Intermediate Frequency Modes Research Articles

Steplike dispersion of the intermediate-frequency Raman modes in semiconducting and metallic carbon nanotubes

Resonance Raman spectra of semiconducting and metallic single-wall carbon nanotube bundles have been investigated in the spectral range between 600 and $1100\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is associated with intermediate frequency modes. A large range of nanotube diameters corresponding to HiPco and electric-arc samples $(0.7--1.8\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$, and laser excitation energies between 1.62 and $2.71\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ have been used in the measurements. A rich set of peaks is observed, some of them independent of the excitation laser energy and some exhibiting a steplike dispersive behavior. The nondispersive peaks are assigned. The model proposed by Fantini et al. [Phys. Rev. Lett. 93, 087401 (2004)] to explain the steplike dispersive behavior of the intermediate frequency modes is then extended to different SWNT diameters and different ${E}_{ii}$ transitions, including semiconducting and metallic SWNTs.

Nanoscale Vibrational Analysis of Single-Walled Carbon Nanotubes

We use near-field Raman imaging and spectroscopy to study localized vibrational modes along individual, single-walled carbon nanotubes (SWNTs) with a spatial resolution of 10-20 nm. Our approach relies on the enhanced field near a laser-irradiated gold tip which acts as the Raman excitation source. We find that for arc-discharge SWNTs, both the radial breathing mode (RBM) and intermediate frequency mode (IFM) are highly localized. We attribute such localization to local changes in the tube structure (n, m). In comparison, we observe no such localization of the Raman active modes in SWNTs grown by chemical vapor deposition (CVD). The direct comparison between arc-discharge and CVD-grown tubes allows us to rule out any artifacts induced by the supporting substrate.

Suppression of spurious intermediate frequency modes in under-integrated elements by combined stiffness/viscous stabilization

Solutions employing perturbation stiffness or viscous hourglass control with one-point quadrature finite elements often exhibit spurious modes in the intermediate frequency range. These spurious frequencies are demonstrated in several examples and their origin is explained. Then it is shown that by critically damping the hourglass modes, these spurious mid-range frequency modes can be suppressed. Estimates of the hourglass frequency and damping coefficients are provided for the plane 4-node quadrilateral and a 4-node shell element. Results are presented that show almost complete annihilation of spurious intermediate frequency modes for both linear and non-linear problems. Copyright © 2005 John Wiley & Sons, Ltd.

Pressure effect on radial breathing modes of multiwall carbon nanotubes

This paper studies the pressure effect on radial breathing modes (RBMs) of multiwall carbon nanotubes (MWNTs). The analysis is based on a multiple-elastic shell model which assumes that each of the concentric tubes of a MWNT is an individual elastic shell and coupled with adjacent tubes through van der Waals interaction. The pressure effect on RBMs of MWNTs is mainly attributed to the pressure-induced reduction of interlayer spacing and the increase of the interlayer vdW interaction coefficient defined by the second derivative of the energy-interlayer spacing relation of MWNTs. In the absence of external pressure, the RBM frequencies and vibration modes predicted by the present shell model are found to agree very well with the available experimental and molecular-dynamics simulation results. In the presence of an external pressure, our results show that high external pressure considerably raises the vdW interaction coefficients especially between the outermost few layers of MWNTs. As a result, some of the RBM frequencies of MWNTs increase significantly with increasing external pressure. The most significant pressure effect occurs for the highest-frequency mode of large-diameter MWNTs (with the innermost diameter greater than 2nm) or an intermediate-frequency mode of small-diameter MWNTs (with the innermost diameter less than 2nm), and is always associated with those RBMs in which adjacent outermost layers vibrate in opposite directions with significant change in interlayer spacing.

Environment effects on the Raman spectra of individual single-wall carbon nanotubes: Suspended and grown on polycrystalline silicon

An enhanced Raman signal is observed from individual suspended single-wall carbon nanotubes (SWNTs) and from isolated SWNTs grown on an n-doped polycrystalline silicon film used in standard silicon processing. The radial breathing modes of the Raman spectra taken from suspended SWNTs exhibit narrow linewidths, which indicate a relatively unperturbed environment for suspended SWNTs. Clear Raman signals from intermediate frequency modes in the frequency range from 520to1200cm−1 are presented, which might allow a detailed study of the phonon band structure of individual SWNTs.

