Calculated Dispersion Curves Research Articles

Wave propagation in submerged piezoelectric layered media

A formulation for the systematic study of wave propagation in a layered piezoelectric solid interacting with an acoustic fluid is presented. The methodology employed is based on an eight‐dimensional vector formalism, due originally to Kraut [Phys. Rev. 57, 1450–1455 (1969)]. Within this framework, one may easily define “characteristic” impedances of a single material. With this as a building block, the invariant‐imbedding technique is employed to construct the “global” surface impedance of an arbitrarily layered piezoelectric solid. In some special cases, the overall problem can be simplified by exploiting material symmetries and so reducing the order of the eigenvalue problem (by a factor of 2). Results presented include calculations of dispersion curves for layered piezoelectric plates and interfacial waves between a fluid and a piezoelectric solid. [Work supported by ONR.]

Lattice Dynamics of Ca and Sr in B. C. C. and F. C. C. Phases. A dynamic treatment

AbstractThe pair potential defined for transition metals in a previous paper is extended to study the phonon dispersion of alkaline earths. The overlap between d states on different ions and the effect of sd hybridization are included in ion‐ion interaction as has been suggested by Wills and Harrison. The temperature dependence is also included through an asymptotic factor. The calculated dispersion curves do not differ from experimental values by more than 10% for both, Ca and Sr in both, f. c. c. and b. c. c. phases except at a few wave vectors near the zone boundary in the case of Ca(b. c. c). The binding energy and elastic constants are also calculated and compared with existing experimental data.

Structure and dynamics of NiAl(110)

We have measured the surface phonon dispersion for the (110) face of the ordered alloy NiAl using high resolution electron energy loss spectroscopy (EELS) with ΔE = 20–45 cm−1. Our experimental results are compared with lattice dynamical calculations employing a Born-von Karman model up to third-nearest neighbour. Good agreement between the experimental and calculated dispersion curves is obtained when the force constant between first layer nickel atoms and second layer aluminum atoms is increased and the force constant between first layer aluminum atoms and second layer nickel atoms is decreased. These force constant changes indicate a surface rippling where first layer nickel atoms are displaced inwards and first layer aluminum atoms are displaced outwards. This is in qualitative agreement with a structural model based on low energy electron diffraction (LEED) I/V data and a medium energy ion scattering (MEIS) study.

First-principles screening calculation of the surface phonon dispersion curves at the (100) surface of sodium

A self-consistent nonperturbative screening calculation of the phonon dispersion relations for sodium has been carried out for both the bulk and the (100) surface. The static density response function for the electrons was calculated self-consistently from the solutions to the single-particle Kohn-Sham equations in the local density approximation with the bare ion-electron interaction taken to be a local Heine-Abarenkov pseudopotential. The dynamical matrix was calculated from the response function and diagonalized to yield the normal mode frequencies and eigenvectors. For the surface problem a crystal slab bounded by (100) surfaces and containing 13 atomic layers was employed.

Magnetic excitations in the two-dimensional random antiferromagnets Rb2CocNi1-cF4

Magnetic excitations in Rb2CocNi1-cF4 have been investigated. Neutron scattering experiments were performed on single crystals with c=0.14 and 0.7. Two bands of excitations have been observed. Spin-wave dispersion relations obtained at 15 K are compared with calculated dispersion curves based on the mean-crystal model. Although the model gives a qualitative description of the concentration dependences of the dispersion relations, good agreement is not obtained when the exchange interaction parameters determined for pure crystals are used. The possibility of a change in the exchange interaction parameter between Co ions in the mixed crystal is discussed.

LATTICE DYNAMICS OF MBa2Cu3O7(M=Y, Gd) and YBa2Cu3O6

We have presented a lattice dynamical calculation of phonon dispersion curves and one-phonon density of states for the high-T c superconducting MBa 2 Cu 3 O x (M=Y, Gd : x=7, 6) compounds. The model we used is in the framework of a rigid-ion model which includes long-range Coulomb potential and a short-range overlap. The results of calculation give quite good agreement with the available Raman and infrared data, and the measurements of phonon density of states. These results therefore can serve as a guide for further experimental investigations of the phonon properties in M-Ba-Cu-O (M=rare earth atom) system.

