Central Force Constants Research Articles

Elastic and photoelastic characteristics of graphene-like compounds

The central and noncentral harmonic force constants of the Keating model, proposed previously for describing elastic graphene constant, are obtained for 13 graphene-like IV–IV and III–V compounds. It is shown that the relative role of the noncentral forces decreases with an increase in the compound ionicity. For graphene, the anharmonic central-interaction constant is estimated and the dependences of the secondorder elastic constants on the two-dimensional pressure are calculated. Values of the photoelastic constants are determined.

Contribution of π-bonds to effective charges, cohesive energy, and force constants of graphene-like compounds

For 14 two-dimensional hexagonal compounds IV–IV and III–V, analytical expressions have been obtained using the Harrison bond-orbital method for the contribution from the π-interaction to the polarity of interatomic bonds, the effective atomic and transverse dynamical charges and their dependences on the deformation, as well as to the binding energy, the cohesive energy, and the central and non-central force constants.

Structural properties of binary semiconductors

Using the plasma oscillations theory of solids, 2 empirical relations have been proposed for the calculation of the structural properties such as bond-stretching central force constant (α) and bond-bending non-central force constant (β) for II-VI and III-V group binary semiconductors. We find that α =D (N›ωp) 2 and β = S (N›ωp) 2, where D and S are constants. The numerical values of D and S are respectively, 0.151 and 0.016 for II-VI and 0.177 and 0.031 for III-V group binary semiconductors. The structural properties of binary semiconductors exhibit a linear relationship when plotted on a log-log scale against the plasmon energy N›ωp (in eV), which lies on the straight lines. We have applied the proposed empirical relations on these binary semiconductors and found a better agreement with the experimental data as compared to the values evaluated by earlier researchers. Key words: Plasmon energy, structural properties, III-V and II-VI Semiconductors.

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

The concentration dependences of the elastic constants of the two-dimensional SixC1 − 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 Gruneisen 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.

2D supracrystals as a promising materials for planar nanoacoustoelectronics

The elastic and acoustic properties of 2D carbon supracrystals are simulated within the scope of modified density functional theory. The central and non-central force constants of carbon atoms and the corresponding elastic moduli, have been calculated in order to determine the velocities of elastic wave propagation in 2D supracrystalline nanoallotropes. It is shown that in sp2 nanoallotropes and graphene these velocities are approximately of the same value, and in sp3 nanoallotropes they are much less than in graphene.

Estimates of the elastic characteristics of graphenes

The central and noncentral force constants have been calculated within the previously proposed model of the binding energy of carbon atoms in graphene, which is based on the Harrison bonding orbital method. The results obtained have been used to estimate the characteristic phonon frequencies and elastic constants of graphene materials.

Polonium bulk and surface vibrational dynamics

AbstractCalculations are presented for the bulk phonons and for surface Rayleigh phonons and resonances for Polonium, the only element known to form in the simple cubic lattice. The static stability of this lattice has been confirmed recently by ab initio simulations which yield two bulk elastic constants, c11 and c12. Constitutive equations are derived for the isotropic cubic lattice based upon the Fuchs's method. This permits effectively a numerical evaluation of central potential force constants for Polonium from the ab initio results. Numerical calculations are then made for the material vibration dynamics in the force constant model with the use of the matching method. The numerical applications yield for Polonium the bulk phonon branches along [100], [110], and [111], and the Rayleigh phonons and surface resonances along the [010] direction in an unreconstructed (001) surface. The local vibration densities of states are calculated for bulk and surface sites for this element. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Phonon dispersion in alkali metals and their equiatomic sodium-based binary alloys

In the present article, the theoretical calculations of the phonon dispersion curves (PDCs) of five alkali metals viz. Li, Na, K, Rb, Cs and their four equiatomic sodium-based binary alloys viz. Na0.5Li0.5, Na0.5K0.5, Na0.5Rb0.5 and Na0.5Cs0.5 to second order in a local model potential is discussed in terms of the realspace sum of the Born von Karman central force constants. Instead of the concentration average of the force constants of pure alkali metals, the pseudo-alloy-atom (PAA) is adopted to directly compute the force constants of the four equiatomic sodium based binary alloys and was successfully applied. The exchange and correlation functions due to the Hartree (H) and Ichimaru-Utsumi (IU) are used to investigate the influence of the screening effects. The phonon frequencies of alkali metals and their four equiatomic sodium-based binary alloys in the longitudinal branch are more sensitive to the exchange and correlation effects in comparison with the transverse branches. The PDCs of pure alkali metals are found in qualitative agreement with the available experimental data. The frequencies in the longitudinal branch are suppressed rather due to IU-screening function than those due to static H-screening function.