Resonance Raman Spectroscopy to Study and Characterize Defects on Carbon Nanotubes and other Nano-Graphite Systems

ABSTRACTThe use of resonance Raman spectroscopy (RRS) to study and characterize single wall carbon nanotubes (SWNTs) is discussed, focusing on preliminary efforts for the development of the RRS to characterize defects in SWNTs. The disorder-induced D-band, disorder-induced peaks just above the first-order allowed graphite G-band, as well as the intermediate frequency modes (IFMs) appearing between the RBM and the D/G spectral region are addressed. RRS on nanographite ribbons and on a step-like defect in highly ordered pyrolytic graphite (HOPG) sheds light into the problem of characterizing specific defects in nano-related carbons.

Kinetics of Isomerization via Photoinduced Electron Transfer. I. Spectral Analysis and Structural Reorganization of Hexamethyl Dewar Benzene Exciplexes

It is well recognized that emission spectra from the reactions of excited-state electron acceptors (A*) with hexamethyl Dewar benzene (D) are typically dominated by fluorescence from exciplexes of its valence isomerization product hexamethylbenzene (B) (i.e., A•-B•+). We were able to obtain well-defined emission spectra of the A•-D•+ exciplexes with several cyanonaphthalenes as the excited-state electron acceptors by subtraction of the dominant A•-B•+ fluorescence from the total emission. Interestingly, a comparison of band shapes and maxima between the exciplexes of D and B reveals that the reorganization energy for return electron transfer in A•-D•+ is much larger than in A•-B•+ (∼1.2 vs 0.57 eV). Furthermore, a comparison between exciplexes of D and of 1,2-dimethylcyclobutene as a model compound showed that a greater reorganization energy is associated with return electron transfer from the A•-D•+ exciplexes. DFT calculations identified much of the “excess” reorganization energy in A•-D•+ with a change in the dihedral angle (flap angle) between the two cyclobutene moieties, which is ∼12° smaller in D•+ than in D. Approximately one-fourth of the total reorganization energy of ∼1.2 eV for the D exciplexes is due to this angle deformation. Spectra of the exciplexes of B and of model olefins were analyzed by using a familiar two-mode model whereas those of D required a three-mode model to account for the intermediate frequency (491 cm-1) mode associated with the flap angle deformation. Remarkably, although the driving forces for return electron transfer are nearly identical for the exciplexes of D and B with the same acceptor, the rate constants for nonradiative return electron transfer are predicted to be 4 to 5 orders of magnitude greater for the A•-D•+ exciplexes because of their larger reorganization energies.

A study on time schemes for DRBEM analysis of elastic impact wave

The precise integration and differential quadrature methods are two new unconditionally stable numerical schemes to approximate time derivative with more than the second order accuracy. Recent studies showed that compared with the Houbolt and Newmark methods, they produced more accurate solutions with large time step for the problems where response is primarily dominated by low and intermediate frequency modes. This paper aims to investigate these time schemes in the context of the dual reciprocity BEM (DRBEM) formulation of various shock-excited scalar elastic wave problems, where high modes have important affect on traction response. The Houbolt method was widely recommended in many literatures for such DRBEM dynamic formulations. However, this study found that the damped Newmark algorithm was the most efficient and accurate for impact traction analysis in conjunction with the DRBEM. The precise integration and differential quadrature methods are shown inapplicable for such shock-excited problems due to the absence of numerical damping. On the other hand, we also found that to achieve the same order of accuracy, the differential quadrature method required much less computing effort than the precise integration method due to the use of the Bartels–Stewart algorithm solving the resulting Lyapunov matrix analogization equation.

The Investigation of Plasmon-Longitudinal Optical Phonon Coupling and Surface Polariton Modes in Donor Doped GaAs-Al 0.33 Ga 0.67 As Multi Quantum Wells

Infrared Fourier transform spectroscopy has been used to investigate phonon, plasmon, surface polariton and plasma-longitudinal optical phonon coupling in highly donor doped multi quantum wells (GaAs/Al0.33Ga0.67As) and direct band gap n- type AlXGa1-XAs thin layer on GaAs substrate. Using different samples with different concentration of free carriers. The dispersion equation of coupling modes have been calculated by using the condition which the dielectric functions of samples are zero for longitudinal coupled modes and experimental papameters which have been obtained from the best fit p-polarized oblique incidence far infrared reflection spectra. In MQW samples, the free carriers confined to the well and carriers are quasi two dimensional. So, plasmon- LO phonon coupling occur in the well (GaAs). In n- type AlXGa1-XAs thin layer, the coupled modes consist of three branches of the high, intermediate and low frequency modes. Their frequencies depend on both concentration and alloy composition. To analyses the surface polariton modes we carry out attenuated total reflection (ATR) measurements. In order to support our assignment the magnetic field profiles and surface polariton dispersion curves have been calculated.

