Empirical modeling of longitudinal tension and compression of graphene nanoparticles and nanoribbons

Longitudinal tension and compression of graphene nanoparticles and nanoribbons have been studied using an empirical model. The pseudo-Young’s modulus of graphene nanoparticles and nanoribbons has been calculated. The size effect, i.e., the dependence of the elastic modulus on linear parameters of graphene objects, has been studied. An increase in pseudo-Young’s modulus discontinues as the length increases during the nanoparticle-to-nanoribbon transition. For the same perimeter, the graphene ribbon edges are characterized by smaller pseudo-Young’s moduli in comparison with uniaxial carbon nanotubes. Elastic deformation of graphene nanoparticles and nanoribbons has been observed in the relative length variation range of 0.93–1.12.     

Concentration dependences of the elastic constants of the two-dimensional graphene-silicene system

The concentration dependences of the elastic constants of the two-dimensional Si _x C_{1 − x} system have been investigated with the use of the Harrison bonding-orbital method and the Keating model. The central and non-central force constants and the Grüneisen parameter have been considered by means of the bonding-orbital method. All quantities under consideration have been shown to exhibit a nonlinear behavior during the transition from graphene to silicene. A nontrivial role of the short-range repulsion has been discussed. The second-order and third-order elastic constants, the pressure dependences of the second-order elastic constants, as well as the Poisson’s ratio and Young’s modulus have been investigated in the Keating model. It has been found that the elastic constants and Young’s modulus change almost linearly upon the transition from graphene to silicene, whereas the other quantities under consideration exhibit nonlinearity.     

Computation of collective modes and acoustic investigations at different temperatures of vitrous silica

This paper is mainly concerned with elastic and acoustic properties of vitrous silica besides the computation of phonon frequencies. Thus the phonon frequencies of vitrous silica have been calculated assuming the electronic bulk modulus,K _e, as equal to zero. New equations have been derived to relate the pressure derivatives of second order elastic constants to the acoustic Gruneisen’s parameters using both Bhatia-Singh’s parameters and Schofield’s equations. The calculated longitudinal and transverse Gruneisen’s parameters and the predicted absorption band spectra from Nagendranath’s equation and Bhatia Singh’s parameters are in good agreement with experiment. The calculated mean acoustic mode Gruneisen’s parameter evaluated from the pressure derivative of Nagendranath’s equation is also in good agreement with experiment. An erratum to this article is available at .     

Mobility of vacancies under deformation and their effect on the elastic properties of graphene

The effect of isolated vacancies on the elastic properties of a graphene sheet has been investigated by the ab initio density functional method. An almost inverse linear dependence of the Young’s modulus on the concentration of vacancies has been revealed. The height of potential barriers for the motion of vacancies in various directions has been calculated as a function of various independent applied strains. The velocity of vacancies at various temperatures has been calculated as a function of applied strains using the transition state theory.     

Micromechanical properties of carbon–silica aerogel composites

Materials’ endurance to mechanical stress is desirable from a technological point of view. In particular, in the case of silica aerogels, an improvement of the material elasticity is needed for some applications. Carbon–silica aerogel composites have been obtained and their mechanical properties, Young’s modulus, elastic parameter and hardness, have been evaluated with a dynamical, non-destructive microindentation technique. Large changes are found in Young’s modulus when only a small amount of carbon is added. This is clearly shown in the shape of the indentation curves as well as in the increase of the elastic parameter value, which evaluates the percentage of elasticity versus plasticity. Young’s modulus values obtained for carbon–silica aerogels show a similar variation with the carbon mass fraction to that predicted by a commonly used model for composite materials. The measured hardness values corresponding to the total elastoplastic deformation do not show such a prominent dependency on the carbon mass fraction as the elastic parameter and Young’s modulus do and they are similar to those measured for the pure-silica aerogel. Received: 18 May 2001 / Accepted: 30 July 2001 / Published online: 30 October 2001     

Effect of different types of pseudopotentials on study of electronic dispersion for graphene and a (5,5) SWCNT

We study the electronic dispersion for a graphene sheet and also a (5,5) single wall carbon nanotube (SWCNT) by using the PWscf code from the ‘Quantum Espresso’ package. Two different types of pseudopotentials, ‘norm conserving’ and ‘ultra soft’, have been employed and the results are more or less similar up to the Fermi level. By energy relaxation, it was found that, if the inter-layer distance of graphite expands up to 4.5 times its in-layer (hexagonal) lattice constant, then each layer can be considered as an individual graphene sheet and, in a bundle of (5,5) SWCNTs, the optimum separation between the tubes’ centers is about 19 a.u. and, if it expands to 22 a.u., then a single wall tube consideration can be made. The calculated band structure and density of states (DOS) for the (5,5) SWCNT show that in the vicinity of the Fermi level there is no energy gap (so that it is metallic) and there is a general agreement between them and zone-folding studies or other ab initio methods in the literature. The effects of curvature on the band shifts and DOS have been considered, and they magnify the departure from Mintmire and White’s universal prediction. PACS  71.20.Tx; 71.15.Mb; 73.61.Wp     

