Effect Of Localized Modes Research Articles

Effect of localized modes in the optical absorption spectra of CuGaSe2 and CuGa3Se5

The optical absorption coefficient α as a function of the incident photon energy hν at different temperatures between 50 and 300K and the infrared spectra between 80 and 375meV have been studied in the ternary compound CuGaSe2 and the ordered defect compound CuGa3Se5. It is found that the phonon energy hνp involved in the formation of Urbach tail is much higher than the highest lattice vibrational modes in these compounds. A combined analysis of the Raman modes and infrared spectra shows, after discarding the possible donor/acceptor transitions, replicas of phonon modes at higher energies in both Raman and infrared spectra, and the peaks originating from the spectrophotometer, that the average phonon energy hνp∗ of the remaining lattice vibrational and localized modes are in good agreement with the phonon energy hνp obtained from the study of Urbach tail. This confirms that in the formation of Urbach tail, in addition to the contribution of lattice vibrational modes, other localized modes caused by structural defects and enhanced electronic distortion, originating from ordered defects, are also involved. It is suggested that this type of study can be a useful tool in determining the quality of the samples and the ingots, important in device applications.

Local modes in vibration–rotation spectroscopy

AbstractThe present paper is concerned with the description of highly excited rotational and/or vibrational states of molecules in terms of localized vibrations or local modes. Local mode effects are most common in molecules with multiple equivalent H–X bonds, which give rise to equivalent H–X local mode stretching vibrations, and the theory is outlined for the simplest such case, that of an H2X molecule. In the local mode picture of molecular vibration, experimentally observed, initially unexpected near‐degeneracies of vibrational states at high vibrational excitation, and of rotation–vibration states at high rotational excitation, can be explained in a relatively straightforward manner. The local mode theory predicts relations between the conventional rotation–vibration parameters whose values are determined in least‐squares fittings to observed rotation–vibration transition frequencies or wavenumbers. It should be emphasized, however, that such relations are valid only for particular forms of the effective rotation–vibration Hamiltonian used in the spectral analysis. We illustrate the theory with examples of experimental spectroscopic work where local mode effects play an important role in the interpretation of the experimental findings. The fact that local mode vibrations not only cause clustering of highly excited vibrational energy levels, but also of highly rotationally excited rotation–vibration energy levels, has been understood fairly recently. We outline the theoretical background for this phenomenon and relate it to the existing experimental work. © 2012 John Wiley & Sons, Ltd.This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy

Exponentially FragilePTSymmetry in Lattices with Localized Eigenmodes

We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting delta approximately exp(-N/xi) where xi is their localization length. The level "evolution" with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous PT symmetry breaking occurs at gammaPT approximately min{delta}, thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gammaPT approximately 1/N2 and the distribution P(gammaPT) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.

Phonon contribution to the hyperfine coupling constant

The temperature dependence of the hyperfine coupling constant A(T) of Mn2+ in MgO is analysed by means of the generalized phonon theory, obtained by treating the phonon wavelength without approximation over the entire phonon spectrum. A comparison is also made of the results obtained with both the generalized and the long-wavelength models as applied to A(T) for Mn2+ and Eu2+ in the alkaline earth fluoride crystals. This comparison suggests that local mode effects and not covalency may be the dominant mechanism required to improve the theoretical fit to the data. Contributions from optical phonons to A(T) of Mn2+ and Eu2+ in MgO, CaF2, SrF2, and BaF2 crystals are also tabulated and discussed.

Tore Supra ITER-like antenna characterization by FEM analysis

Abstract This paper describes the method used for the high-frequency electromagnetic (EM) analysis of the TS ITER Prototype array and of its associated tuning system by 3D finite elements modelling (FEM) and discusses some of the results obtained. This method is a new approach to the design of high frequency systems, when physical dimensions are a non-negligible fraction of the radiation wavelength, and the effects of local modes cannot be accounted for by a pure TEM analysis.

