S. B. Feodosyev

Local vibrational modes in crystal lattices with a simply connected region of the quasi-continuous phonon spectrum

It is shown that the use of the mode classification adopted in the Jacobi matrix method and which is the most natural one for describing localized states leads to extremely rapid convergence of the Green functions for frequencies lying outside the quasi-continuum band of the crystal. This has made it possible to obtain rather general analytical expressions for the conditions of formation and the characteristics of local modes due to the presence of light impurity atoms in crystal lattices having a simply connected region of the quasi-continuous phonon spectrum. The accuracy with which the frequencies and intensities of the local modes are determined using these expressions is illustrated for examples of light substitutional impurities (isotopic and weakly coupled) and close-packed structures (fcc and hcp) and also isolated pairs of isotopic impurities in an fcc crystal lattice. In particular, the results permit simple and extremely accurate evaluation of the parameters of the host lattice and defect from ...

To the theory of rare gas alloys: heat capacity

The low-temperature heat capacity of cryocrystals containing impurity clusters is investigated theoretically and experimentally. Such defects might essentially enrich the low-frequency part of the phonon spectrum by introducing both localized and delocalized vibrations. The effect of both types of vibrations on the temperature dependence of the heat capacity is analyzed. The heat capacity of the disordered solid solution Kr–Ar (Ar concentration ∼25%) is studied as an example of the effect of the light, weakly coupled impurities on the low-temperature thermodynamic characteristics of a system. The mass defect of such an impurity induces “phonon pumping” from the low-frequency part of the spectrum into the high-frequency part and decreases the low-temperature heat capacity, while the weakened interaction between the impurity and the host atoms, combined with even weaker interaction between the impurities, leads to the formation of a low-temperature maximum on the heat capacity temperature dependence. The an...

Phonon spectrum and vibrational characteristics of linear nanostructures in solid matrices

The atomic dynamics of linear chains embedded in a crystalline matrix or adsorbed on its surface is studied. A linear chain formed by substitutional impurities in a surface layer and at the same time offsetting from this layer was analyzed particularly. This system models the actively studied experimentally structures in which gas molecules are adsorbed on the walls of the bundles of carbon nanotubes located in certain medium. It is shown that the quasi-one-dimensional features are typical for the chains in which the interatomic interaction is higher than the interaction between the atoms of the chain and the atoms of the crystal matrix. On the local phonon density of atoms of the chain the transition to quasi-one-dimensional behavior has the form of the kink. In other words, it is the first (lowest-frequency) van Hove singularity, which in 3D structures (the system under consideration is generally three-dimensional) corresponds to the transition from closed to open constant frequency (quasi-plane) surfac...

Low-frequency properties of the phonon spectra, and low-temperature thermodynamics of disordered solid solutions

This is an analysis of the properties of quasi-local vibrations, and the conditions of the formation thereof, in a realistic model of the crystal lattice on a microscopic scale. The evolution of quasi-local vibrations with an increase in the concentration of impurity atoms, is examined. It is shown that the formation of boson peaks occurs mainly due to the additional dispersion of high-velocity acoustic phonons (connected to the atomic vibrations of the main lattice), caused by the scattering of these phonons by the quasi-local vibrations localized at the impurities. We demonstrate a connection between the boson peaks in disordered systems, and the first van Hove singularity, in regular crystal structures. We analyze the manifestation of quasi-local vibrations and boson peaks, as it relates to the behavior of low-temperature heat capacity, and how it changes with an increasing impurity concentration.

