Phonon bands

The application of infrared photoacoustic spectroscopy to characterize silica and alumina samples is reported. High quality infrared photoacoustic spectra illuminate structural changes between different forms of silica and alumina, as well as permit adsorbate structure to be probed. Adsorption studies on aerosil suggest adsorbed species shield the electric fields due to particle-particle interactions and induce changes in the vibrational spectra of the adsorbates as well as in the bulk phonon band. It is shown that different forms of aluminum oxides and hydroxides could be distinguished by the infrared spectra. 

Further dehydration of boehmite at 600 0 produces y-alumina, whose spectrum is shown in Figure 3b. There is a loss in surface area in going from boehmite to y-alumina. The sample shown here has a surface area of 234 m /g (this sample was obtained from Harshaw A23945 the calcined Kaiser substrate gave an identical infrared spectrum). The y-alumina sample shows two major differences from o-alumina. First, there is a more intense broad absorption band at 3400 cm" due to adsorbed water on the y-alumina. Second, the y-alumina does not show splitting of the phonon bands between 400 and 500 cm" as was observed for o-alumina. The y-alumina is a more amorphous structure and has much smaller crystallites so the phonon band is broader. The y-alumina also shows three features at 1648, 1516 and 1392 cm" due to adsorbed water and carbonate. 

In the time-domain detection of the vibrational coherence, the high-wavenumber limit of the spectral range is determined by the time width of the pump and probe pulses. Actually, the highest-wavenumber band identified in the time-domain fourth-order coherent Raman spectrum is the phonon band of Ti02 at 826 cm. Direct observation of a frequency-domain spectrum is free from the high-wavenum-ber limit. On the other hand, the narrow-bandwidth, picosecond light pulse will be less intense than the femtosecond pulse that is used in the time-domain method and may cause a problem in detecting weak fourth-order responses. 

In fact, in order to optimize the rectifying effect, one should avoid the overlapping of the phonon bands in the low temperature limit (Eq.6) and that in the high temperature limit (Eq.7) for each segment of the system. According to the above estimates, one should have V > 4k, which is satisfied for the case of Fig.8. 

Apart from the one-way heat flow , the negative differential thermal resistance phenomenon observed in a certain temperature intervals in the thermal diode is of particular interest. As illustrated in Fig.7 for A < —0.2, a smaller temperature difference (A), can induce a larger heat current since, due to nonlinearity, it can result in a better match in phonon bands. 

A substantial linewidth broadening of the adlayer modes in the whole region near T where they overlap the bulk phonon bands of the substrate the excited adlayer modes may decay by emitting phonons into the substrate they become leaky modes. These anomalies were expected to extend up to trilayers even if more pronounced for bi- and in particular for monolayers. 

We used short broadband pump pulses (spectral width 200 cm 1, pulse duration 130 fs FWHM) to excite impulsively the section of the NH absorption spectrum which includes the ffec-exciton peak and the first three satellite peaks [4], The transient absorbance change signal shows pronounced oscillations that persist up to about 15ps and contain two distinct frequency components whose temperature dependence and frequencies match perfectly with two phonon bands in the non-resonant electronic Raman spectrum of ACN [3] (Fig. 2a, b). Therefore the oscillations are assigned to the excitation of phonon wavepackets in the ground state. The corresponding excitation process is only possible if the phonon modes are coupled to the NH mode. Self trapping theory says that these are the phonon modes, which induce the self localization. 

As an example, we consider the multiphonon relaxation of a local mode caused by an anharmonic interaction with a narrow phonon band. We suppose that the mode is localized on an atom and take into account two diagonal elements of the Green function which stand for the contribution of two nearest atoms of the lattice to the interaction the non-diagonal elements are usually much smaller [16] and approximate the density of states of the phonon band by the parabolic distribution... 