A 3D measurement procedure for internal local crack driving forces via synchrotron X-ray microtomography

Synchrotron X-ray microtomography has been utilized for the in situ observation of fatigue crack opening/closure during load cycles. High-resolution phase contrast imaging technique has enabled the reconstruction of clear crack images together with the details of microstructural features. Physical displacements of micro-pores in a crack-tip stress field are used to obtain local mixed-mode crack driving forces along a crack front, and its feasibility is confirmed. Complicated crack closure behaviour are observed due to the combined effects of local modes II and III displacements. The technique used provides a highly effective way of assessing local crack driving forces together with supplementary ways of verifying and interpreting it by visualising and quantifying various forms of crack-tip shielding behaviour. The proposed technique is clearly advantageous compared to the limited procedures available in the current literature, where detailed internal information can only be achieved for limited types of material.

Effect of localized modes in the absorption spectra of CuInTe 2, CuIn 3Te 5 and CuIn 5Te 8

The optical absorption coefficient α as a function of the incident photon energy hν at different temperatures between 10 and 300 K and the infrared spectra between 50 and 300 meV have been studied in CuInTe 2, CuIn 3Te 5 and CuIn 5Te 8 of the Cu–In–Te system. It is found from the analysis of Urbach tail, observed in these compounds just below the fundamental absorption edge, that the phonon energy involved in the electron/exciton–phonon interaction is much higher than the average of their corresponding lattice vibrational modes. However, after discarding the donor/acceptor transitions and also the replicas of phonon modes of lower energies observed in their infrared spectra, the combined average energy hν p ∗ of the remaining localized and lattice vibrational modes is found to be in good agreement with the phonon energy hν p obtained from the study of Urbach tail in these compounds. This confirms the suggestion made earlier [Phys. Rev. B 64 (2001) 195101] that in the formation of Urbach tail, in addition to the contribution of the lattice vibrational modes, other localized modes that have their origin in the structural defects caused by the deviation from ideal stoichiometry are also involved.

Local Mode Effects in the Absorption Spectrum of H2S between 10 780 and 11 330 cm−1

The absorption spectrum of H2S (1159 lines) has been recorded between 10 780 and 11 330 cm−1 by intracavity laser absorption spectroscopy (ICLAS). As a result of the increase of sensitivity of ICLAS over previous Fourier transform investigations in the same spectral region, the number of experimental energy levels of the (40+, 1) and (40−, 1) local mode states ((212) and (311) in normal mode notation) has been triplicated for the main isotopic species H232S (198 compared to 62). Moreover, 112 energy levels of H234S and 25 energy levels of H233S, present in natural abundance in the sample, could also be determined. Three rotational levels of the (30±, 3) local mode pair of dark states ((132) and (231) in normal mode notation) of H232S could also be observed through extra lines borrowing their intensities via resonance interactions with line-partners of the dominant bands. The (40+, 1) and (40−, 1) local mode states form a degenerate local mode pair, with the same rotational structure for the two components. The observed energy levels were reproduced by an effective Hamiltonian including the (40±, 1) and (30±, 3) interacting local mode pairs. This Hamiltonian was applied either in the C2v or Cs symmetry groups leading to an rms deviation of 0.0058 and 0.0068 cm−1 respectively, comparable to the experimental accuracy (0.0028 cm−1). The degeneracy of the rotational structure of the (40±, 1) pair is unaffected by the interaction with the nearby (30±, 3) local mode states. On the contrary, an additional interaction with dark states lifts in some cases this degeneracy. The same effective Hamiltonian with scaled parameters was success fully used to reproduce the energy levels of the H233S and H234S isotopic species. Finally, the extremely weak 3ν1+3ν2 band of H232S at 11 097.161 cm−1 could also be detected leading to the determination of 70 levels of the corresponding (21+, 3) upper state ((330) in normal mode notation). The integrated intensities have been estimated for the bands corresponding to the (40+, 1) and (40−, 1) upper states. A total of six transformed dipole moment parameters were derived from the measured line intensities allowing to simulate very satisfactorily the observed spectrum. The transition moment relative to the (40−, 1) upper state is found about twice as large as the one relative to the (40+, 1) state.

