Discrete breathers in alpha-uranium

Uranium is an important radioactive material used in the field of nuclear energy and it is interesting from the scientific point of view because it possesses unique structure and properties. There exist several experimental reports on anomalies of physical properties of uranium that have not been yet explained. Manley et al. [Phys. Rev. Lett. 96, 125501 (2006); Phys. Rev. B 77, 214305 (2008)] speculate that the excitation of discrete breathers (DBs) could be the reason for anisotropy of thermal expansion and for the deviation of heat capacity from the theoretical prediction in the high temperature range. In the present work, with the use of molecular dynamics, the existence of DBs in α-uranium is demonstrated and their properties are studied. It is found that DB frequency lies above the phonon band and increases with DB amplitude. DB is localized on half a dozen of atoms belonging to a straight atomic chain. DB in uranium, unlike DBs in fcc, bcc and hcp metals, is almost immobile. Thus, the DB reported in this study cannot contribute to thermal conductivity and the search for other types of DBs in α-uranium should be continued. Our results demonstrate that even metals with low-symmetry crystal lattices such as the orthorhombic lattice of α-uranium can support DBs.     

Interaction of phonons with discrete breathers in one-dimensional chain with tunable type of anharmonicity

In this paper, we consider the interaction of small amplitude waves (phonons) with standing discrete breather (DB) in the one-dimensional chain of harmonically coupled particles interacting with the anharmonic one-site potential, which can be of hard-type or soft-type anharmonicity. The coefficients of phonon reflection and transmission are calculated numerically. It is found that for the case of hard-type anharmonicity (soft-type anharmonicity) DBs are more transparent for short-wavelength (long-wavelength) phonon waves, while they efficiently reflect long-wavelength (short-wavelength) phonons. In thermal equilibrium, when all phonons have equal energy density, it is found that for the same width of the transparency window, DB transmits less energy in the case of the hard-type anharmonicity. This is so because, in this case, DB reflects long-wavelength phonons, which have larger group velocity and hence greater contribution to the net energy flux through the DB. In this sense, DBs more efficiently suppress thermal conductivity in the chain with hard-type anharmonicity. Our results contribute to a better understanding of the role of discrete breathers in the heat flow in nonlinear chains.     

Discrete breathers in biatomic crystals of <Emphasis Type="Italic">AB</Emphasis> and <Emphasis Type="Italic">A</Emphasis><Subscript>3</Subscript><Emphasis Type="Italic">B</Emphasis> composition

The conditions for the existence of discrete breathers (DBs) in biatomic crystals of AB and A ₃ B composition are established, and their properties are studied by means of molecular mechanics using the examples of CuAu and Pt₃Al, respectively. The phonon spectra of the crystals are analyzed, and a gap in the phonon spectrum of CuAu is obtained via considerable homogeneous elastic strain. There is a gap in the phonon spectrum of the Pt₃Al crystal at zero strain, due to the considerable difference between the atomic weights of its components. The frequencies at which discrete breathers can exist in the considered crystals are determined. The energy localized on different types of DBs is estimated. The propagation of a current pulse through Pt₃Al resulting in the excitation of DBs with mild nonlinearity is simulated.     

Localized vibrational,edges and breathing modes of graphene nanoribbons with topological line defects

Peculiar vibrational modes of graphene nanoribbons (GNRs) with topological line defects were presented. We find that phonon dispersion relations of the topological defective GNRs are more similar to those of perfect armchair-edge GNR than to zigzag-edge GNR in spite of their zigzag edge. All vibrational modes at Γ point are assigned in detail by analyzing their eigenvectors and are presented by video. Three types of characteristic vibrational modes, namely, localized vibrational modes in defect sites, edges, and breathing modes, are observed. Five localized vibrational modes near the defect sites are found to be robust against the width of the topological line-defective GNR. The Raman D’ band just originates from one localized mode, 1622 cm^-1. The vibrational mode is sensitive to symmetry. The edge modes are related with structural symmetry but not with widths. Two edge modes are asymmetrical and only one is symmetrical. The breathing modes are inversely proportional to the width for wide-defect GNRs, and inversely proportional to the square root of the width for narrow-defect GNRs. The breathing mode frequencies of defective GNRs are slightly higher than those of perfect GNRs. These vibrational modes may be useful in the manipulation of thermal conductance and implementation of single phonon storage.     

