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.     

Stability range for a flat graphene sheet subjected to in-plane deformation

The effects of the elastic deformation on the mechanical and physical properties of graphene are a subject of intensive current studies. Nevertheless, the stability range for a flat graphene sheet subjected to in-plane deformation is still unknown. Here, this problem is solved by atomistic simulations. In the three-dimensional space corresponding to the ɛ _xx , ɛ _yy , and ɛ _xy components of the planar strain tensor, the surface bounding the stability range for a flat graphene sheet has been constructed disregarding the thermal vibrations and the effects of boundary conditions. For the points of this surface, force components T _x , T _y , and T _xy have been calculated. It is shown that graphene is structurally stable up to strains on the order of 0.3–0.4, but it is unstable with respect to the shear in the absence of stretching forces. In addition, graphene cannot preserve its flat shape under the effect of a compressive force since it has zero flexural stiffness.     

Failure mechanisms of graphene under tension

Recent experiments established pure graphene as the strongest material known to mankind, further invigorating the question of how graphene fails. Using density functional theory, we reveal the mechanisms of mechanical failure of pure graphene under a generic state of tension at zero temperature. One failure mechanism is a novel soft-mode phonon instability of the K1 mode, whereby the graphene sheet undergoes a phase transition and is driven towards isolated hexagonal rings resulting in a reduction of strength. The other is the usual elastic instability corresponding to a maximum in the stress-strain curve. Our results indicate that finite wave vector soft modes can be the key factor in limiting the strength of monolayer materials.     

First-principles investigation of the phonon spectrum of β-GaS

This paper presents the results of the first-principles density functional theory calculation of the phonon spectrum of the ??-GaS semiconductor with a layered structure. The elastic constants and velocities of sound along and across the layers of the ??-GaS semiconductor have been determined. Investigation of the equilibrium structure and the phonon spectrum of the (0001) surface of the ??-GaS crystals has demonstrated that the bulk and surface structural and dynamical properties of these crystals differ only slightly. The calculated frequencies and symmetries of phonon modes at the center of the Brillouin zone of the semiconductor are in satisfactory agreement with the experimental data obtained from the Raman and infrared spectra.     

Spin currents in graphene under tension

Based on the Tight-Binding model, we have asymmetric massless Dirac fermions as the carriers in graphene under tension. Because of uniaxial strain, the velocities of Dirac fermions depend on their directions. This work studies the effect of the uniaxial strain on the spin transport through a single magnetic barrier of the strained graphene system. The result shows that graphene has a great potential for applications in nano-mechanical spintronic devices. This is because of strain in graphene can induce the spin-dependent pseudo-potentials at the barrier to control the spin currents of the junction.     

Elastic instability of bilayer graphene using atomistic finite element

In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite element approaches. The equivalent homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the C–C bonds of the graphene lattice. The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. The overall mechanical properties and geometric configurations of the nano-structures represented as truss assemblies are then calculated minimising the total potential energy associated to the loading, thickness and average equilibrium lengths of the bonds. Different boundary conditions and aspect ratios are considered for both bilayer and single-layer graphene sheets. The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.     

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.     

Crystal structures,elastic, and lattice dynamical properties of BeB2, NaB2, and CaB2 from the first principles

Based on density functional theory, we have studied the structural stability, elastic, mechanical, and lattice dynamical properties of BeB₂, NaB₂, and CaB₂ compounds in AlB₂, OsB₂, and ReB₂ structures, respectively. Generalized gradient approximation has been used for modeling exchange-correlation effects. Our calculations indicate that ReB₂, AlB₂, and OsB₂ structures are energetically the most stable for BeB₂, NaB₂, and CaB₂ compounds, respectively. The results show that these structures are both mechanically and dynamically stable. The bulk modulus, elastic constants, shear modulus, Young’s modulus, Poisson’s ratio, Debye temperature, sound velocities, and anisotropic factors are also calculated and discussed. Furthermore, the phonon dispersion curves and corresponding phonon density of states are presented. Our structural and some other results are in agreement with the available experimental and theoretical data.     

The dispersion of acoustic phonons in CoCl2

The acoustic phonon dispersion curves for CoCl₂ have been measured, in the three principal symmetry directions, by inelastic neutron scattering at room temperature. From the initial slopes the sound velocities have been derived and the elastic constants calculated. The two dimensional nature of the structure of CoCl₂ is apparent in the difference between the sound velocities parallel and perpendicular to the closed packed layers.     

