Phonon Structure

Phonon Structure and Raman Effect of Single-Walled Carbon Nanotubes... 

Yamaguchi K (1993) Phonon structure of single-crystal gallium thiophosphide (Ga2/3PS3) from inelastic electron tunneling spectroscopy. Phys Status Solidi B 179 K11-K15... 

We have seen in the previous section that Raman spectra are complementary to infrared spectra. Both spectroscopies provide quite useful information on the phonon structure of solids. However, infrared spectra correspond to a range from about 100 cm to about 5000 cm that is, far away from the optical range. Thus, infrared absorption spectra are generally measured by so-called Fourier Transform InfraRed (FTIR) spectrometers. These spectrometers work in a quite different way to the absorption spectrophotometers discussed in Section 1.3. 

Figure 6. Superconducting gap minima (left panel) and phonon structure (right panel) in the spectra of thin film MgE>2-Ag PCs with different resistances at T = 4.2K, B = 0 with Ro=45, 43, and 111 fi for curves 1,2 and 3, respectively. The modulation voltage Vl when measuring the Vh signal is 3.31, 2.78, and 2.5 mV, for curves 1,2 and 3, respectively. The numbers of curves in (b) are the same as in (a). The curves in (a) are offset for clarity. After Yanson et al. [17],...

The phonon structure in the PC spectra of MgB2 can be revealed by i) the inelastic backscattering current, like for ordinary PCS, and ii) by the energy dependence of the excess current. They can be discriminated after destroying the superconductivity by magnetic field and/or temperature, and by varying the electron mean free path. 

PHONON STRUCTURE IN POINT-CONTACT SPECTRA OF MGB2... 

Abstract In strong-coupling superconductors with a short electron mean free path the self-energy effects in the superconducting order parameter play a major role in the phonon manifestation of the point-contact spectra at above-gap energies. We compare the expressions for the nonlinear conductivity of tunnel, ballistic, and diffusive point-contacts and show that these expression are similar and correspond to the measurements of the phonon structure in the point-contact spectra for the 7r-band of MgB2. 

In diffusive point contacts (d dt> /, ) the role of the scale, where the backscattering inelastic processes become essential, turns from d in l, and in the case when li/l property will be essential when we consider the phonon structure in point-contact spectra of dirty MgB2 contacts in the c-direction. 

Phonon structure in point-contact spectra of MgB2... 

In this section we review what has recently become known about the phonon structure in the point-contact spectra [12]. In order to do this, we should refer to the works where the excess current in point contact is considered in terms of the strong-coupling theory. That was first done in the paper of Omel yanchuk, Beloborod ko and Kulik for ballistic S — c — N point contact [10]. The first derivative of /(IP)-characteristic at T = 0 has the following form in this case ... 

Figure 3. Comparison of experimental (upper panel) and calculated (lower panel) phonon structures in point-contact spectra of MgB2. The contact axis is oriented along the c-axis. The normal state resistances are given for each curve. In the experimental panel the upper curve corresponds to the ordinate scale, and the other two are shifted down for clarity. T = 4.2 K. In the theoretical (lower) panel three transport regimes are illustrated on the same scale as in the experimental graph. Here, the lower curve corresponds to the ordinate scale, the other two are shifted up for clarity. The 7r-band EPI function (dashed curve) [15] is shifted to higher voltages by A,r = 2.4 meV. The modulation voltage is taken equal to 3 mV.

The question may arise whether the self-energy effects are important in the normal state. These are known to be smaller than the inelastic backscattering nonlinearities in the ballistic regime [18]. If we decrease the contact size d or the elastic mean free path li in order to make the inelastic contribution negligible, the latter parameters become comparable to the Fermi wave length of charge carriers and the strong nonlinearities connected with localization occur, which masks the desired phonon structure [19]. 

Phonon Structure in Point Contact Spectra of MgB2 249... 

In this section, per-deuterated n-octane (n-octane-dig) is used as the matrix material, and the emission properties of Pd(2-thpy)2 are compared with those obtained with a per-protonated n-octane matrix (n-octane-hig). This latter matrix was used for the investigations discussed in the preceding sections. Three different issues are addressed, namely the occurrence of different sites for Pd(2-thpy)2, changes of low-energy vibrational/phonon structures, and changes of the emission decay behavior. 

The detailed analysis of the first- and the second-order Raman spectra of SWNTs has been done. It is emphasized particularly that the second-order Raman features are rich in information about electron and phonon structure of SWNTs, which cannot be obtained from the first-order Raman spectra. 

The vibrational modes of an individual SWCNT can be derived from the phonon structure of two-dimensional graphite (graphene) by applying a zone-folding procedure that considers the one-dimensionality of CNTs and a chirality-dependent confinement [33], Due to CNT s complex stmcture, their Raman spectra show many size- and chirality-dependent features. In this section, however, only the most prominent first and second order Raman features will be discussed. 

Fig. 9. Structures of vibrational spectra in impure crystals, (a) represents impurities whose electronic states (e, e, ...) are uncoupled from the vibrations of the crystal. The phonon-spectra are superimposed on the eletron-ic levels (shaded area). Resonance (cor) or localised (coi) levels may appear, (b) If the impurity states are coupled to local vibrations, vibronic levels (v, v, .. .) appear whose spacings are generally much closer than for the electronic levels in (a). The superimposed phonon structures will fill in the energy range...

Below the Debye temperature, only the acoustic modes contribute to heat capacity. It turns out that within a plane there is a quadratic correlation to the temperature, whereas linear behavior is observed for a perpendicular orientation. These assumptions hold for graphite, which indeed exhibits two acoustic modes within its layers and one at right angles to them. In carbon nanotubes, on the other hand, there are four acoustic modes, and they consequently differ from graphite in their thermal properties. StiU at room temperature enough phonon levels are occupied for the specific heat capacity to resemble that of graphite. Only at very low temperatures the quantized phonon structure makes itself felt and a linear correlation of the specific heat capacity to the temperature is observed. This is true up to about 8 K, but above this value, the heat capacity exhibits a faster-than-Unear increase as the first quantized subbands make their contribution in addition to the acoustic modes. 

While these observations would be hard to explain in terms of multiphonon relaxation, they are readily understood consequences of the vibration — rotation transfer model. Isotopic substitution will change not only the vibrational frequency of the guest but also the spacing of the rotational levels, and will modify the localized phonon structure. Whereas the vibrational spacing is proportional to the square root of reduced mass, the rotational constant changes even faster, linearly in fi. As a consequence, the closest rotational level to i = 1 is 7= 13 in NH and 7= 16 in ND. Thus, in spite of a smaller vibrational spacing, the deuteride relaxation is a higher order and hence less efficient process. 

Band structure details of insulators can be determined from their UV/VIS spectra. Defects in the crystal produce electronic levels within the gap between the conduction and the valence bands. Spectroscopic measurements at low temperature allow the investigation of the phonon structure of a crystal. Absorptions due to lattice or point defects can be used to describe the optical and electronic properties of the insulator. For example, Cr in AI2O3 crystals leads to an intense color change of the crystal. Many so-caUed color centers are based on lattice defects caused by intercalation of atoms in the crystal lattice. 

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