The total electron densities of states for graphene nanoribbons with edges of different chirality, as well as the electron local densities of states for individual atoms in these nanoribbons, are calculated and analyzed. There are sharp resonance peaks near the Fermi level in the total electron densities of states of graphene nanoribbons with zigzag edges, which emerge only in the local densities of atoms from the sublattice that goes directly to the nearest edge (i.e., whose atoms have dangling bonds). Semiconducting gaps appear in the spectra of graphene nanobands with armchair chirality edges having a number of constituent atomic lines that is either a multiple of three, or gives a remainder of one when divided by three. The width of this gap only depends on the width of the nanoribbon, and is the same for all its atoms. The electron spectra of graphene nanoribbons with armchair-chirality edges have a metallic behavior if the number of atomic lines gives a remainder of two when divided by three. However, semiconducting gaps still manifest on the local densities of the atoms belonging to some lines of such nanoribbons. Published under license by AIP Publishing.

Based on calculations conducted on a microscopic level, the phonon heat capacity of ultrathin graphene nanofilms such as bigraphene and trigraphene, and single-wall graphene nanotubes, is quantitatively described. The nature of the flexural stiffness of graphene monolayers is analyzed, and the temperature intervals at which the shape of the temperature dependence of heat capacity is determined by contributions made by flexural vibrations are identified. The contribution to the phonon heat capacity derived from graphene nanotube flexural waves that propagate along the surface thereof is analyzed, as are the bending vibrations of the tube as a whole one-dimensional object, and the contribution from torsional vibrations.

Phonon spectra of solid substitutional solutions with finite concentrations of impurities were analyzed on the microscopic level. The local phonon densities of impurity atoms were calculated, in particular the formation of quasilocal vibrations and their evolution with increasing of the concentration of impurities were investigated. Modification of the local spectral densities of atoms of the host lattice by impurities and manifestation of the phonon Ioffe-Regel crossover (scattering of fast propagating phonons on quasi-localized vibrations) were analyzed. It is shown that such scattering causes the manifestation of the features such as "boson peak" in the phonon spectrum of solid substitutional solutions. A commonality of the physical nature of such singularities in disordered structures and van Hove singularities in ideal crystals was established, notably, reducing of the group velocity of acoustic phonons due to their scattering on slow phonons.

A modification of Twist Extrusion (TE) process, Planar Twist Extrusion (PTE) with a die having two flat parallel walls moving by the plunger, was designed and implemented in the present study. Characteristics of the deformed state after PTE and TE as well as pressures involved in the processes were studied by means of experiments on aluminum samples and finite element modelling. The differences in a character of the strain distribution and mechanisms of its accumulation during PTE and TE were established. Both processes permitted mixing of the samples on a microscale.

The calculation of the local density of electronic states of graphene with vacancies, using the method of Jacobi matrix, was performed. It was shown that for atoms in the sublattice with a vacancy the local density of electronic states conserves the Dirac singularity, similarly as in an ideal graphene. A quasi-Dirac singularity was observed also in the phonon spectra of graphite for the atom displacements in the direction perpendicular to layers. Changes of phonon spectra of graphite intercalated with various metals were analyzed. On the basis of our results and using the BCS theory and Eliashberg equation we proposed what dynamic properties an intercalated graphite system should show to obtain an increased T-c.

Phonon spectra of solid substitutional solution with finite concentration of impurities have been analyzed on the microscopical level. The phonon densities of states and local phonon densities of impurity atoms are calculated. The formation of quasilocal vibrations and their evolution with increasing of the concentration of impurities are investigated.

A model of the niobium diselenide crystal lattice has been proposed. This model sufficiently describes the vibrational characteristics of both bulk samples and nanofilms with a thickness beyond one three-layered structural element. Calculation of the local Green functions and mean-squared atom amplitudes have been performed using the Jacobi-matrix method.Phonon density of states features stipulated by acoustic branches and low-frequency low-dispersion optical modes crossover have been analyzed. (C) 2009 Elsevier Ltd. All rights reserved.

It is shown that in graphite the spectral density of phonons polarized along the c axis has a V shaped feature similar to the so-called Dirac singularity characteristic of the electron density of states in graphene. The formation of quasilocal states, which increase the occupation of the quasiparticle levels near this feature, is analyzed from a unified standpoint for the phonon spectrum of metal-intercalated graphite and the electronic spectrum of graphene with vacancies. It is determined that in the electronic spectrum of graphene with an isolated vacancy quasilocal states are characteristic only of atoms belonging to the sublattice that does not contain this vacancy.