Simulation of structural response under high‐frequency ground excitation

AbstractThe structural response to high‐frequency ground motions is complicated due to the involvement of local‐mode vibration. At present such a characteristic is not well recognized and this can cause confusion over the analytical and experimental modelling of the corresponding response and damage. The fact that most existing regulatory guides for limits on allowable construction vibrations are necessarily simplified for administrative reasons calls upon the derivation of more sophisticated approaches for special cases. This requires accumulation of pertinent experimental evidence. This paper attempts to provide some insights into the local‐mode dynamic response characteristics, with emphasis on appropriate modelling techniques and experimental measurements. A preliminary testing program is reported, in which efforts were made to reproduce high‐frequency response with a reduced scale reinforced concrete model with shaking table facilities. The results demonstrate the dependence of the response amplitudes with the excitation frequency. On a ppv‐basis, the current test results indicate that a substantial increase of the allowable ppv value from those specified by various standards may be considered for structural damage to reinforced concrete building structures. More analytical and experimental data are needed for further evaluation of the local‐mode effects and to quantify their impact on the structural damage process. Copyright © 2001 John Wiley & Sons, Ltd.

Theoretical Study of Mode Localization Phenomenon in Bottom-Hole Assemblies in Oil-Well Drilling

The mode localization phenomena in bottom-hole assemblies (BHA) used in oil-well drilling is investigated. A fully gaged stabilizer model is shown to produce weak coupling between segments of drillcollars separated by stabilizers. It is observed that in a weakly coupled BHA, small disorder in span length can cause strong mode localization. For the first time, it is demonstrated that gravity induces a stiffness disorder, which in turn causes strong mode localization in an inclined wellbore, even though no other disorder is present. The effect of localized modes for failure is presented by examining the maximum bending stresses with and without mode localization. The results show that design and operation of drillstrings should consider the possibility of mode localization for an accurate prediction of dynamic behavior.

Dynamic analysis of trusses including the effect of local modes

The dynamic analysis of trusses using the finite element method tends to overlook the effect of local member dynamic behavior on the overall response of the complete structure. This is due to the fact that the lateral inertias of the members are omitted from the global inertia terms in the structure mass matrix. In this paper a condensed dynamic stiffness matrix is formulated and used to calculate the exact dynamic properties of trusses without the need to increase the model size. In the examples the limitations of current solutions are presented together with the exact results obtained from the proposed method.

The First Si–H Stretching Overtone of H3SiD: Emergence of Local Mode Effects

The FTIR spectrum of H3SiD in the 4100–4500-cm−1region was recorded at Doppler-limited resolution, and four bands were studied. At lower wavenumbers, two strong bands, which in the local mode picture can be assigned to (200,E) (ν0= 4308.5667 cm−1) and (200,A1) (ν0= 4307.8441 cm−1), were analyzed, and at higher wavenumbers, two weaker bands, namely (110,E) at 4378.1950 cm−1and (110,A1) at 4375.9763 cm−1, were analyzed. A total number of ∼1900 lines in the strong dyad and 1000 lines in the weak one were assigned and fitted with standard deviations of the residuals ≈0.0008 cm−1. The strong system (200) is close to local mode behavior, with nox,yCoriolis term needed and only a smallzCoriolis term, and simple arithmetic relations between vibration–rotation parameters are fulfilled as expected. The local mode behavior of the weak system (110) is less pronounced, butzandx,yCoriolis effects are smaller than in the Si–H stretching fundamentals. Comparison of computed and observed spectra provided a good estimate for the ratios of transition moments of the different bands: they are, in absolute value, proportional to 3.5:1.75:1:1 for (200,E), (200,A1), (110,E), and (110,A1), respectively.

Near Infrared Spectroscopy

Some of the concepts that make a near infrared spectrum understandable are reviewed. The origin of vibrational anharmonicity which determines the occurrence and the spectral properties (frequency, intensity) is discussed. The importance of the effects of the resonances which increase with increasing excitation are mentioned. Some of the characteristics of high energy overtone/combination spectra are considered in relation to local mode effects. The location of some particular group frequencies is provided.

Local Mode Effects on the High-Resolution Overtone Spectrum of H2S around 12 500 cm−1

The overtone spectrum of H2S has been studied by intracavity laser absorption spectroscopy in the wavenumber region 12 270–12 670 cm−1. The rovibrational analysis has provided upper state rotational parameters for the three interacting vibrational states, (401), (104), and (024), observed in the region. The rotational levels of the first two states, constituting the local mode pair 41±, are strongly coupled by a strongH22type interaction. The (024) state is observed via a local perturbation. Altogether, 399 rovibrational lines have been assigned, including 172 rotational upper state sublevels which have been reproduced calculationally within the experimental accuracy of 0.015 cm−1. A local mode type behavior is evidenced by the values of the rotational parameters.