Elastic behavior of bilayer graphene under in-plane loadings

Due to its many superior properties, bilayer graphene is expected to serve as a proper candidate in various applications, and further provokes intensive research on how it deforms. Based on atomistic simulations, the elastic behavior of bilayer graphenes, including fracture under tension and buckling under compression, is investigated under in-plane loadings. The elastic property, e.g. Young's modulus and fracture strain, of either armchair or zigzag graphene is sensitive to both chirality and loading direction when tension is applied. However, the armchair-zigzag bilayer graphene with mixed chirality has no dependency on loading direction and its tensile rupture process is in a step-by-step manner. Under different loading histories, the bilayer graphene also exhibits quite different mechanical response. These results are useful for both further investigation and potential application of graphene in nano-electromechanical systems.     

Theoretical studies on mechanical and electronic properties of s-triazine sheet

Abstract

Mechanical and electronic properties of s-triazine sheet are studied using first-principles calculations based on density functional theory. The in-plane stiffness and bulk modulus for s-triazine sheet are found to be less than that of heptazine. The reduction can be related to the nature of the covalent bonds connecting the adjacent sheets and the number of atoms per unit cell. The Poisson’s ratio of s-triazine sheet is half the value to that of graphene. Additionally, the calculated values of the two critical strains (elastic and yielding points) of s-triazine sheet are in the same order of magnitude to that for heptazine which was calculated using MD simulations in the literature. It is also demonstrated that s-triazine sheet can withstand larger tension in the plastic region. These results established a stable mechanical property for s-triazine sheet. We found a linear relationship of bandgap as a function of bi-axial tensile strain within the harmonic elastic region. The reduced steric repulsion of the lone pairs (p_x-, p_y-) causes the p_z-like orbital to shift to high energy, and consequently an increase in the bandgap. We find no electronic properties modulation of the s-triazine sheet under electric field up to a peak value of 10 V/nm. Such noble properties may be useful in future nanomaterial applications.     

First-principles study of the phonon spectrum of ɛ-GaSe

The phonon spectrum and phonon density of states of ?-GaSe layered semiconductor have been studied from the first principles in the linear-response approximation. The elastic constants and acoustic velocities along and across layers have been determined. The study of the equilibrium structure and phonon spectrum of the (0001) surface of ?-GaSe has demonstrated that the volume and surface structural dynamic properties of these crystals differ insignificantly. The calculated frequencies and symmetries of the phonon modes in the center of the Brillouin zone are in good agreement with the experimental data obtained from the Raman scattering and infrared spectra.     

Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets

In this article, an atomistic model is developed to study the buckling and vibration characteristics of single-layered graphene sheets (SLGSs). By treating SLGSs as space-frame structures, in which the discrete nature of graphene sheets is preserved, they are modeled using three-dimensional elastic beam elements for the bonds. The elastic moduli of the beam elements are determined via a linkage between molecular mechanics and structural mechanics. Based on this model, the critical compressive forces and fundamental natural frequencies of single-layered graphene sheets with different boundary conditions and geometries are obtained and then compared. It is indicated that the compressive buckling force decreases when the graphene sheet aspect ratio increases. At low aspect ratios, the increase of aspect ratios will result in a significant decrease in the critical buckling load. It is also indicated that increasing aspect ratio at a given side length results in the convergence of buckling envelops associated with armchair and zigzag graphene sheets. The influence of boundary conditions will be studied for different geometries. It will be shown that the influence of boundary conditions is not significant for sufficiently large SLGSs.     

Brillouin scattering by pure-transverse phonons in GaSe and GaS

Brillouin scattering experiments in the layer-type semiconductors GaSe and GaS by the pure-transverse phonon domains have been carried out at room temperature. Weak resonant enhancement and cancellation have been found for both materials in the region of transparency. The non-diagonal elastic constants C₁₂ have also been determined to be 3.77 × 10¹¹ dyn cm^?2 (GaSe) and 5.35 × 10¹¹ dyn cm^?2 (GaS) by measuring the sound velocities of the phonon domains.     

Ab initio calculations of the elastic, electronic, optical, and vibrational properties of PdGa compound under pressure

The structural, elastic, electronic, optical, and vibrational properties of cubic PdGa compound are investigated using the norm-conserving pseudopotentials within the local density approximation (LDA) in the framework of the density functional theory. The calculated lattice constant has been compared with the experimental value and has been found to be in good agreement with experimental data. The obtained electronic band structures show that PdGa compound has no band gap. The second-order elastic constants have been calculated, and the other related quantities such as the Young’s modulus, shear modulus, Poisson’s ratio, anisotropy factor, sound velocities, and Debye temperature have also been estimated. Our calculated results of elastic constants show that this compound is mechanically stable. Furthermore, the real and imaginary parts of the dielectric function and the optical constants such as the electron energy-loss function, the optical dielectric constant and the effective number of electrons per unit cell are calculated and presented in the study. The phonon dispersion curves are also derived using the direct method.     