Low-frequency features of the phonon spectra of disordered solid solutions and heterogeneous crystalline structures are analyzed at the microscopic level. It is shown that boson-peak type excitations can arise in disordered solid solutions whose sites have only translational degrees of freedom. Thus it is established that such excitations appear mainly because of the additional positional dispersion of sound waves which is due to the disordering. The influence of boson-peak excitations on the low-temperature specific heat is investigated. It is found that in a number of cases the specific heat is more sensitive to excitations of this kind than the low-frequency density of states is. It is shown that anomalies similar to Ioffe–Regel’ crossover and boson peaks can also arise in disordered heterogeneous crystalline structures with a complicated lattice.

The density of states g(ω) of disordered solutions of solidified inert gases are calculated using the Jacobian matrix method. The transformation of a discrete vibrational level into an impurity band at a growing concentration of light impurity atoms is investigated. It is shown that a 1-10% change in the impurity concentration leads to smearing the local discrete level into an impurity band. As this occurs, additional resonance levels appear which carry important information about the impurity-impurity and impurity-basic lattice force interactions in such solutions.

The phonon densities of states in disordered solid solutions of aluminum in silver are determined using the Jacobi matrix method. The transformation of discrete vibrational levels (local vibrational modes) into an impurity band with increasing concentration of impurity atoms is investigated. The formation of discrete vibrational levels is associated with the presence of individual aluminum impurity atoms in the lattice. It is demonstrated that, at relatively low (approximately 5–15%) aluminum concentrations, the broadening of the main local level is accompanied by the appearance of additional resonance peaks, which contain important information on the interatomic interactions in these solid solutions.

Characteristics of the discrete vibration levels of substitution impurity are calculated for frequencies belong to gap between acoustic and optical zones (deuterium in PdH) as well as for the areas outside the phonon spectra (hydrogen in PdD). Data of neutron diffraction analysis are used to determine the force constants of pure palladium as well as PdH solid solutions. Diverse configurations of vacancies close to impurity atoms are discussed. With the help of the calculated frequencies and intensities of the local and “gap” vibrations in the system “isotope-defect + vacancies” it is possible to analyze behavior of the certain characteristics in disordered solid solutions PdH(D)x<1 and to obtain information about the vacancy structure of the considered compounds.

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.

The spectrum of oscillations localized near an interface between two identical infinite layered crystals is studied. It is shown that some important characteristics of oscillations polarized normally to the layers in layered crystals are almost completely defined by the value of interatomic anisotropy. Quasi-one-dimensional character of oscillations localized near an interface and polarized normally to it is demonstrated.

Solutions of a modified (with higher-order dispersion taken into account) sine-Gordon equation in the form of a double soliton (4π kink) and a pair of spatially separated bound kinks are investigated. An analytical condition for the absence of radiation from the soliton at large distances is formulated. The previous finding of the existence of a discrete set of nonradiative composite solitons is confirmed. The physical meaning of this result is that at certain distances between kinks the radiation generated by one of the kinks completely quenches the field of the other kink outside the soliton as a result of ordinary interference of waves in antiphase.

It is shown that the interaction between vibrational modes polarized parallel and perpendicular to the layers in a strongly anisotropic layered crystal is very weak for frequencies above the van Hove frequency, which corresponds to a transition from closed isofrequency surfaces to surfaces which are open in the weak-coupling direction. Such mode quasisplitting results in quasi-two-dimensional behavior of phonons polarized along layers and quasi-one-dimensional behavior of phonons polarized in a direction perpendicular to the layers and localized near light or strongly coupled impurity atoms or monolayers.

Vibrations localized near the surface have been analyzed by the Jacobian matrix method taking into account discreteness of the lattice. It has been shown that localized surface vibrations in layered crystals with the complex lattice have quasi-one-dimensional character and their properties are described by exact solutions obtained in the framework of the one-dimensional model.

The partial phonon densities for different displacements of mono-atomic micro-clusters on atomically smooth surfaces of FCC crystals as well as for pyramidal micro-clusters on the surface of a BCC crystal are calculated by the Jacobi matrix method. The stability of these clusters is analyzed and the temperature dependencies of root-mean displacements are obtained for atoms in different positions of such structures.

Phonon densities of Ni3Al are theoretically calculated with both partial phonon densities of each element of this alloy and the modification of these characteristics under influence of isotopic impurities, which substitute aluminium. All calculations are performed by Jacobi matrixes method, which appears to be extremely effective during the calculation of phonon densities and oscillating characteristics of crystals with polyatomic-basis lattice, and also for structures with broken regularity in arrangement of atoms.