High-resolution spectroscopic study of 2? 1, 2? 3 and ? 1+? 3 stretching states: the local-mode effects of H2Se

High-resolution spectra of the coupled 2ν1, 2ν3 and ν1+ν3 states of H2Se have been studied. The vibration–rotation transitions of H2nSe (n= 82, 80, 78, 77 and 76) were assigned by using the ground-state combination differences and least-squares fitted to yield the vibration–rotation parameters. Several striking local-mode effects are observed and discussed.

Local-mode effects on the rotational structure of the first stretching overtone band system of stibine, SbH3

A high-resolution Fourier-transform infrared spectrum, resolution about 0.006 cm−1, of the first stretching overtone band system of stibine has been measured and rotationally analyzed in detail up to J′=22 for both 121SbH3 and 123SbH3 isotopic species. The rotational levels of the A1 and E vibrational states have been analyzed simultaneously by including vibration–rotation coupling terms in the Hamiltonian for the two isotopic species. The A1/E vibrational energy-level separation has been found to be 0.0727(8) cm−1 for 121SbH3 and 0.0763(8) cm−1 for 123SbH3 with the A1 state being higher in energy in both cases. Fits including 1445 transitions with the standard deviation of 0.0024 cm−1 for 121SbH3 and 1322 transitions with the standard deviation of 0.0022 cm−1 for 123SbH3 have been obtained by optimizing altogether 33 upper-state parameters in both cases. A simple local-mode model is shown to account very well for the vibrational dependence of the rotational constants and the coefficients of vibrationally off-diagonal H22 operators.

Anharmonicity and local mode effects in the vibrational spectra of Ni(CO)4and Co(CO)3NO

Previously published data on the vibrational fundamentals and overtones of the carbonyl stretching modes of Ni(CO)4 and Co(CO)3NO are reinterpreted using the recent model of Mills and Robiette, including Darling-Dennison resonances and local mode effects. The harmonic wavenumber θm and anharmonicity constant x m associated with the carbonyl and nitrosyl stretching modes are derived, and the 13C and 18O isotopic shifts are discussed in relation to the harmonic and anharmonic force field.

Resistivity, thermopower and susceptibility of Y9CO7and local-mode effects

The compound Y9Co7 is an unusual system that exhibits strong spin fluctuations and superconductivity on cooling before losing its magnetism and becoming a true superconductor at lower temperatures. The author reports new measurements of the temperature dependence of the resistivity thermopower and susceptibility in Y9Co7. The data are discussed in terms of a simple picture involving 'hopping' of the Co atoms from one site to another along the c axis. The strong hopping creates large fluctuations in the spin density, which give rise to local phonon modes and determine the interplay of magnetism and superconductivity in Y9Co7.

Local modes and x, k relations in ethene and propadiene

The results recently obtained by Mills and Robiette on local-mode effects in H 2O, NH 3 and CH 4 type molecules are extended to ethene (C 2H 4) and propadiene (C 3H 4) type molecules. General relations among the anharmonic x rs constants and the Darling-Dennison K rrss constants for the stretching vibrations are derived, called “ x, K relations”, which allow local-mode effects to be generated by adding the appropriate anharmonic and Darling-Dennison constants to the familiar normal-mode model of molecular vibrations. The general utility of x, K relations is discussed, and the results are reviewed for the molecular types for which they have so far been derived.

The effects of local modes and Morse oscillator potentials on the nonradiative ‘‘communicating states’’ rate calculations in benzene

By means of ‘‘communicating states’’ model calculations it is shown that the sharp increase of nonradiative transitions with excess vibrational energy in the first excited electronic state S1(B2u) of benzene has to be interpreted as an internal conversion process. Intersystem crossing S1uT1 cannot explain the disappearance of fluorescence quantum yields. This remains true even if a Morse potential for the ν2(a1g) vibration or for all C–H stretching modes in a local mode description is assumed. The sharp increase of the rate in the ‘‘channel-three’’ excess energy region is still governed by the ν4(b2g) out-of-plane mode. In addition, the excess energy dependence of the nonradiative rates is found to be extremely nonexponential.