Phonon Dispersion in Equiatomic Li-Based Binary Alloys

The computations of the phonon dispersion curves (PDC) of four equiatomic Li-based binary alloys, namely Li0.5Na0.5, Li0.5K0.5, Li0.5Rb0.5 and Li0.5Cs0.5, to second order in the local model potential is discussed in terms of the real-space sum of Born von Karman central force constants. Instead of the concentration average of the force constants of metallic Li, Na, K, Rb and Cs, the pseudo-alloy atom (PAA) is adopted to compute directly the force constants of four equiatomic Li-based binary alloys. The exchange and correlation functions due to Hartree (H) and Ichimaru–Utsumi (IU) are used to investigate the influence of screening effects. The phonon frequencies of four equiatomic Li-based binary alloys in the longitudinal branch are more sensitive to the exchange and correlation effects in comparison with the transverse branches. However, the frequencies in the longitudinal branch are suppressed due to IU-screening function than the frequencies due to static H-screening function.

Laser-induced defects in fused silica by UV laser irradiation

The structure of fused silica with irradiation of the third harmonic of the Nd:YAG laser was investigated by Fourier transform infrared, Raman and Photoluminescence spectroscopy. Some variation in the Si/O stoichiometry of silica in the ablated spot was induced. The primary defect species are oxygen deficient centers and oxygen interstitials. The frequency shift of the Si–O–Si vibration proves that the central force constant between oxygen and silicon atoms, and the band angle of Si–O–Si increases in the UV-laser ablation spot. Small silicon clusters within SiO x appear to be a possible explanation for the 564 nm Fluorescence peak, and the 181 cm −1 Raman peak.

Static and vibrational properties of equiatomic Na-based binary alloys

The computations of the static and vibrational properties of four equiatomic Na-based binary alloys viz. Na 0.5Li 0.5, Na 0.5K 0.5, Na 0.5Rb 0.5 and Na 0.5Cs 0.5, to second order in local model potential is discussed in terms of real-space sum of Born von Karman central force constants. The local field correlation functions due to Hartree (H), Ichimaru–Utsumi (IU) and Sarkar et al. (S) are used to investigate the influence of the screening effects on the aforesaid properties. Results for the lattice constants C 11, C 12, C 44, C 12– C 44, C 12/ C 44 and bulk modulus B obtained using the H-local field correction function have higher values in comparison with the results obtained for the same properties using IU- and S-local field correction functions. The results for the Shear modulus ( C′), deviation from Cauchy's relation, Poisson's ratio σ, Young modulus Y, propagation velocity of elastic waves, phonon dispersion curves and degree of anisotropy A are highly appreciable for the four equiatomic Na-based binary alloys.

Infrared (IR) investigation of the structural changes of silica glasses with fictive temperature

Effects of fictive temperatures on the structure of silica glass were investigated using infrared (IR) spectroscopy. From the IR peak positions of the three fundamental structural bands (asymmetric stretching, bending, and rocking vibrations), the average values of the silica structural parameters – central force constant, α, non-central force constant, β, and Si–O–Si bond angle, θ – were obtained. It was found that the Si–O–Si bond angle and the non-central force constant decreased, while the central force constant increased with increasing fictive temperature.

Rayleigh waves modeling using an elastic lattice model

The elastic lattice (percolation) model, used in statistical physics studies, has been quite successful in simulating dynamic fracture phenomena, including their associated acoustic emission. This discrete model is suitable for representing disordered media such as rocks. Thus, motivated by its advantages to deal with discontinuous realistic media, in comparison to the continuum theory, we performed simulations of elastic wave propagation by using a vector percolating network that includes central and bond‐bending force constants allowing local microscopic variation of the Poisson's ratio. The validity of the proposed approach is tested by comparing our numerical results with those from Garvin's exact analytical solution for a buried dilatational line source in a half space. In the free‐surface response the Rayleigh waves play a prominent role.

Study of phonons and normal mode analysis of perovskite-type superionic conductors

A de Launey angular force (DAF) model has been used to calculate the phonon frequency at zone centre (ZC) and normal modes in phase I of CsPbCl 3 and the γ-phase of Ag 3SI and Ag 3SBr by assuming them to be ideal perovskite (P)-type structures. Three central force constants, α 1, α 2 and α 3, and three angular force constants, α 1′, α 2′ and α 3′, for Pb–Cl (S–Ag), Cs–Cl (I or Br–Ag) and Cs–Pb (S–I or Br) atoms are employed and determined from the experimental values of transverse infrared (IR) active phonon frequencies at ZC. The α 3 value between Cs and Pb is the strongest among all of these compounds. This is reasonable since both kinds of ions compose the cage lattice in the superionic conduction phase. The normal coordinate of the highest frequency ( ν 1) mode is assigned to be different from that for other perovskites. It reasonably interprets the higher values of ν 2 and ν 3 for CsPbCl 3 than those of Ag 3SX (X=Br,I) and also the lower value of ν 1 for CsPbCl 3. Based on these results, the complete phonon dispersion curve is calculated.

