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[en] This review examines the elastic response of solids under load. The definitions of isothermal and adiabatic elastic constants of () for a loaded crystal are given. For the case of hydrostatic pressure, two techniques are proposed for calculating the second-, third-, and fourth-order elastic constants from the energy-strain and stress-strain relations. As an example, using the proposed approach within the framework of the density functional theory, the second- to fourth-order elastic constants of bcc tungsten are calculated for the pressure range of 0–600 GPa. (methodological notes)
[en] Crystalline lattices can become unstable to uniform shear strains, which may lead to a structural transformation to less symmetric structures. Transitions of this type are called elastic phase transitions. In this paper, elastic phase transitions in metals with cubic and hexagonal structures are considered. The relation between the elastic constants of second, third, and fourth order corresponding to the case of a first-order elastic phase transition are given. As an example, the structural transformation in vanadium, which is experimentally observed at P≈69 GPa, and the possibility of structural transformation in molybdenum at P higher than 700 GPa are analyzed. (methodological notes)
[en] The isothermal and adiabatic nth-order (n ≥ 2) elastic constants of a loaded crystal are defined. These constants fully determine the behavior of solids at an arbitrary load and are controlled by both an interatomic interaction and an applied load. Expressions that relate these constants (of the second, third, and fourth order) to Brugger elastic constants of the corresponding order, which are only determined by an inter-atomic interaction, are found for cubic symmetry crystals under hydrostatic pressure. These expressions are used to calculate the equation of state and the second- and third-order elastic constants of bcc tantalum at T = 0 K over a wide pressure range (0–600 GPa) using an electron density functional method. The results of calculating the equation of state and the second-order elastic constants agree with available experimental data and the calculation results obtained in other works.
[en] The electronic structure, charge state, and hydrogen diffusion in icosahedral Ti-based alloys have been investigated by the methods based on the density-functional theory. The charge state of the hydrogen atom in Ti36Zr32Ni13 has been determined for different types of tetrahedral voids. The charge state of hydrogen atoms in Ti36Zr32Ni13, Ti36Hf32Ni13, and Ti48Zr8Fe18 is calculated for the ratio H/M = 1.7, where H is the number of hydrogen atoms and M is the number of metal atoms. It is established that hydrogen atoms in all objects studied are in an almost neutral state. The hydrogen diffusion coefficient is determined for Ti36Zr32Ni13
[en] Structural transformations in elementary metals under high pressures are considered using the Landau theory of phase transitions, in which the finite strain tensor components play the role of the order parameter. As an example, the phase transition in vanadium observed at a pressure of 69 GPa is analyzed. It is shown that it is a first-order elastic phase transition, which is close to a second-order transition.
[en] The structure and properties of quasicrystals are discussed. The short-and long-range atomic orders and the effect of these factors on the physical characteristics are considered. It is noted that investigations of the physical properties of quasicrystals at temperatures above room temperature should be performed. Promising applications are briefly outlined
[en] Electronic and excitonic excitations in aperiodic sequences of quantum dots (Thue-Morse, Cantor, Fibonacci, Double-period) were studied in external electrical and magnetic field. Single-particle and two-particle tunneling probability was taken into consideration. Transmission coefficient was determined using quasi-classical approximation and range of values of confining potential and interdot distances when tunneling is essential was estimated. An external electrical and magnetic field effect on electron localization was taken into consideration, an effective steepness of confining potential in magnetic field was appeared as control parameter of the problem. Energy spectrum of aperiodic quantum dot sequences in external magnetic field was obtained. Possibility to tune the state of the system by magnetic field was studied. The increase of the external electrical field shifts the energy states of the particle in a quantum dot and contributes to particle localization. The localization of the excitations is possible at the finite values of the perturbation in the case of aperiodic sequences of quantum dots (contrary to the case of periodical sequences).
[en] The elastic properties and structural stability in ruthenium under pressure are investigated. The analysis is performed in the framework of Landau theory and nonlinear elasticity. For this purpose the definition of effective elastic constants (EC) of n-th (n≥2) order characterizing elastic properties of loaded crystal and the relations between effective EC and corresponding EC of Bragger type for hcp crystals is given. The conditions of hcp lattice stability to the uniform shear strain under the pressure P are expressed in terms of the second order effective EC. The method of effective EC calculations for hcp crystals under hydrostatic pressure is presented. The equation of state and EC of second and third order and phonon dispersion relations in high-symmetry directions in the pressure range of 0 – 600 GPa are calculated in the framework of the density functional theory (DFT) and the density functional perturbation theory (DFPT) respectively. EC are in the good agreement with available experimental data and increase monotonically with pressure, no softening or stability condition violation are observed. Softening of phonon frequencies near the Brillion zone center is also not observed
[en] The energy spectra and transport of electronic excitations in one-dimensional aperiodic sequences of quantum dots of Thue-Morse and double-periodic type are studied. The influence of external magnetic and electric fields on the energy spectra and transport is considered. For aperiodic sequences of quantum dots, in contrast to aperiodic sequences of atoms, the influence of relatively small magnetic and electric fields is essential, but localization occurs at finite values of the perturbations. The transmission coefficient is determined using the quasiclassical approximation with the Coulomb blockade taken into account. The resonance tunneling is studied.
[en] The exact muffin-tin orbitals (EMTO) technique in conjunction with the coherent-potential approximation (CPA) as well as the projector-augmented-wave (PAW) method have been used to calculate the surface segregation energy of Cr at the (100) surface of Fe-rich bcc Fe-Cr alloys. We find that PAW results strongly depend on the supercell size used in the calculations. In particular, for large supercells, the surface segregation energy of Cr is positive, which means that Cr should not segregate toward the surface of diluted alloys. This is in agreement with our EMTO-CPA results as well as previous surface Green's-function calculations. However, the surface segregation energy of Cr is negative if small unit cells are used for simulations. This is in agreement with previous full-potential supercell calculations. We explain such a size dependence by a peculiar concentration dependence of interatomic interactions in ferromagnetic Fe-Cr alloys