Finite-size effect on the Raman spectra of carbon nanotubes

Using nonresonant bond polarization theory, we have calculated the Raman intensity of a single-wall carbon nanotube of finite length. The calculations show that the Raman peaks in the intermediate frequency range $(500--1200{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1})$ have no intensity for infinite nanotubes, but do have some intensity for finite nanotubes. These intermediate frequency modes, which are sensitive to the nanotube length, correspond to vibrations along the nanotube axis. We also found an edge state of the breathing phonon mode at an open end of the carbon nanotube, which is Raman active.

A Vibrational Eigenfunction of a Protein: Anharmonic Coupled-Mode Ground and Fundamental Excited States of BPTI

We present detailed methodology and results for the approximate calculation of the anharmonic vibrational wave functions for a given structure of a protein. The ground state and the fundamental vibrationally excited states of hydrated BPTI are computed with an approach that is of very good accuracy for low-lying states. The eigenfunctions are used to predict quantum properties such as vibrational excitation frequencies and IR intensities as well as atomic mean square displacements at T = 0 K. The method treats diagonal anharmonic effects exactly up to fourth order in normal mode coordinates, while using a mean-field approximation, the vibrational self-consistent field (SCF) approximation for the mode−mode couplings. The inclusion of the diagonal effects (exact in fourth order) makes the potentials stiffer than quadratic. When the mode−mode coupling is included as a mean field, the system becomes even stiffer. These effects produce significant modifications of such observables as the vibrational spectrum and Debye−Waller factors. The results presented here should be considered essentially exact except for potentially important approximations: (a) that the potential energy used bears some resemblance to reality, (b) that the system is restricted to a single minimum in the potential energy surface, and (c) that the quartic expansion in normal modes, when truncated to fourth order, provides a good description of the potential. These issues will be addressed in the main text. The results show that the vibrational absorption spectrum is strongly affected by anharmonic and mode−mode coupling effects. Deviations from the corresponding harmonic absorption intensities are very large. Unlike our previous study that found only weak mode−mode coupling effects for the lowest 100 modes, the SCF corrections calculated here for the intermediate frequency modes are seen to be very significant. The results have important implications for the vibrational spectroscopy and other properties of proteins at low temperatures.

Vibrational wave functions and spectroscopy of (H2O)n, n=2,3,4,5: Vibrational self-consistent field with correlation corrections

Vibrational energy levels, wave functions, and ir absorption intensities are computed for (H2O)n clusters with n=2, 3, 4, and 5. The calculations were carried out by the vibrational self-consistent field (VSCF) approximation, with corrections for correlations between the modes by perturbation theory. This correlation corrected VSCF (CC-VSCF) is analogous to the familiar Möller–Plesset method in electronic structure theory. Test calculations indicate that this method is of very good accuracy also for very anharmonic systems. While the method is of highest relative accuracy for the stiffest modes, it works very well also for the soft ones. Some of the main results are (1) the frequencies calculated are in good but incomplete agreement with experimental data available for some of the intramolecular mode excitations. The deviations are attributed to the inaccuracy of the coupling between intramolecular and intermolecular modes for the potential function used. (2) Insight is gained into the pattern of blue- or redshifts from the corresponding harmonic excitation energies for the various modes. (3) Anharmonic coupling between the modes dominates in general over the intrinsic anharmonicity of individual modes in determining the spectrum. (4) The anharmonic corrections to the frequencies of some intermolecular modes (shearing, torsional) are extremely large, and exceed 100% or more in many cases. (5) An approximation of quartic potential field in the normal mode displacement is tested for the clusters. It works well for the high and intermediate frequency modes, but is in error for very soft shearing and torsional modes. (6) The relative errors of the VSCF approximation are found to decrease with the cluster size. This is extremely encouraging for calculations of large clusters, since the VSCF level is computationally simple.

A local stability analysis of astronomical disks

Abstract A fifth-order dispersion relation describing the local stability of a differentially rotating flow against small perturbations is derived. Finite viscosity and conductivity and both vertical (parallel to the rotation axis) and radial gradients in density, temperature and pressure are included. A general form is assumed for the equation of state, although this is not exploited in the paper. A number of special cases are studied: with negligible viscosity and conductivity, it is shown that modes can often be separated into two high frequency (modified acoustic), two intermediate frequency (combined inertial and internal waves) and a low frequency mode. In convectively unstable situations the intermediate frequency modes may be replaced by a damped/growing pair of instablities. Various criteria for mode excitation are given. It is shown that viscosity always inhibits instability at very short wavelengths, while non-zero conductivity may destabilize the flow. At intermediate wavelengths viscosity cou...

