The quantum tunnel effect from the point of view of quantum mechanics and classical physics

Parallel analyses of matter penetrating a barrier are analyzed, one using electrodynamics, the other using quantum mechanics. Mathematical operations are performed to show the identical nature of the phenomena of reflection above the barrier and of penetration of the barrier in quantum mechanics and in classical electrodynamics. It is shown that, in reality, the tunneling effect is not a “purely quantum phenomenon”. Проведено параллельное рассмотрение прохождения материи через барьер методами электродинамики и квантовой механики. Математически строго получена абсолютная идентичность надбарьерного отражения и подбарьерного прохождения, как в квантовой механике, так и в классической электродинамике. Показано, что определение туннельного эффекта как «чисто квантового явления» – не соответствует действительности. Проведено паралельне дослідження проходження матерії через бар’єр методами електродинаміки та квантової механіки. Математично виключно отримана абсолютна ідентичність надбар’єрного відбиття та підбар’єрного проходження як у квантовій механіці так і в класичній електродинаміці. Показано, що визначення тунельного ефекту як «чисто квантового явища» – не відповідає дійсності

On the theory of structuring magnetic suspensions

The results of the three-dimensional computer and analytical simulation are presented for the kinetics of chain-shaped aggregate growth in suspensions of magnetizable non-Brownian particles. The results of the computer experiment show that, when the volume fraction of particles is no larger than 2-3%, chain-shaped aggregates are formed in the suspensions under the action of a field. The dependence of average number <n> of particles in a chain on time t is adequately described by the power law <n> = Ct k . The experiment indicates that, in contract to the common power approximations, in which exponent k is considered to be a universal constant parameter, it depends on the concentration of particles and their interactions with walls bounding a suspension. At concentrations noticeably exceeding 2-3%, dense bulk aggregates are formed in suspensions. The kinetics of their growth depends on the sizes of a suspension-containing vessel. © 2013 Pleiades Publishing, Ltd

Electronic structure and stability of nonstoichiometric titanium monoxide TiOy with structural vacancies in one of the sublattices

The electronic structure of nonstoichiometric titanium monoxide TiOy with different compositions y, which contains structural vacancies either in the metallic sublattice or in the nonmetallic sublattice, has been investigated using the supercell method within the DFT-GGA approximation with pseudopotentials. The cases of ordered and disordered arrangements of vacancies have been considered. It has been found that the complete removal of vacancies from the sublattice is energetically unfavorable, and the ordering of oxygen vacancies according to the type of the Ti6O5□1 superstructure, as well as titanium vacancies according to the Ti5black small square1O6 type, does not lead to the stabilization of the B1 basic structure of titanium monoxide. © 2013 Pleiades Publishing, Ltd

Internal energy and parameters of the order-disorder phase transition in titanium monoxide TiO y

Quantum-mechanical ab initio calculations are used to simulate the free energy functions for titanium monoxide TiO y . The effect of the long-range order of the Ti5O5 type superstructure on the internal energy of the compound is studied by the supercell method. The dependences of the configuration entropy and free energy on the long-range order parameter are determined. It is found that the order-disorder phase transition in titanium monoxide must occur in accordance with the mechanism of the first-order phase transition with a critical value of the long-range order parameter of 0.971. The calculated parameters of the phase transition are compared with the experimental data and the results obtained using the model of point charges and by calculating the Madelung energy. It is concluded that the short-range order and the phonon entropy must be taken into account in calculating the equilibrium phase diagrams for strongly nonstoichiometric compounds. © 2013 Pleiades Publishing, Ltd

Simulation of the short-range order in disordered cubic titanium monoxide TiO1.0

A model of the atomic structure with the short-range order in the vacancy distribution for the disordered cubic phase of titanium monoxide TiO1.0 has been proposed. The effect of the short-range order on the electronic structure and the stability of the compound has been studied by the supercell method within the DFT-GGA approximation with the use of pseudopotentials. It has been established that the appearance of the short-range order considerably decreases the total energy. The decrease in the energy is comparable with the energy gain during the ordering of the vacancies according to the type of monoclinic superstructure Ti5O5 to the long-range order parameter η = 0.7. It has been shown that the discrepancies between the theoretical and experimental electronic spectra of titanium monoxide can be explained by allowance for the short range order. © 2013 Pleiades Publishing, Ltd