Site-selective luminescence study of defects. in gamma-irradiated glassy germanium dioxide

Luminescence of γ-irradiated samples of GeO 2 glass was studied using dye laser excitation in the wavelength region between 590 and 656 nm. An inhomogeneously broadened luminescence band with a peak around 1.86 eV, halfwidth of 0.16 eV and decay constant τ ≈ 5.1 μs was found. At temperatures below 20 K a resonance ZPL and a vibronic peak 710 cm −1 below the laser photon energy emerge when laser is tuned to energies between 1.95–1.89 eV. The site-selective luminescence spectra are qualitatively similar to those of the non-bridging oxygen hole center (NBOHC) in SiO 2 glass and are attributed to NBOHC in glassy GeO 2. The measured ratio between the energies of the observed local vibrations in GeO 2 (710 cm −1) and SiO 2 (890 cm −1) is close to the ratio, calculated on the basis of the known SiO and GeO central force constants and taking the reduced mass of SiO and GeO molecules for the mode mass. This confirms the assignment of the 710 and 890 cm −1 vibronic lines to the non-bridging oxygen stretching modes of the NBOHC in glassy GeO 2 and SiO 2 respectively.

Some static and vibrational properties of aluminium by a local pseudopotential

The pseudopotential investigation of various properties of aluminium is studied in terms of the real-space sum of Born-von Karman central-force constants. A simple local model potential depending on a single parameter has been used to investigate the ion-ion interaction, interatomic force constants, dynamical elastic constants, bulk modulus, deviation from Cauchy relation, Poisson's ratio, Young's modulus, propagation velocity of elastic waves, phonon dispersion curves and degree of elastic anisotropy. The effect of exchange and correlation on conduction electrons is also considered separately by using various forms of the dielectric (screening) functions. Overall good agreement with the available theoretical and experimental data is achieved in the present work.

New Results in Raman Scattering in Diluted Magnetic Semiconductors (DMS)

New results in Raman scattering in DMS are presented. The alloys MxA1-xIIBIV are DMS in which a fraction of the cations of the II–VI compounds are randomly substituted transition metal ions. In this paper we study by Raman scattering ZnS ad the following DMS: Zn0.99Mn0.01S, Zn0.80Mn0.20S, Zn0.95Cr0.05S, Zn0.95Fe0.05S, Zn0.95Co0.05S, Zn0.97Ti0.03S, Zn0.90Ni0.10S. The measurements are compared with numeric calculations of the first order Raman intensities induced by the magnetic ion. The calculated results agree very closely with the experimental data. It was found that the incorporation of a magnetic ion greatly altered the central force constant and this modified considerably the vibration spectrum of the crystal.

Vibrational properties of an octagonal quasicrystal

The vibrational densities of states for an octagonal quasiperiodic lattice are calculated. Crossovers from phonon excitations to fracton-like excitations are found in the low-frequency parts of the spectra (this part is referred to as the continuous spectrum); meanwhile, localized vibrational modes are observed in the high-frequency parts (this part is referred to as the characteristic spectrum). The spectral features are governed by alpha and beta , the central and non-central force constants of the Born model. For the low-frequency continuous spectrum when alpha / beta equals unity (isotropic model) and when alpha / beta is not very large, a power law is satisfied in the fracton-like excitation frequency regime but, when alpha / beta approaches infinity, the spectrum deviates from the original power law. For the high-frequency characteristic spectrum, in an isotropic situation, i.e. in the case when alpha / beta =1, the localized mode is isolated and a gap separates it from other modes but, when there is no longer isotropy, the gap disappears.

Perturbative Approach to Dilute Off‐Diagonal Defects

AbstractA diagrammatic approach is developed to the problem of dilute concentration of off‐diagonal defects for short range interactions. The method is illustrated with the calculation of phonons when impurities that change the central force constant of the harmonic interaction with the nearest neighbors are present in three different structures: on the linear chain, on the square planar lattice, and the simple cubic structure. Systematic rules are obtained for the summation of the series. The procedure can inspire a more general algorithm for matrix inversion based on an eventually summable series.

Optical properties and structure of thin SiO x films

The optical properties of SiO x films of variable composition obtained by reactive r.f. sputtering of silicon were investigated. The experimental results show that the films have a single-phase structure consisting of a continuous random network with a dominance of six-membered molecular rings of Si-(Si y O 4- y tetrahedra, where 0⩽ y⩽4, joined together by bridging oxygen atoms. The difference between the films investigated and those obtained by vacuum evaporation is determined by the dominance of four-membered rings in the evaporated films. Analysis of the IR spectra reveals that the shift in the absorption band with varying structure is connected with a variation in the central force constant.