Iterated-moment method for the analysis of optical waveguides of arbitrary cross section

An iterated-moment method is presented and formulas are derived for the accurate calculation of dispersion curves of guided modes in optical waveguides of arbitrary cross sections. Applications of the method to homogeneous dielectric structures of various cross sections (rectangular, elliptical, and triangular guides; homogeneous optical fibers with deformed boundaries; and composite dielectric waveguides) are illustrated. The method is simple, and numerical results obtained agree well with computer-aided exact numerical methods (finite-element method, point-matching method, etc.), which involve a large amount of computation. The method can be extended readily to graded-index guides and couplers as well as to anisotropic dielectric structures.

Surface lattice dynamics of the Pandey-reconstructed Si(111)-2 × 1: No pathologies in the experimental findings

In this paper we report a slab calculation of the surface phonon dispersion curves for Si(111)-2 × 1 in the framework of the bond charge model dynamics. Our results are in very good agreement with the existing experimental data and provide a comprehensive interpretation for the dynamical structures of this surface, based on the relationships with the unreconstructed one. This “ intrinsic” perspective stands in opposition to a recently published analysis, which is grounded on the uniqueness of this surface dynamics, as due to the atomic chains produced by the Pandey reconstruction. The intriguing role of the interface between the 1 × 1 (bulk) and the 2 × 1 (surface) patterns is pointed out in relation to recent EELS measurements and the possibility of exploiting surface characterization via phonon spectroscopy is described.

Surface Phonons in Si(111) 2 × 1: Folding and Chain Effects of the Reconstruction

In the present paper we report a slab calculation of the surface phonon dispersion curves for Si(111) 2 × 1 in the framework of the Bond Charge Model dynamics. Our results are in very good agreement with the existing experimental data and provide an interpretation for the dynamical structures of this surface, based on the relationship with the unreconstructed one. This latter perspective stands in opposition to a recently published analysis, which points out the uniquity of the chain dynamics, and comparison is made between the two on the grounds of the experimental information.

Flexible dielectric waveguides with powder cores

Flexible dielectric waveguides have been demonstrated at 10 GHz and 94 GHz using thin-wall polymer tubing filled with low-loss, high-dielectric-constant powders. Absorptive losses of the order of 10 dB/m were measured at 94 GHz. with nickel-aluminium titanate and barium tetratitanate powder in polytetrafluoroethylene (PTFE) lightweight electrical tubing. Bending losses at 94 GHz were negligible for curvature radii greater than 4 cm. M.H. Kuhn's (1974) theory of three-region cylindrical dielectric waveguide was used to calculate dispersion curves for the lower-order modes for several combinations of dimensions and dielectric constants. Good agreement was obtained between experimental and theoretical values of guide wavelength. A scheme is proposed for classifying hybrid modes of three-region guides based on the ratio mod E/sub z//H/sub z/ mod . For two-region guides, this reduces to E. Snitzer's (1961) familiar scheme.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Self-consistent-screening calculation of surface-phonon dispersion curves at the (110) surface of aluminum.

We have calculated the dynamical matrix for an aluminum slab bounded by a pair of (110) surfaces using a self-consistent implementation of pseudopotential perturbation theory. The screening response of the conduction electrons to the field of the ions is obtained within the local-density approximation of density-functional theory. Both relaxed and unrelaxed geometries are treated. We present numerical results for the dispersion curves of surface phonons. Comparison is made with recent theoretical and experimental results.

Application of the matching procedure to the calculation of surface phonons and surface resonances of Ni(100) in the (011) direction

Phonon dispersion data on Ni(100) for the (011) direction are calculated using the matching procedure. The Rayleigh mode is shown to be a surface state over the whole of the two-dimensional Brillouin zone, and a new odd surface state is found. The Van Hove singularities are analysed in detail and a practical definition of surface resonances is given. A new initial condition describing the scattering of an incoming bulk phonon by the surface is introduced. The calculated dispersion curves of surface resonances are compared with other authors' work. Eventually a new interpretation of EELS data is proposed.

A SIMPLE APPROACH FOR THE CALCULATION OF FORCE CONSTANTS OF SEMICONDUCTORS——APPLICATION TO THE STUDY OF PHONONS AT THE GaAs(111)-2×2 SURFACE

An analytical expression for the force constants of semiconductors with arbitrary hybridization is derived by using the bond orbital approximation to simplify the calculation of electronic band structure energy of the system. This method is shown to be simple and effective by the comparison between the theoretical calculation and experimental results of phonon dispersion curves of several materials. Applying this method to the study of phonon at GaAs (111)-2×2 sarface, the dispersion curves of phonons that are strongly localized at the surface are obtained.