Quasi-Particle Spectra on Substrate and Embedded Graphene Monolayers

Graphite, graphene, and compounds based on them are of great interest both as objects of fundamental research and as some of the most promising materials for modern technologies. The two-dimensional form of graphite – graphene was prepared only very recently, immediately attracting a great deal of attention. Graphene can be deposited on solid substrates and has been shown to exhibit remarkable properties including large thermal conductivity, mechanical robustness and two-dimensional electronic properties. Note that electrons in graphene obey linear dispersion relation resulting in the observation of a number of very peculiar electronic properties. These properties are essentially changed when different defects are introduced into material. Special interest is devoted to graphite intercalated by metals, since in such graphitic systems the temperature of superconducting transition essentially depends on the type of intercalating metal. Besides, the discovery of superconductors as MgB2 and iron pnictides intensified the search for high-temperature superconductivity in materials other than copper oxides. It is known that in the formation of the superconducting state the electron-phonon interaction plays a crucial role (according to the Bardeen-Cooper-Schrieffer theory). Therefore it is necessary to analyze in detail the phonon spectra of pure graphite and to find out how these spectra are influenced by different defects and by intercalation. This chapter consists of three sections. The first section is devoted to the calculation of the local electronic density of graphene containing a substitutional impurity, vacancy defects due to the substrate surface roughness and adsorbed atoms. The local densities of states for atoms of the sublattice which not contains the vacancy show sharp peaks at energy F e e = ( F e is the energy of the Dirac singularity for ideal graphene). Local spectral densities of atoms of the sublattice which contains the vacancy conserve the same Dirac singularity as is observed in an ideal graphene. The second section will present our model, which allows to quantitatively describe the phonon spectrum of graphite and to determine the relaxation of force constants for the formation of the surface of the sample and the formation of thin films (bigraphene,

Vibrational dynamic and thermodynamic characteristics of metal–hydrogen superlattices

The phonon spectra and vibrational thermodynamic characteristics of Pd–H superlattices are investigated. Our calculations show that the neutron scattering and calorimetric data are consistent with one another and make it possible to explain for such systems the atomic mean-square amplitudes and the correlations between them.

Effect of local defects on vibrational characteristics of infinite and semi-infinite one-dimensional structures in an external periodic field

Exact analytic expressions for Green’s functions of the chain type structures with defects in an external periodic field are obtained by the method of Jacobi matrices. A diatomic impurity molecule in a monatomic chain as well as adsorbed chains with a monatomic and a diatomic unit cell are considered. The conditions for the formation and the characteristics of local and gap vibrations are investigated. The evolution of the threshold values of mass of the defect required for the formation of localized vibrations by two isotopic impurities upon a change in the separation between them is analyzed.

Role of acoustic phonons in the negative thermal expansion of layered structures and nanotubes based on them

Calculations on a microscopic level are used to explain the experimentally observed negative linear thermal expansion along some directions in a number of crystalline compounds with complicated lattices and anisotropic interactions between atoms. Anomalies in the temperature dependence of the coefficient of linear thermal expansion are analyzed in layered crystals made up of monatomic layers (graphite and graphene nanofilms) and multilayer “sandwiches” (transition metal dichalcogenides), in multilayered crystal structures such as high-temperature superconductors where the anisotropy of the interatomic interactions is not conserved in the long-range order, and in graphene nanotubes. The theoretical calculations are compared with data from x-ray, neutron diffraction, and dilatometric measurements.

Effect of step-edge on spectral properties and planar stability of metallic bigraphene

Phonon and electron spectra of metallic bigraphene are analyzed in the presence of step-edge crystal imperfection. Different geometries of step-edge are considered. The dynamic planar stability of the considered structure is proved for temperatures above the ambient. The number of phonon states is shown to grow near the K-point of the first Brillouin zone, compared to pristine graphene. It is found, that this type of defects causes substantially nonuniform distribution of electron states and the pronounced increase in the number of states with energies close to Fermi energy can be expected in electron spectrum of the graphene-based compounds. The performed calculations are in good agreement with inelastic neutron, x-ray and Raman measurements.

Distinctive features of thermal expansion of niobium diselenide

The characteristic features of thermal expansion of bulk samples of niobium diselenide have been determined experimentally and analyzed theoretically. The manifestation of the so-called membrane effect in this compound due to the significant difference in the temperature dependences of the mean-square amplitudes of atomic displacements in the parallel and perpendicular directions toward the layers has been investigated.