Potential energy surfaces for water dynamics. II. Vibrational mode excitations, mixing, and relaxations

Dynamical behavior of liquid water is investigated by analyzing the potential energy surface involved. Multidimensional properties of the potential energy surface are explored in terms of vibrational mode excitations at its local energy minima, called inherent structures. The vibrational mode dynamics, especially mechanism of mode relaxation and structure transitions, is analyzed. It shows very strong excitation energy dependence and mode dependence. There are three kinds of vibrational coupling among modes. For excitations of energy near the room temperature, most modes (more than 90% of total modes) individually interact with only one or two other modes, and yield near recurrence of the mode energy in a few tens picoseconds (very slow relaxation). Spatially localized modes in the intermediate frequency range couple with many delocalized modes, yielding fast relaxation. The coupling is governed by atomic displacement overlaps and frequency matching. Each mode couples with nearby frequency or double frequency modes through the Fermi resonance. Lowest frequency modes almost always lead to transitions from a potential energy well to neighbor potential wells, called inherent structure transitions. In high energy excitation, some intermediate frequency modes also yield such transitions. There exist very low energy paths involving single or few water molecule displacements at almost every inherent structure, indicating that certain facile molecular movements occur even in very low temperature states. Different energy excitations of a low frequency mode result in different inherent structure transitions; transitions caused by high energy excitations involve many large molecular displacements. These inherent structure transitions are the source of the water binding structural reorganization dynamics. Significance of these vibrational mode dynamics in the water dynamics is discussed.

Scattering of electromagnetic waves by a relativistic electron beam in a plane waveguide

In the framework of the three-wave parametric interaction, an investigation is conducted of the scattering of electromagnetic (EM) waves by a relativistic beam completely filling a plane waveguide. Investigated are the conditions of wave amplification due to a process of up-conversion of a lower frequency wave, resulting from the negative energy of the intermediate frequency mode. In the approximation of the given pumping field, the increment of the EM wave parametric instability is found.

Accretion disk oscillations - A local analysis in a disk of finite thickness

Two types of oscillations are observed to occur in dwarf novae: 'coherent' and 'quasi-periodic' oscillations. These may be associated with the pulsation of the white dwarf or the accretion disk components of the dwarf nova. Here a local (short-wavelength) analysis is utilized to study the oscillation of a self-consistent, two-dimensional model of an accretion disk. The linearized equations describing adiabatic, inviscid, nonaxisymmetric oscillations are used to derive a fifth-order algebraic equation for the (complex) pulsation frequency of the disk. The solutions of this equation for various values of the wavevector k reveal that the disk is capable of supporting (1) a pair of high-frequency acoustic modes (p-modes); (2) a pair of intermediate-frequency modes which may share the characteristics of internal gravity waves (g-modes) and inertial waves; and (3) a mode associated with a dynamical instability (purely imaginary frequency). The role played by the shear in determining the stability or instability of these modes is also considered. Finally, the global oscillation frequencies of the disk are discussed.

Propagation of intermediate frequency waves in a bounded magnetoplasma

The paper presents a study of the propagation of intermediate frequency waves in a plasma column magnetized axially and enclosed in a conducting cylinder. The general dispersion relation for the waves, obtained by the dynamic method, is found to reduce to four distinct equations associated with different forms of the field components. The ω-β plane is divided into several regions of four types so that within each region only one of the above four equations would apply. Dispersion characteristics are obtained for all possible types of intermediate frequency modes in a hydrogen plasma for a typical set of ωce/ωpe and aωpe/c, where ωce is the electron cyclotron frequency, ωpe is the electron plasma frequency, a is the plasma radius, and c is the velocity of light in free space. It is discussed how the dispersion characteristics of the different modes would change with variations in the plasma parameters. The investigations show that, contrary to the predictions of the usual quasistatic approximation, propagation of all intermediate frequency modes is possible at frequencies below the lower hybrid frequency ωlh. Moreover, the I−n1 modes with n≠0 and the superscript indicating the polarization form a special category of modes in the sense that they have a resonance at the ion cyclotron frequency ωci and that their propagation below the frequency ωlh is confined to the domain 0<ω<ωci. In the case of all other modes the phase coefficient β increases gradually to a finite value as ω increases from its cutoff value to ωlh ; this value of β lies within two specified limits, β1 and β2 ( β2>β1), which are functions of ωpe, ωce, and ωci. The dispersion characteristic of each of these modes has a sharp discontinuity at ω=ωlh. If ω is increased beyond ωlh, the characteristic of the I01 mode starts off from the point (ωlh,0), while the corresponding point for all other modes is given by (ωlh, β1) . However, all the modes have a resonance at ωpe(ωpe<ωce). It is interesting to note that if the mode number is increased or the plasma radius is reduced, keeping the other parameters fixed, the phase coefficient β at any given frequency increases in the frequency domain ωlh<ω<ωpe, while in the domain 0<ω<ωlh it falls until it becomes zero. Finally, it is shown that there is considerable discrepancy between the results given by the quasistatic approximation and those by the dynamic analysis even in the most favorable case of the I01 mode in the frequency domain ωlh<ω<ωpe if the plasma radius a is relatively large, compared to c/ωpe.

