Vibrational spectra and dynamic properties of ionic-covalent crystals

A lattice dynamical model for complex crystals containing multiatomic molecules or complex ions, that takes into account the long-range Coulomb interactions in such crystals, is described and used to determine various dynamical properties of β-SiC and α-quartz, such as the TO-LO splittings and the piezoelectric constants.     

Vibrational properties of thin films adsorbed on crystals with strong spatial dispersion

The effect of strong spatial dispersion of the substrate crystal onto the dynamics of thin epitaxially adsorbed films is described in a simple model through the following quantities: i) phonon reflection coefficients ii) depth-dependent local densities of states (LDOS) and iii) finite-lifetime surface states called leaky waves. The correspondence of these three types of characteristics accessible in different experimental methods is established. The bulk band of the substrate crystal consists of two distinct frequency ranges separated by an edge singularity: above the singularity the substrate supports two different waves for a given frequency, whereas only one wave can exist for each frequency in the low-frequency range. The resonances in the low-frequency range are found to correspond to maxima in the LDOS, to maxima in the amplitude of a near field arising in phonon reflection and to leaky waves involving a single leakage wave packet. The antiresonances in the same frequency range are characterised by minima in LDOS and in the near field, whereas the corresponding leaky waves involve two leakage wave packets. The only leaky waves found in the high-frequency range involve two leakage wave packets and are related to resonances. The antiresonances then are characterised by an anomalous increase in the extraordinary reflected wave. The edge singularity manifests itself in an additional quasi resonance, whose features depend on the coupling between the substrate and the thin film.     

Vibrational properties of the adsorbed monolayer on face-centered cubic crystals

Calculations of mean-square displacements 〈u²〉 of the atoms in adsorbed monolayers on fcc crystals are presented and compared with LEED experimental results. This text is restricted to the case of a C(2 × 2) adsorbed layer on a (100) surface [experimental case of Ni(100) with adsorbed sulfur, sodium, cesium or oxygen]. 〈u²〉's perpendicular to and parallel to a (100) surface are calculated for the adsorbed atoms and the atoms of the first surface layer of the crystal. The values obtained are compared with those for a clean (100) surface and the volume of the crystal. Every possibility for force constants between adsorbate and substrate atoms is examined. It is shown that the measurement of 〈u²〉 perpendicular to the (100) surface yields the adsorbate-substrate force constants and that 〈u²〉 parallel to the (100) surface yields the adsorbate-adsorbate force constants.     

Dispersion properties of two-dimensional phonon crystals with a hexagonal structure

Acoustic and optical properties of two-dimensional phonon crystals with a hexagonal symmetry are described. Differential-difference equations describing plane oscillations of a two-dimensional lattice of material structures are derived in a harmonic approximation, and dispersion dependences of acoustic and optical phonons are calculated. Branches of optical oscillations and intervals of forbidden frequencies are shown to appear when a lattice consists of two types of atoms.     

Static and thermophysical properties of chalcogenide crystals with NaCl structure

In the present communication an analysis of interionic potentials in fourteen chalcogenide crystals has been performed. This interionic potential has been used to predict the values of cohesive energy, isothermal bulk modulus and the pressure derivatives of bulk modulus in the solids under study. The many body interaction (MBI) effects have been taken into account within the framework of Hafemeister Zarht potential. Instead of using BM potential the Hafemeister-Zarht (HZ) type short range overlap potential has been considered between nearest as well as between next nearest neighbour ions. The short-range interactions, effective up to second neighbours are treated by considering the hardness parameter as an ionic property. The hardness parameter ρ_ij is evaluated using the data on overlap integrals. The results achieved in the present study are generally in good agreement with available experimental data. Values of cohesive energy, bulk modulus and its pressure derivatives calculated by previous investigators have also been shown for the sake of comparison.     

The properties of two-dimensional photonic crystals bandgap structure with rhombus lattice

The relative bandgap ω_R of photonic crystals structure with rhombus lattice for both TE and TM modes is studied by the plane wave expansion method. Based on the analysis, a bending waveguide of U type can be easily obtained. The steady-state distribution of the electric field with ω = 0.4765(a/λ) of TM mode is given by FDTD method and the transmission is obtained by FFT of the time domain field. All of the sufficient analysis shows the conceptual framework of the proposed rhombus lattice PCs and its great potential application in photonic integration circuit.     

Thermal expansion and elastic properties of the crystals with modulated structure

An experimental study of structure characteristics and elastic properties of the incommensurate crystals is reported.     

Experimental investigations of some optical properties in liquid crystals with spiral structure

Summary Some experimental investigations of the diffraction of light by the supermolecular periodic structure (pitch) in liquid crystals with spiral structure (for three different cases of spiral pitch) are presented. Work presented at the First USSR-Italy Bilateral Meeting on Liquid Crystals held in Portonovo, Ancona (Italy), September 30–October 2, 1987.     