Gap discrete breathers in a two-component two-dimensional crystal in thermal equilibrium

Crystals having a gap in the phonon spectrum can maintain gap discrete breathers (DBs), i.e., nonlinear localized oscillatory modes existing in the absence of defects and having a frequency lying in the gap. The lifetime of gap DBs in a two-dimensional perfect crystal of the composition A ₃ B in thermal equilibrium has been studied by the molecular dynamics method. As was shown earlier, the existence of gap DBs in such a crystal is provided by the presence of a wide gap in the phonon spectrum if the component mass ratio m _A /m _B is sufficiently large. For comparison, a crystal with a relatively small ratio m _A /m _B is considered when the gap in the spectrum is absent and the existence of gap DBs is impossible in the case of a weak nonlinearity realized in the considered case. It has been shown that, in contrast to the opposite case, in a crystal maintaining gap DBs, long-lived localized oscillatory modes of large amplitude can emerge, whose concentration and lifetime increase with temperature.     

Molecular dynamics calculations of anharmonic properties of the vibrational spectrum of BCC zirconium under pressure

The structural stability and lattice dynamics of the high-pressure bcc phase of Zr at a constant temperature T = 500 K are studied for various volumes using molecular dynamics simulation with the Animalu pair pseudopotential. Dispersion curves of the vibrational spectrum calculated by the molecular dynamics method for various volumes are compared to the phonon spectrum obtained in the harmonic approximation. It is demonstrated that, as the volume decreases, all frequencies of the vibrational spectrum increase gradually and bcc zirconium remains strongly anharmonic along all high-symmetry directions of the Brillouin zone over the entire range of volumes studied. The strongly anharmonic N _T1 phonon is significantly softened near the point of structural instability of bcc-Zr at T = 500 K and V = 0.87V ₀. As the volume decreases to V = 0.73V ₀ under pressure, the anharmonic corrections for this phonon decrease by almost an order of magnitude and the phonons near the H point of the Brillouin zone become anharmonic. The damping of the T ₁ phonon mode along the [110] direction is calculated as a function of pressure.     

Structure and phonon spectrum of a submonolayer Ni film on the surface of Cu(100)

The equilibrium atomic structure and the phonon spectra of a submonolayer (θ = 0.5 monolayer) Ni film deposited on the surface of Cu(100) are calculated using the potentials obtained by the embedded atom method. We consider atomic relaxation, the vibrational state density distribution on Ni and substrate atoms, and polarization of vibrational modes. Variation of the phonon spectrum upon segregation of Cu atoms on the film surface is considered. It is shown that mixing of vibrations of Ni adatoms with vibrations of substrate atoms occurs in the entire frequency range, leading to a frequency shift of the vibrational modes of the substrate and to the occurrence of new vibrational states atypical of a clean surface. The Cu(100)–c(2 × 2)–Ni structure is dynamically stabler when placed in the subsurface layer of the substrate.     

Investigation of weakly-nonlinear development of unsteady Görtler vortices

We have examined, both experimentally (using fully controlled disturbances) and theoretically, the weakly-nonlinear development stages of unsteady (in general) Görtler instability of a boundary layer over a concave surface. Primary attention was given to early manifestations of nonlinearity in the development of unsteady Görtler vortices belonging to the first, most rapidly growing, mode in the discrete spectrum of the stability problem. We have investigated the manifestations of instability versus the frequency of the fundamental (primary) Görtler mode and the initial disturbance amplitude. The weakly-nonlinear stage of development of unsteady Görtler vortices was found to display the following characteristic features: (a) nonlinear interaction among the combination modes in the frequency-wavenumber spectrum, (b) distortion of the wall-normal profiles of disturbance amplitudes and phases, (c) reduction of the growth rate of the fundamental Görtler mode and the majority of combination modes, and (d) a decrease in the phase velocities of unsteady disturbances. It was found that the disturbances enter the region of weakly-nonlinear development after the amplitude of the fundamental frequency-wavenumber mode reaches a threshold of 4–6 %, this value being much greater than that for Tollmien — Schlichting waves (1–2 %) but significantly lower than that for the cross-flow instability modes in three-dimensional boundary layer (more than 10 %).     

Peculiarities of FeSi phonon spectrum induced by a change of atomic volume

We analyze in detail the results of experimental investigations of the evolution of the thermal vibration spectra for iron atoms in iron monosilicide FeSi depending on two external parameters, viz., temperature T (in the range 46–297 K at pressure P = 0.1 MPa) and pressure P (in the range 0.1 MPa–43 GPa at temperature T = 297 K), obtained by nuclear inelastic scattering of synchrotron radiation. The decrease of the atomic volume is accompanied by a rearrangement of the phonon spectrum, which is manifested, in particular, in the splitting of the low-energy peak in the spectrum and in an increase of the energy for all phonons. The changes of the average energy of the iron atom vibrational spectrum and of the Debye energy with decreasing atomic volume are analyzed. Different versions of FeSi electron spectrum variation, which can be used to explain the observed phonon anomalies, are considered.     