Effect of the configuration of a wrinklon on the distributions of the energy and elastic strain in a graphene nanoribbon

The formation of wrinkles in thin membranes is a widespread phenomenon. In particular, wrinkles can appear in graphene, which is the thinnest natural membrane, and affect its properties. A region where wrinkles with different wavelengths are linked is called wrinklon. Conditions of the fixing of an elastically deformed graphene sheet dictate a certain wavelength of wrinkles near the fixed edge. Wrinkles with a longer wavelength become more energetically favorable with an increase in the distance from the edge. As a result, wrinklons appear and reduce the potential energy of the system by uniting wrinkles into larger wrinkles with an increase in the distance from the edge. The possibility of implementing various equilibrium configurations of wrinklons at given plane strains in graphene has been demonstrated by the molecular quasistatic method. The distributions of the energy and elastic strain components in wrinklons with various configurations for nanoribbons with different widths have been calculated.     

A structural mechanics approach for the phonon dispersion analysis of graphene

A molecular structural mechanics model for the numerical simulation of phonon dispersion relations of graphene is developed by relating the C-C bond molecular potential energy to the strain energy of the equivalent beam-truss space frame. With the stiffness matrix known and further based on the periodic structure characteristics, the Bloch theorem is introduced to develop the dispersion relation of graphene sheet. Being different from the existing structural mechanics model, interactions between the fourth-nearest neighbor atoms are further simulated with beam elements to compensate the reduced stretching stiffness, where as a result not only the dispersion relations in the low frequency field are accurately achieved, but results in the high frequency field are also reasonably obtained. This work is expected to provide new opportunities for the dynamic properties analysis of graphene and future application in the engineering sector.     

Phonon instabilities and the ideal strength of aluminum

We have calculated the phonon spectra of aluminum as a function of strain using density functional perturbation theory for <110>, <100>, and <111> uniaxial tension, as well as relaxed <112>[111] shear. In all four cases, phonon instabilities occur at points away from the center of the Brillouin zone and intrude before the material becomes unstable according to elastic stability criteria. This is the first time the ideal strength of a metal has been shown to be dictated by instabilities in the acoustic phonon spectra. We go on to describe the crystallography of the unstable modes, all of which are shear in character. This work further suggests that shear failure is an inherent property of aluminum even in an initially dislocation-free perfect crystal.     

Influence of atomic order on TA1[110] phonon softening [4] and displacive phase transition in Fe72Pt28 Invar alloys

The acoustic phonon dispersions of two Invar crystals , one ordered with the () structure, the other disordered fcc, have been investigated between 3.4 K and 470 K by inelastic and elastic neutron scattering. For the ordered crystal, pronounced softening of the whole phonon branch is observed on cooling below the Curie temperature. Particularly strong phonon softening at the M-point zone boundary of the structure leads to a displacive, antiferrodistortive phase transition at low temperatures. For the disordered crystal, much weaker softening of the phonons is observed and restricted to the region near the Brillouin zone center, where increasing elastic scattering with decreasing temperature indicates the growth of local tetragonal strain. This strain is considered as a typical precursor of the transformation to bct martensite. Specific heat measurements, performed at low temperatures on both crystals confirm the neutron scattering results and reveal considerable enhancement of the low energy phonon density of states in the ordered crystal. Received 18 January 1999     

Acoustic phonon engineering in coated cylindrical nanowires

We have theoretically investigated the effect of a coating made of the elastically dissimilar material on the acoustic phonon properties of semiconductor nanowires. It is shown that the acoustic impedance mismatch at the interface between the nanowire and the barrier coating affects dramatically the phonon spectra and group velocities in the nanowires. Coatings made of materials with a small sound velocity lead to compression of the phonon energy spectrum and strong reduction of the phonon group velocities. The coatings made of materials with a high sound velocity have opposite effect. Our calculations reveal substantial re-distribution of the elastic deformations in coated nanowires, which results in modification of the phonon transport properties, and corresponding changes in thermal and electrical conduction. We argue that tuning of the coated nanowire material parameters and the barrier layer thickness can be used for engineering the transport properties in such nanostructures.