Intra- and interlayer contributions to the lattice vibrations in MoO 3

We report new experimental results for the Raman- and infrared-active modes in the layered compound MoO 3. The observed frequencies are explained in terms of a valence-force-field model, including interlayer interactions. Most of the 45 optical modes are dominated by either intralayer or interlayer contributions. However, in spite of the weak interlayer coupling, some of the intermediate-frequency modes are strongly perturbed by the interlayer interactions, which explains the large Davydov splittings observed. Moreover, the two lowest-frequency shear modes cannot be described within the rigid-layer approximation. These facts are a direct consequence of the specific bond geometry in MoO 3.

Cutoff frequencies of intermediate frequency waves in a bounded magnetoplasma

The paper presents a study of the cutoff frequencies of a class of electromagnetic waves, designated here as intermediate frequency waves, which can propagate in a plasma column enclosed in a conducting cylinder and embedded in a static axial magnetic field. These waves reduce to lower hybrid waves or magnetohydrodynamic TE waves under suitable conditions. The cutoff frequencies of the intermediate frequency modes have been investigated, covering all possible values of ωpe,ωce, and a, where ωpe is the plasma frequency, ωce is the electron cyclotron frequency, and a is the plasma radius. The study includes all the possible types of modes, namely, circularly symmetric I0m modes and asymmetric Inm modes with n ? 1, each Inm mode being split into two, called I+nm and I−nm modes, corresponding to two different polarizations of the field components. The cutoff frequency ωc 0 of any Inm mode with n ? 0 is found to be confined to the frequency domain 0 to ωnm, where ωnm is the cutoff frequency of the TEnm mode in an empty waveguide. The zero frequency is approached if ωpe or a tends to infinity or ωce tends to zero, the other parameters remaining constant in each case. The frequency ωc 0 tends to ωnm if ωce is sufficiently large for any given set of ωpe and a. The study of intermediate frequency modes reveals that these modes can broadly be divided into the following two categories: (1) I−n1 modes with n ? 1, and (2) modes other than I−n1 modes. The nature of variation of ωco ith ωpe for fixed values of ωce and a for I−n1 modes is, in general, quite different from that for the other modes. Furthermore, ωc 0 tends to ωci as a tends to zero with ωpe and ωce held fixed in the case of I−n1 modes, while for other modes ωc 0 tends to ωlh under the same condition, where ωci is the ion cyclotron frequency and ωlh is the lower hybrid frequency. Any Inm mode with n ? 0 is found to reduce to the magnetohydrodynamic TEnm mode at or near the cutoff under the condition: ωpi≫ωnm, where ωpi is the ion plasma frequency. Finally, it is shown how the charge density in a bounded magnetoplasma can easily be determined in most experimental situations by using the cutoff frequency characteristic of the dominant I−11 mode.

Temperature dependence of the 59Co quadrupole coupling constant in K3Co(CN)6

Expressions are presented for calculating the effects of bond-stretching and rotational modes of vibration on the temperature dependence of quadrupole coupling constants in crystals. Contributions to the motional averaging of the electric field gradient tensor arising from point charges, point dipoles, and overlap of closed wave functions are evaluated and the resulting expressions applied to analyse the temperature variation of the 59Co quadrupole coupling constant in K3Co(CN)6. Both stretching and rotational internal modes of vibration of the Co(CN)6 octahedron had to be taken into account to analyse the data. In particular, an intermediate frequency mode of wavenumber 414 cm−1 has been found to make a substantial and positive contribution to the shift in coupling constant arising from the low (~ 100 cm−1) and intermediate frequency (~ 400 cm−1) modes. The remainder of the shift (~ 90%) has been attributed to a rotary mode of wavenumber 26 cm−1. The extracted temperature dependence of this mode points to the possible existence of a structural phase transition in K3Co(CN)6 below 100 K.