Discrete breather on the edge of the graphene sheet with the armchair orientation

Linear and nonlinear vibrations of a graphene nanoribbon with free armchair edges subjected to tensile deformation have been studied by atomistic simulation methods. It has been shown that the phonon modes are split into two subsets. Atoms in some (XY) modes vibrate in the nanoribbon plane and in other (Z) modes vibrate along the normal to this plane. The possibility of the excitation of a gap discrete breather in an extended nanoribbon in the spectrum of the Z modes, the frequency of which lies in the gap of the spectrum of the XY modes, has been demonstrated. This breather is a large-amplitude vibrational mode in the XY plane localized on the four atoms on the nanoribbon edge. The breather is unstable with respect to small perturbations in the form of displacements of atoms out of the nanoribbon plane. Nevertheless, the discrete breather decays slowly owing to its weak interaction with the Z modes, so that its lifetime can be on the order of 103 vibrational periods.     

Discrete breathers in deformed graphene

The linear and nonlinear dynamics of elastically deformed graphene have been studied. The region of the stability of a planar graphene sheet has been represented in the space of the two-dimensional strain (? _xx , ? _yy ) with the x and y axes oriented in the zigzag and armchair directions, respectively. It has been shown that the gap in the phonon spectrum appears in graphene under uniaxial deformation in the zigzag or armchair direction, while the gap is not formed under a hydrostatic load. It has been found that graphene deformed uniaxially in the zigzag direction supports the existence of spatially localized nonlinear modes in the form of discrete breathers, the frequency of which decreases with an increase in the amplitude. This indicates soft nonlinearity in the system. It is unusual that discrete breather has frequency within the phonon spectrum of graphene. This is explained by the fact that the oscillation of the discrete breather is polarized in the plane of the graphene sheet, while the phonon spectral band where the discrete breather frequency is located contains phonons oscillating out of plane. The stability of the discrete breather with respect to the small out-of-plane perturbation of the graphene sheet has been demonstrated.     

Submonolayer adsorption of Na onto the Cu(110) surface: Structure and vibrational properties

The submonolayer adsorption of Na onto the Cu(110) surface is studied. At small Na coverages (Θ = 0.16–0.25 ML), the substrate surface subjected to missing-row reconstruction (1 × 2) is shown to be most stable dynamically. When the coverage increases to Θ = 0.5 ML, the unreconstructed substrate surface with a c(2 × 2) sodium adlayer becomes dynamically stable. For an analysis, we used data on the equilibrium atomic configuration, the adsorption energy, the phonon spectra, the local density of phonon states, and the polarization of localized vibrational modes. All calculations were performed using the interatomic potentials obtained in terms of the embedded-atom method. The calculated frequencies of localized vibrational modes agree well with the existing experimental data.     

<Emphasis Type="Italic">q</Emphasis>-Breathers in discrete nonlinear Schrödinger arrays with weak disorder

Nonlinearity and disorder are key players in vibrational lattice dynamics, responsible for localization and derealization phenomena. q-Breathers—periodic orbits in nonlinear lattices, exponentially localized in the reciprocal linear mode space—is a fundamental class of nonlinear oscillatory modes, currently found in disorder-free systems. In this paper we generalize the concept of q-breathers to the case of weak disorder, taking the Discrete Nonlinear Schrödinger chain as an example. We show that g-breathers retain exponential localization near the central mode, provided that disorder is sufficiently small. We analyze statistical properties of the instability threshold and uncover its sensitive dependence on a particular realization. Remarkably, the threshold can be intentionally increased or decreased by specifically arranged inhomogeneities. This effect allows us to formulate an approach to controlling the energy flow between the modes. The relevance to other model arrays and experiments with miniature mechanical lattices, light and matter waves propagation in optical potentials is discussed.     

Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling

We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings.With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions.When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone.Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach.The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed.In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.     

Analysis of the crystal lattice instability for cage–cluster systems using the superatom model

We have investigated the lattice dynamics for a number of rare-earth hexaborides based on the superatom model within which the boron octahedron is substituted by one superatom with a mass equal to the mass of six boron atoms. Phenomenological models have been constructed for the acoustic and lowenergy optical phonon modes in RB₆ (R = La, Gd, Tb, Dy) compounds. Using DyB₆ as an example, we have studied the anomalous softening of longitudinal acoustic phonons in several crystallographic directions, an effect that is also typical of GdB₆ and TbB₆. The softening of the acoustic branches is shown to be achieved through the introduction of negative interatomic force constants between rare-earth ions. We discuss the structural instability of hexaborides based on 4f elements, the role of valence instability in the lattice dynamics, and the influence of the number of f electrons on the degree of softening of phonon modes.     