Elastic properties and spectroscopic studies of lithium lead borate glasses

Elastic properties of xLi₂O — 20PbO — (80-x)B₂O₃ glasses have been measured at a frequency of 10 MHz using X-cut and Y-cut quartz transducers. The trends in the variation of elastic moduli, Poisson’s ratio and Debye temperature have been studied. The elastic moduli namely longitudinal and young’s modulus show strong linear dependence while bulk and shear modulus vary marginally as a function of Li₂O concentration. The Poisson’s ratio is found to be almost constant and Debye temperature increases with the increase of Li₂O concentration. IR, MAS-NMR and glass transition temperature studies have been also carried out. Glass transition temperature is found to increase with increase of Li₂O concentration. IR and MAS-NMR spectra show characteristic features of borate network and systematic change as a function of Li₂O concentration. The variation in the elastic properties and structural features of IR and MAS-NMR indicate that Pb²⁺ ions are likely to occupy network forming positions in this glass system. Paper presented at the 2nd International Conference on Ionic Devices, Anna University, Chennai, India, Nov. 28–30, 2003.     

Young’s modulus and internal friction in porous biocarbon white pine wood precursors

This paper reports on a study performed in the temperature range 100–293 K, in air and in vacuum, for the amplitude and time dependences of the Young’s modulus and the internal friction (ultrasound damping) of biocarbon precursors prepared from white pine wood at two pyrolysis (carbonization) temperatures of 1000 and 2400°C. The measurements have been conducted by the resonance technique with a composite vibrator on samples cut along and across the tree growth direction. The desorption of molecules of the external medium at low amplitudes of ultrasonic vibrations has been found to produce the pronounced influence on the effective elastic modulus and elastic vibration decrement. The data obtained from acoustic measurements of the amplitude dependences of the elastic modulus have been used to estimate the microplastic properties of the samples. It has been shown that increasing the carbonization temperature gives rise to noticeable changes in the Young’s modulus and internal friction, as well as to reduction of the microplastic stress σ _y of the biomaterial studied. The stress σ _y of the samples cut across the growth direction has been found to be substantially smaller than that of the “longitudinal” samples. The elastic and microplastic properties of precursors prepared from white pine wood have been compared with those of the white eucalyptus wood.     

Equation of state and temperature variation of the bulk modulus of the alkaline earth fluorides

The isotherms for the alkaline earth fluorides (CaF₂, SrF₂ and BaF₂) have been computed using the expression for the total free energy of a crystal in the quasiharmonic approximation. The theoretical points for SrF₂ and BaF₂ have been compared with the points derived from Bridgman’s experimental relation. The temperature variation of the isothermal bulk modulus of the alkaline earth fluorides has been worked out on the basis of Axe’s shell model. The theoretica points are compared with the points obtained from the temperature variation of the elastic constants data. It is found that the vibrational contribution to the temperature variation of the elastic constants in these crystals is significant.     

Micromechanical properties of carbon nitride films deposited by radio-frequency-assisted filtered cathodic vacuum arc

Super-hard and elastic carbon nitride films have been synthesized by using an off-plane double-bend filtered cathodic vacuum arc combined with a radio-frequency nitrogen-ion beam source. A nanoindenter was used to determine the micromechanical properties of the deposited films. X-ray photoelectron spectroscopy was used to study the composition and bonding structure of the deposited films. The influence of nitrogen ion energy on the structure and micromechanical properties of the deposited films was systematically studied. As the nitrogen ion energy is increased, the microhardness, Young’s modulus and elastic recovery also increase, reaching a maximum of 47 GPa, 400 GPa, and 87.5%, respectively, at a nitrogen ion energy of 100 eV. Further increase in nitrogen ion energy results in a decrease in microhardness, Young’s modulus and elastic recovery of the deposited films. The formation of five-membered rings, as indicated by XPS, which causes bending of the basal planes and forms a three-dimensional rigid covalent bond network, contributes to the super-hardness, Young’ s modulus and high elastic recovery of the films deposited at a nitrogen ion energy of 100 eV. Revised version: 29 October 2001 / Accepted: 7 November 2001 / Published online: 2 May 2002     

Perturbation theory for a hamiltonian linear in quasimomentum

Perturbation theory has been proposed to take into account small terms in the multiband Hamiltonian, which lead to significant changes such as the trigonal warping of the Fermi surface. The theory is similar to the “cross technique” and is reduced to the self-energy corrections to the matrix Green’s function. A particular application to graphite and a graphene bilayer has been given.     

Ultrashort optical pulses in carbon nanotubes and graphene with periodic impurities

The dispersion law for electrons has been derived by the Green’s function method using the Anderson periodic model, which has been proposed to describe the electron subsystem in carbon nanotubes and graphene with impurities. The combined dynamics of electrons and an electromagnetic field has been considered in the low-temperature limit, and the effective equation describing the propagation of ultrashort optical pulses has been obtained. The solutions to this equation as functions of the parameters of the problem have been presented.     