To elucidate the effect of temperature, we performed calculations of the rate of multiphonon non-radiative transitions. We considered a case when l and l1 belong to different rows of the same representation. The phonons, contributing to a nondiagonal vibronic interaction are considered in an Einstein-like model with the parabolic distribution function (14) (note that the results are not sensitive to the actual shape of the phonon bands) interaction is arbitrary. In this model the Green function is described by simple expression (16). In the case of a strong linear diagonal vibronic interaction one can expand the gr(f)-function into a series and take into account the terms up to the quadratic terms with respect to t gT(—t) iSjt — Ojt2/2. Here = Oq/wq, cD0 is the mean frequency of totally symmetric... 

Fig. 7 For the two-state XT-CT model, the projection of the three effective modes (Xi, X2, X3) (shown in red, blue, and green, respectively) onto the primitive phonon modes xi is illustrated, for a model comprising 14 primitive high-frequency modes and 14 primitive low-frequency modes (i.e., 28 modes overall). Even though the projection involves contributions from both phonon bands, the low-frequency contributions are small, and all three effective modes are of high-frequency type. (Note the change in scale between the l.h.s. and the r.h.s. of the figure.) Furthermore, since the primitive modes are localized on the individual molecular units, the effective modes can be shown to be partially localized as well. Thus, two of the effective modes (shown in blue and green) are dominated by local contributions coming from either the F8BT chain or the TFB chain. The third mode (shown in red) exhibits contributions from both chains. (Reproduced from Ref. [93].)...

The emission spectra for LiYF4 Pr3+ are shown in fig. 7 as an illustration, where the top and bottom panels present the calculated and experimental spectra, respectively. As can be seen from this figure, the calculations correctly reproduce the relative intensities of the emission bands. The calculated spectra are produced by superimposing a Gaussian band that is offset from the zero-phonon line by 600 cm-1 on the calculated zero-phonon lines. The FWHM is set to 1000 cm-1 for the Gaussian (phonon) bands, and 20 cm-1 for the zero-phonon lines. The zero-phonon lines for the 4f5d - 3H4 emission are not observed, most likely due to resonant reabsorption. 

Spectroscopic measurement is a particularly favored analytical technique because spectra can be compared in a direct way to interpret the chemical and mineralogical composition of dust in various astronomical environments. Depending upon the different spectral regions under analysis and depending on the optical properties of the material, one must use different techniques. In regions of strong absorption, such as in the phonon band range (mid-infrared) or the ultraviolet, direct absorption measurements require very low column densities of material, which can only be achieved with thin films or diluted powder samples. 

Optical Phonons. For a narrow optical phonon band we can set 8q 8i I scattering rates are then... 

The spectra obtained for ice Ih, LDA and HDA, using the TFXA spectrometer at 10K [53] is shown in Fig. 11. Ice Ih is the most common and readily obtainable phase of ice which has now been well studied [14,15,48,49]. Its spectrum has a very simple structure, the translational modes below 40 meV are well separated from the librational modes (or hindered rotations) in the energy region between 65-125 meV (very few system shows similar behaviour and this is due to the large mass difference between O and H). The observed acoustic phonon peak is at 7 meV. The two sharp peaks at 28 and 37 meV are the optic-phonon bands and have an unusual triangular-shape. In contrast, only a single feature appears in the IR spectrum, at 27 meV, and the Raman spectrum has an additional shoulder at 36 meV (see Fig. 10). 

Figure 11.49. FT-IR spectrum of a diamond film in the C-H vibrational region. The band around 1700-2700 cm is the two-phonon band [352].

Parameters (18) include vibronic coupling constant, V, and phonon band-structure factors, (/, y K j, A). For a particular crystal, finding these factors is a laborious problem of crystal lattice dynamics. Instead, in the OOA, 7y are used as free parameters of the theory. Still consistent with the fundamental theory of the JT effect, in this form the OOA is not directly derived from the theory. In other words, in the theory of cooperative JT effect, the OOA is a phenomenological approach. 

Stress, strain and impurities in Si samples can be detected based on frequency, intensity, shape and width changes of the Si phonon band. Due to the ongoing miniaturization of semiconductor structures, there is a need for imaging of these features with nanometer-scale resoluhon. 

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