Ab initio simulation of gap discrete breathers in strained graphene

The methods of the density functional theory were used for the first time for the simulation of discrete breathers in graphene. It is demonstrated that breathers can exist with frequencies lying in the gap of the phonon spectrum, induced by uniaxial tension of a monolayer graphene sheet in the “zigzag” direction (axis X), polarized in the “armchair” direction (axis Y). The found gap breathers are highly localized dynamic objects, the core of which is formed by two adjacent carbon atoms located on the Y axis. The atoms surrounding the core vibrate at much lower amplitudes along both the axes (X and Y). The dependence of the frequency of these breathers on amplitude is found, which shows a soft type of nonlinearity. No breathers of this type were detected in the gap induced by stretching along the Y axis. It is shown that the breather vibrations may be approximated by the Morse oscillators, the parameters of which are determined from ab initio calculations. The results are of fundamental importance, as molecular dynamics calculations based on empirical potentials cannot serve as a reliable proof of the existence of breathers in crystals.     

Phonon structures of GaN-based random semiconductor alloys

Accurate modeling of thermal properties is strikingly important for developing next-generation electronics with high performance. Many thermal properties are closely related to phonon dispersions, such as sound velocity. However, random substituted semiconductor alloys A _x B_1-x usually lack translational symmetry, and simulation with periodic boundary conditions often requires large supercells, which makes phonon dispersion highly folded and hardly comparable with experimental results. Here, we adopt a large supercell with randomly distributed A and B atoms to investigate substitution effect on the phonon dispersions of semiconductor alloys systematically by using phonon unfolding method [F. Zheng, P. Zhang, Comput. Mater. Sci. 125, 218 (2016)]. The results reveal the extent to which phonon band characteristics in (In,Ga)N and Ga(N,P) are preserved or lost at different compositions and q points. Generally, most characteristics of phonon dispersions can be preserved with indium substitution of gallium in GaN, while substitution of nitrogen with phosphorus strongly perturbs the phonon dispersion of GaN, showing a rapid disintegration of the Bloch characteristics of optical modes and introducing localized impurity modes. In addition, the sound velocities of both (In,Ga)N and Ga(N,P) display a nearly linear behavior as a function of substitution compositions.     

Fine-structure phosphorescence and radiative deactivation of the lowest triplet states in the most toxic dioxins

The transition dipole moments for the transition T₁(ππ*) → S₀ to vibrational energy levels of the nontotally symmetric vibrational modes of 2,3,7,8-tetrachloro-and 1,2,3,7,8-pentachlorodibenzo-p-dioxins are calculated. The interpretation of the fine-structure phosphorescence spectrum of the first of these compounds is refined, and the radiative deactivation rate constants for the s sublevels of the lowest triplet state T₁ are estimated. For a number of polychlorinated compounds, the effect of chlorine atoms occupying the α and β positions in a molecule on the T^s → S₀ transition dipole moments is discussed.     

Interaction of longitudinal phonons with discrete breather in strained graphene

We numerically analyze the interaction of small-amplitude phonon waves with standing gap discrete breather (DB) in strained graphene. To make the system support gap DB, strain is applied to create a gap in the phonon spectrum. We only focus on the in-plane phonons and DB, so the issue is investigated under a quasi-one-dimensional setup. It is found that, for the longitudinal sound waves having frequencies below 6 THz, DB is transparent and thus no radiation of energy from DB takes place; whereas for those sound waves with higher frequencies within the acoustic (optical) phonon band, phonon is mainly transmitted (reflected) by DB, and concomitantly, DB radiates its energy when interacting with phonons. The latter case is supported by the fact that, the sum of the transmitted and reflected phonon energy densities is noticeably higher than that of the incident wave. Our results here may provide insight into energy transport in graphene when the spatially localized nonlinear vibration modes are presented.     

Intrinsic Localized Spin Wave Modes and Modulational Instability in a Two-Dimensional Heisenberg Ferromagnet

An analytical study on the properties of intrinsic localized modes and modulational instability in a quantum two-dimensional ferromagnet with single-ion uniaxial anisotropy is completed in the semiclassical limit. By making use of the semidiscrete multiple-scale method, we obtain a line localized solution and a radially symmetric localized solution, and analyze their existence conditions. Taking into account that the existence of bright localized solutions is closely linked to the modulational instability of plane waves, we analytically study the discrete modulational instability of plane spin waves. The result of the modulational instability analysis show that the uniaxial anisotropy plays a key role in the appearance of our intrinsic localized spin wave modes.