Synthesis,mechanical, and barrier properties of LDPE/graphene nanocomposites using vinyl triethoxysilane as a coupling agent

Precise interface control and dispersal of graphene nanosheets in polymer hosts are challenging to develop high performance graphene-based nanocomposites due to their strong interlayer cohesive energy and surface inertia. Here, we firstly report an efficient and novel method to functionalize graphene nanosheets with vinyl triethoxysilane (VTES) and successfully blend them with low density polyethylene (LDPE) to prepare nanocomposites. Fourier transforms infrared spectra (FTIR), Raman spectra, and thermogravimetric analysis (TGA) proved that the graphene sheets were covalently bonded with VTES. The resulting nanocomposites obtained the increases of up to 27.0 and 92.8% in the tensile strength and Young’s modulus, respectively, compared to neat LDPE. The VTES–graphene not only remarkably improved the tensile strength of the composites, but also enhanced its toughness by 17.7%. Oil permeability measurements showed that the absorption ratio of toluene by the LDPE/graphene composites decreased from 56 to 39%, and its barrier properties have obviously been improved. This study opens a new route to optimize interface structures and improve the comprehensive performances of graphene–polymer nanocomposites.     

Elastic constants of lead-bismuth alloys

A study of ultrasonic velocities and internal friction has been carried out in Pb-Bi alloys in the concentration range of 0 to 49.5 atomic % Bi using the composite oscillator technique. From the velocity and density data a set of elastic constants namely, Young’s modulus, rigidity modulus, bulk modulus and Poisson’s ratio are estimated. The results are interpreted in terms of the phase changes occurring in the alloy system. Internal friction is found to be more sensitive than the elastic constants to the phase changes.     

Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

Fifty years of Szigeti’s dielectric theory — A review

During the period 1949–1961 Szigeti published four seminal papers on the dielectric behaviour of crystals. Szigeti’s theory is applicable to isotropic and anisotropic, ionic and covalent crystals with different structures. Szigeti’s theory connects dielectric, spectroscopic and elastic properties. An important outcome of Szigeti’s theory is the concept of the effective ionic charge (s). It is pointed out that s correlates with a number of physical properties and is a measure of ionicity of the interatomic bond. Since Szigeti’s work, several theoretical models have been proposed to account for the fact that s < 1. These models provide an insight into the complex polarization mechanisms in solids. This review summarizes Szigeti’s work and the work that followed; the implications and applications of Szigeti’s theory are discussed. Some new results are also included. Dedicated to the memory of late Prof. P S Narayanan.     

Theoretical LSP detection rates for dark-matter detectors

Low-energy structure of the dark-matter detector nuclei ⁷¹Ga, ⁷³Ge and ¹²⁷I has been studied by using the nuclear shell model. The calculations have been done in realistic model spaces by using renormalized microscopic two-body interactions. The resulting ground states have been used to calculate theoretical predictions for detection rates of the lightest supersymmetric particle (LSP) in experiments studying elastic scattering of the LSP’s from atomic nuclei. Presented by T.S. Kosmas at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Relation between the parameters of the elasticity theory and averaged bulk modulus of solids

A relation between the elastic moduli and Poisson’s ratio of crystalline and vitreous solids is considered. The feasibility of introducing the averaged bulk modulus, which has the same attributes as other elastic moduli, is substantiated. A relationship between the Grüneisen parameter and Poisson’s ratio is discussed.     

Third-order elastic moduli of single-layer graphene

In the framework of the Keating model with allowance made for the anharmonic constant of the central interaction between the nearest neighbors μ, analytical expressions have been obtained for three third-order independent elastic constants c _ijk (μ, ζ) of single-layer graphene, where ζ = (2α − β)/(4α + β) is the Kleinman internal displacement parameter and α and β are the harmonic constants of the central interaction between the nearest neighbors and the noncentral interaction between the next-nearest neighbors, respectively. The dependences of the second-order elastic constants on the pressure p have been determined. It has been shown that the moduli c ₁₁ and c ₂₂ differently respond to the pressure. Therefore, graphene is isotropic in the harmonic approximation, whereas the inclusion of anharmonicity leads to the appearance of the anisotropy.     

Mechanical properties of semicrystalline polymer-polypropylene

The elastic properties of polypropylene have been investigated in terms of a phenomenological model, which is a modified form of the Takayanagi’s two-phase model. In the present model both the change of crystallinity and orientation of the crystalline chains have been taken into account. The orientation effect at the drawn state has been considered in a simplified manner. It has been shown that a partially aligned crystalline phase may be considered as a superposition of a perfectly aligned crystalline region in an elastically isotropic randomly oriented crystalline phase. The predicted values of elastic modulus agree with experimental values.