Energy band structure and refractive properties of LiRbSO4 crystals

The energy band structure of mechanically free and compressed LiRbSO₄ single crystals is investigated. It is established that the top of the valence band is located at the D point of the Brillouin zone [k = (0.5, 0.5, 0)], the bottom of the conduction band lies at the Γ point, and the minimum direct band gap E _g is equal to 5.20 eV. The bottom of the conduction band is predominantly formed by the Li s, Li p, Rb s, and Rb p states hybridized with the S p and O p antibonding states. The pressure coefficients corresponding to the energies of the valence and conduction band states and the band gap E _g are determined, and the pressure dependences of the refractive indices n _i are analyzed.     

Photonic band gaps structure properties of two-dimensional function photonic crystals

The tunable two-dimensional photonic crystals band gap, absolute photonic band gap and semi-Dirac point are beneficial to designing the novel optical devices. In this paper, tunable photonic band gaps structure was realized by a new type two-dimensional function photonic crystals, which dielectric constants of medium columns are functions of space coordinates. However for the two-dimensional conventional photonic crystals the dielectric constant does not change with space coordinates. As the parameter adjustment, we found that the photonic band gaps structures are dielectric constant function coefficient, medium columns radius, dielectric constant function form period number and pump light intensity dependent, namely, the photonic band gaps position and width can be tuned. we also obtained absolute photonic band gaps and semi-Dirac point in the photonic band gaps structures of two-dimensional function photonic crystals. These results provide an important theoretical foundation for design novel optical devices.     

Vibrational properties of hierarchical systems

The vibrational properties of one-dimensional hierarchical systems are investigated and results are obtained for both their eigenvalues and eigenvectors. Two cases are considered, the first one with a hierarchy of spring constants and the latter with a hierarchy in the masses. In both cases the eigenspectrum is found to be a zero-measure, two-scale Cantor set with a fractal dimension between 0 and 1. The scaling properties of the spectra are calculated using renormalization group techniques and are verified by extensive numerical work. The low-frequency density of states and low-temperature specific heat are calculated and a singularity is found in the scaling behavior. The eigenvectors are found to be either extended or critical and self-similar. A transfer matrix formalism is introduced to calculate the scaling properties of the envelope of the critical eigenvectors. Furthermore, a connection is established between the hierarchical vibration and diffusion problems, as well as to the same problems in random systems, thus showing the universality of the observed features.     

Vibrational properties of Cu nanowires

We have calculated local vibrational density of states (LDOS) of a center atom (CA) of a rectangular Cu nanowire with the axial orientation of 〈100〉, using a real space Green’s function approach with force constants extracted from interaction potentials based on the embedded atom method. The LDOS of a center atom of a strained nanowire is found to exhibit quite distinctive characteristics as compared to that of a strain-free nanowire, the most striking feature of which is the existence of high frequency modes above the bulk band even for small strain of 2.5%. We further find that these high frequency modes are shifted to even higher frequencies when the nanowire is exposed to an increasing axial strain.     

Electro-optical properties of strontium-barium niobate crystals and their relation to the domain structure of the crystals

The electro-optical coefficients r _ij and half-wave voltage V_λ/2 of strontium-barium niobate crystals poled in the ferroelectric phase are shown to vary along the polar axis. The r _ij (z) and V_λ/2(z) dependences indicate the presence of a residual domain density D(z) and clearly depend on the sign of the polarizing field, with r _ij being minimum (D being maximum) near the negative electrode. This character of the D(z) distribution and, hence, the r _ij (z) and V_λ/2(z) coordinate dependences can be explained by predominant domain nucleation near the negative electrode, which is revealed when the switching processes are studied using 90° (Rayleigh) light scattering from domain walls.     

Computer simulation of structure and mechanical properties of polymer liquid crystals

In this contribution, we report on a study of the self-organization and mechanical properties of polymer liquid crystals (PLCs). Both processes are computer simulated by the method of molecular dynamics. We investigated two real longitudinal PLCs (thermotropic polyesters) with macromolecules that consist of rigid and flexible parts arranged in a regular way. One rigid and one flexible part form a monomer containing 45 or 47 atoms. The total number of atoms in the macromolecules studied was 4700 (100 monomers) and 5400 (75 monomers). The self-organization was similar to that obtained earlier for a beads-on-a-string model, so compression calculations were done using this simpler model containing 1200 beads (100 monomers). Macroscopic characteristics such as the stress-strain relation, temperature change during deformation, as well as microscopic changes in structure, were investigated.