Three-dimensionality of space in the structure of the periodic table of chemical elements

The effect of the dimension of the 3D homogeneous and isotropic Euclidean space, and the electron spin on the self-organization of the electron systems of atoms of chemical elements is considered. It is shown that the finite dimension of space creates the possibility of periodicity in the structure of an electron cloud, while the value of the dimension determines the number of stable systems of electrons at different levels of the periodic table of chemical elements and some characteristics of the systems. The conditions for the stability of systems of electrons and the electron system of an atom as a whole are considered. On the basis of the results obtained, comparison with other hierarchical systems (nanostructures and biological structures) is performed.     

Gamma-resonance study of nanopowders with different dispersion and quasicrystalline phases in the Al-Cu-Fe system

⁵⁷Fe Mössbauer spectroscopy has been used to monitor synthesis of quasicrystals in the Al-Cu-Fe system and study the influence of the size of quasicrystalline particles in powder samples of the Al_63.1Cu_25.6Fe_11.3 alloy on the properties of synthesized materials. Quasicrystalline samples of different dispersion with particle sizes from 0.3 to 15 μm have been studied in the temperature range 80–295 K. It is established that iron atoms in an Al_63.1Cu_25.6Fe_11.3 quasicrystals occupy four types of structural positions, which differ in the atomic composition of the nearest environment. The results of the analysis suggest the dependence of the hyperfine-interaction parameters on the degree of sample dispersion. The components corresponding to iron atoms in both the surface layer and bulk of microparticles are isolated in the Mössbauer spectra. No magnetic hyperfine splitting has been found in the Mössbauer spectra in the entire temperature range. This fact suggests that a localized magnetic moment is absent in iron atoms.     

Magnetic susceptibility of quasicrystalline Al<Subscript>65</Subscript>Cu<Subscript>22</Subscript>Fe<Subscript>13</Subscript> powders

Magnetic properties of quasicrystalline Al₆₅Cu₂₂Fe₁₃ powders synthesized by the solid-phase diffusion method via thermal treatment in vacuum or a hydrogen atmosphere have been studied. The powders synthesized in vacuum are found to contain a ferromagnetic fraction. The formation of iron oxide Fe₃O₄ is shown to be the most probable cause of the existence of this fraction. It is possible to avoid the formation of the ferromagnetic fraction in the powders synthesized or annealed in hydrogen. Removal of the ferromagnetic fraction from the powder by repeated magnetic separation made it possible to obtain a quasicrystalline fraction, for which the behavior of the magnetic susceptibility can be explained by the formation of nanoclusters. Such behavior is a general and integral property of quasicrystalline powders synthesized in both vacuum and hydrogen.     

Extremely short electromagnetic pulses in a resonant medium with a permanent dipole moment

The propagation of an extremely short (one cycle long) pulse of an electromagnetic field in a medium whose resonant transition is characterized by both diagonal and off-diagonal matrix elements of the dipole-moment operator is considered theoretically. The set of Maxwell-Bloch equations without the approximation of the slowly varying envelopes is used. Two types of solutions of this set, which are found describing the steady-state propagation of an electromagnetic pulse in such a medium.     

Criterion for identification of ferroelectric domains in TGS crystals from AFM images

Criteria for identification of actual (dynamic) domains and morphologically similar domain “memory” regions are proposed based on the study of various types of contrast of topographic atomic-force microscopy images of lenslike regions on the polar surface of TGS crystals. Inaccuracy in identification may result in further errors in estimating the parameters of the domain structure. The images of ferroelectric domains in the spreading-resistance mode that indicate directly the presence of conductive properties of the domain walls have been obtained for the first time.     

On the evaluation of rotational transition probabilities from distribution functions

A method is described for the evaluation of rotational transition probabilities from the nonequilibrium distributions possessed by the products of certain chemical reactions. Results obtained from the method are compared with those provided by theoretical calculation.     

Symbol algebras and cyclicity of algebras after a scalar extension

For a field F and a family of central simple F-algebras we prove that there exists a regular field extension E/F preserving indices of F-algebras such that all the algebras from the family are cyclic after scalar extension by E. Let \( \mathcal{A} \) be a central simple algebra over a field F of degree n with a primitive nth root of unity ρ _n . We construct a quasi-affine F-variety Symb(\( \mathcal{A} \)) such that for a field extension L/F Symb(\( \mathcal{A} \)) has an L-rational point if and only if \( \mathcal{A}{ \otimes_F}L \) is a symbol algebra. Let \( \mathcal{A} \) be a central simple algebra over a field F of degree n and K/F be a cyclic field extension of degree n. We construct a quasi-affine F-variety C(\( \mathcal{A} \) ,K) such that, for a field extension L/F with the property [KL : L] = [K : F], the variety C(\( \mathcal{A} \) ,K) has an L-rational point if and only if KL is a subfield of \( \mathcal{A}{ \otimes_F}L \).