Lattice-dynamical analysis of the anomalous mode of W(001).

We construct dynamical models of W(001) by least-squares fitting the surface modes of a W(001) slab to the surface-phonon data (along $\overline{\ensuremath{\Gamma}}\overline{M}$) of Ernst et al. We find that the measured phonon dispersions can be explained on the basis of changes in the short-range force constants at the surface. The calculated dispersion curves along $\overline{\ensuremath{\Gamma}}\overline{X}$ depend on longer-range interactions. Thus, surface-phonon measurements along $\overline{\ensuremath{\Gamma}}\overline{X}$ may reveal whether these interactions are significant at the W(001) surface.

Guided Wave Mode of the Surface Exciton Polariton in Anthracene Crystal

The stable solution of the TE-guided wave mode (TE-GWM) of the surface exciton polariton is obtained in the (001)-surface of anthracene crystal. The luminescence band observed around the surface exciton energy is ascribed to the radiative decay of the TE-GWM. The peak energy and the large width of this band are interpreted by the calculated dispersion curve of the TE-GWM. The incoming and outgoing resonances are observed in the Raman scattering by a surface phonon. The Raman line energy at the outgoing resonance coincides with the energy of the TE-GWM. The outgoing resonance is interpreted by the model of the TE-GWM. The luminescence structure observed below the surface exciton energy is assigned to the side-band of theTE-GWM associated with the emission of the surface phonon.

Domain-wall modes for krypton monolayers on graphite.

We present calculations of phonon dispersion curves for krypton on graphite. We concentrate our attention on the in-plane vibrational states of the incommensurate phases near registry. Under these conditions it is found that the three lowest-lying modes (two corresponding to shear and one corresponding to compression) separate out and have much lower energy than the rest. These modes correspond to motion of the domain-wall structures. The results for the lowest-lying modes are presented for a variety of misfits and orientations of the equilibrium configuration. The smooth density modulations in the incommensurate phases allow us to describe the eigenvectors of the low-frequency modes with Fourier expansions that contain only a few terms.

Phonon dispersion curves of V B group of metals

The phonon frequencies of vanadium, niobium and tantalum along the principal symmetry directions are computed using an angular force model. The calculated dispersion curves are in very good agreement with the experimental results.

Vibrational analysis of polyacetylene and copoly(acetylene+acetylene-d2): In-plane vibrations of t r a n s-polyene chains

Normal coordinate calculations have been performed for the in-plane vibrations of several trans-polyene chains from butadiene to polyacetylene in order to obtain a set of force constants commonly applicable to short and long polyenes. The force field finally obtained consists of short range forces, which are primarily determined by the frequency data on short polyenes, and long range interactions which are important in explaining the data on polyacetylene. The long range interactions between the C=C stretching coordinates as far as the fifth neighbor have significant effects on the dynamical properties of the infinite chain. Frequencies of some Raman active vibrations are greatly lowered by the long range terms to become comparable with the experimental frequencies of polyacetylene. These vibrations shift to higher frequencies steeply as the phase difference between adjacent HC=CH units increases from zero. Such steep dispersion as well as the other features of calculated dispersion curves are fully consistent with the expectation based on the Raman spectra of copoly(acetylene+acetylene-d2). Further support for the dispersion curves is given by a general agreement between the experimental Raman spectra and theoretical spectra calculated for model copolymer chains using an approximate equation of resonance Raman intensity.

Propagation Characteristics of SH–Waves in Piezoelectric Ceramic Plates

Propagation characteristics of shear horizontal (SH) waves in a piezoelectric ceramic plate have been investigated as a function of the product of the frequency F and the substrate thickness D. The distribution of displacement in the zeroth-order symmetrical and antisymmetrial modes is illustrated for various FD values. Calculated dispersion curves and electromechanical coupling constant values are well consistent with the experimental results obtained in five kinds of SH-wave devices.

Calculation of dispersion curves in periodic structures

The SUPERFISH [1] equations are adapted to the computation of the dispersion curves for TM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</inf> and TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</inf> modes in a periodic structure with azimuthal symmetry.