with coated inclusions was used. Model calculations were carried out for syntactic foam with an organosilicon binder polydimethylsiloxane and hollow microspheres with E-glass shell with some moisture presence in the material. Frequency dielectric characteristics of this material were obtained in the range of 10-10 Hz. It has been shown that an increase in the volume fraction of hollow microspheres leads to a decrease in the dielectric constant and the tangent of the dielectric loss angle. It has also been shown that the calculated values are in satisfactory accordance with the experimental data obtained at an electromagnetic field frequency of 9.8 GHz.

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The theory of conductivity of inhomogeneous materials with texture has been developed. Using the generalized effective-medium approach the tensor of electric conductivity components of the polycrystalline medium as the function of values of the tensor components of the crystallites conductivity, crystallites' orientation dispersion and the sample orientation in the laboratory coordinates system have been found. The recommendations for experimental determination of the sample basic characteristics (including the dispersion of the crystallites axes directions with reference to the texture axis) have been given.

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