A mathematical relation has been obtained that makes it possible to calculate the polarizability of a polyatomic molecule in the structure of a cluster. It is shown that the scattered frequencies in the Raman effect are proportional to the square root of the number of particles in the most probable (or average) cluster in the liquid structure. The appearance of frequencies in the far part of the Raman spectrum region is caused by the processes of intermolecular interactions in clusters and the processes of disintegration or formation of cluster systems in the structure of disordered condensed media. According to the proposed model and experimental data in the frequency range 20–1300 cm-1, it has been carried out the comparison of the values of the calculated frequencies of the Raman spectrum and their mutual position, which has shown the adequacy of the proposed model. The cluster model of liquid structure and the methods of mathematical statistics and statistical thermodynamics make it possible to expand the capabilities of the classical theory of Raman scattering in liquids and to predict the position of spectral bands in Raman spectra in the far long-wavelength region of the spectrum. It is revealed that the formation and breakdown of the most probable clusters is associated with the correlations of the most stable clusters (in terms of the number of particles) in a condensed medium with the Fibonacci numbers.
It is demonstrated theoretically that the initial (both elastic and viscous) magnetic susceptibility components for nanocrystalline magnets caused by the processes of rotations (in the region of linear response) have resonant rather than relaxation character typical already for the susceptibility component caused by displacements of domain boundaries. Magnetic susceptibility of magnets and ferrites is a very structurally sensitive parameter [1, 2]. According to S. V. Vonsovskii and V. K. Arkad'ev, this is the case for its elastic ( ′ χ ) and viscous components ( ′′ χ ). Each of them, in turn, has a rotational component ( r χ ) and a component ( v χ ) caused by displacements of domain boundaries. In this case, ( ) r ′ χ ω first remains virtually unchanged with increasing frequency and then fast decreases to zero, and r ′′ χ , on the contrary, first increases from zero to a maximum and then decreases to zero. The dependence ( ) v ′ χ ω has resonant character: at the beginning it is maximal like ( ) r ′ χ ω , then passes through zero and, remaining negative, vanishes. The v ′′ χ value, like ( ) r ′′ χ ω , has a maximum. Similar dependences ( ) χ ω , correlating with the experimental data [1, 2], were obtained based on the macroscopic approach [3, 4] that allows the prehistory of the system and the orientation and frequency of the variable magnetic field Н to be considered in ample detail. Analogous situation is observed for ferroelectrics [5]: ( ) v χ ω has the same resonant character of the dispersion, and ( ) rχ ω has the relaxation character. However, all this refers to conventional, that is, non-nanodimensional materials. In nanocrystalline materials, the dispersion of the magnetic susceptibility is rather specific and has a number of special features [6]. We first dwell on a model description of one of them caused by the presence of internal stresses in nanocrystalline materials formed during their manufacture. We consider triaxial nanocrystalline materials that, in addition to the interphase component that does not have even near order [6], have a crystalline component. In nanocrystalline materials with grain sizes k d greater than or equal to the domain boundary width δ, magnetic phases with spontaneous magnetization vectors S
Quasicrystalline film with densest package of atoms can be formed on a crystal surface under irradiating crystal surface with protonion flows at a certain ratio of atoms diameters of irradiated crystal and the ions of irradiating flow. Atom-free area of 1 Å order is formed. These are traps for protons from the irradiation stream, thus a quantum dot appears. Atomic package of quasicrystalline film is a package of equilateral Penrose rhombs and there are centers of atoms mass at the vertices. A mathematical relation is obtained that allows predicting radii of irradiation flux ions to form quasicrystalline film and select atomic composition of the obtained film with predetermined properties. Nanostructuring of materials is an entire family of physicochemical processes associated with proton transfer and their localization in crystal lattice and these include ion exchange, diffusion, and ion implantation. Ion and proton exchange can be considered an established universal method of surface modification technology [24– 26]. The case of implantation of protons into the structure of cluster systems formed on the surface of crystals is described in this paper. In this case, a quantum dot is formed in the cluster structure, which is a potential hole with quantized proton motion, wherein the radiation of quantum dot is in IR area of electromagnetic spectrum.
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