Lattice mode absorption

Spectral Region Probed Limited to 4000-1200 cm" from Absorption by Lattice Modes of Solid 4000-400 cm"" Only Spectral Limitations are Imposed by Spectrometer... 

The infrared spectra for various aluminum oxides and hydroxides are shown in Figure 3. Figure 3a is a-alumina (Harshaw A13980), ground to a fine powder with a surface area of 4 m /g. The absorption between 550 and 900 cm is due to two overlapping lattice modes, and the low frequency band at 400 cm is due to another set of lattice vibrations. These results are similar to those obtained by reflection measurements, except that the powder does not show as... 

On the other hand however, the cluster-anions P7 and Pii are thermally remarkably stable. In the condensed state (in the crystal as well as in melts), the characteristic vibrations can be observed both in i.r. spectra and in Raman spectra upto temperatures of 900 K (25, 26,27). As an example, the Raman spectra of Ha3P7 in Figure 7 clearly show that the typical cluster-vibrations of the P7 -anion are maintained up to the region of the plastic phase, although the absorption bands become increasingly broader and less distinct with temperature. The lattice vibrations at 50-100 cm " behave completely differently. As expected they disappear at the transition to the plastic phase. Completely unexpected however, they remain sharply resolved up to the critical temperature Tc. This effect can be connected with the presence of two undamped lattice modes (25). 

Remarkably, the combined electronic-lattice mode vibronic level f8 x l obviously also needs a promotion of the complex by odd molecular vibrations in order to be detected in the d-d absorption spectrum. 

IThe name optic mode comes from the behavior of ionic crystals such as Na+Cl . When Na and Cl in a given cell move out of phase with each other, there is an oscillating electric dipole. Optical absorption will occur for light having frequency equal to that of the optic lattice mode. 

Now we can consider the electromagnetic field absorption by the lattice mode (the first mode) and the intracellular one (the second mode) when the modes are perturbed by described fluctuations. We suppose that the operator in the Hamiltonian (D19) is a small perturbation that is, the fluctuation energy is smaller than the energy of regular vibrations. 

Having calculated the absorption by the lattice mode, we should substitute the operator p0 for the following ... 

Fig. 4. IR spectra of NO Os in the range 100-2500 cm measured at room temperature for five pressures (indicated in GPa on right hand ordinate). The absorbance has been normalized with respect to the beam current of the synchrotron light source. The sample thickness was about 23 pm. The region 1900-2200 cm is omitted because of interfering absorptions from the Type Ila diamonds used as anvils. Asterisks ( ) indicate lattice modes or combinations, (from Ref. [80])...

IR absorption spectra (see Fig. 7) reveal a multiplet of modes in the vibron spectral range and also a newly discovered mode of lattice vibrations (see below). The pressure dependencies of IR vibron frequencies match well the extrapolation of the lower pressure data reported in Refs. [44, 45]. The pressure dependence of the lattice mode frequency is very close to that of the high-frequeney Raman lattice mode (Fig. 8). As in the case of Raman vibrons, the IR vibrons show branching with pressure, so that up to 5 vibrons can be observed at high pressure, all of which originate from the V2 multiplet. The Raman and IR vibrons probe different points of the large Brillouin zone and become accessible because of its folding. The lowest-frequency Raman vibron corresponds to the lowest frequency of the Brillouin zone and represents the case where all molecules on the faces of the unit cell (e.g. 

We probed the forward and reverse transformations of the molecular to the t) phase in different regions of P-T space (Fig. 8) We used IR transmission spectra as diagnostics of the degree of transformation to the nonmolecular phase. The absence of IR bands corresponding to vibrons and lattice modes of the molecular phase was used as a criterion. Since both the molecular and nonmolecular phases are transparent in the mid-IR, the amount of the phase present is simply proportional to the amplitude of the corresponding IR peaks. This is unlike the situation with Raman spectra, which are attenuated by absorption of the t] phase. We... 

First let us compare the librational mode found for ice by Marchi [8] using lattice mode spectroscopy (see Fig. 18) with our smooth water-like absorption dependence illustrated by the right-hand part of Fig. 20a. This spectrum evidently agree much better with the experimental data than the noise-like pattern calculated by the MD method and depicted in the lower part of Fig. 18. It is important that in the work by Marchi [8] the dipole-induced-dipole terms provide the dominant contribution to the total intensities. However, in view of a recently MD modeling of water spectra by Sharma et al. [29], the polarization effects depend on the environment in a strong intermolecular way, which possibly was not taken into account in the cited treatment by Marchi. 

Solid Lattice modes Impurity modes Absorption edges (semiconductors)... 

NgO. The absorption intensities of two i.r.-active lattice modes (at 67 and 117 cm ) of crystalline NgO have been measured. Both the frequencies and intensities are very close to those of solid COg, any differences being explicable in terms of differences in the quadrupole moments. Hisatsune has made a detailed study of the i.r. spectrum of NgO in alkali-metal halide matrices (principally KCl, KBr, and KI) from 90 to 200 K. NgO was conveniently... 

High hydrostatic pressure was applied to the Ti sapphire Al203 Ti [77, 80] and to YA103 Ti " [80]. In both materials, blue shifts of the emission and absorption bands were observed, which is in accordance with Eq. (4.3.7). To analyze the pressure-induced shifts of all bands, the interaction with totally symmetric lattice mode ai and two-dimensional lattice mode e(j2 , Qv) have been considered. In the paper [80], the contributions from the linear and quadratic Jahn-Teller effect have been considered. 

Solid COj. Table V summarizes the available data for solid CO. The far infrared absorption spectrum in the lattice mode region was reported first by Anderson and Walmsley (1964) at 77 K and later by Ron and Schnepp (1967) at 20°K. Recently, helium temperature measurements were carried out by Kuan (1969) and 35°K measurements by Brown and King (1970). Of these workers, only Kuan prepared the solid sample from the vapor under equilibrium conditions. The results show that the frequencies of the two infrared active modes are not very sensitive to temperature or to sample preparation. On the other hand, the line widths observed by Kuan are about half those reported by Brown and King. Kuan s line widths are given in Table V. Moreover, the measured intensity ratios differ markedly (both values are listed in the table). 

Few papers have appeared which are concerned with the intensities of infrared absorption by lattice modes in molecular solids. For polar molecules, it is clear that librational motions will cause the absorption of light by a mechanism analogous to that which occurs for rotational spectra in the gas phase. Calculations have been made of such infrared absorption intensities by Schnepp (1967) and by Friedrich (1970). Friedrich used a theory which takes into account the polarizability of the medium in a specific way. For this case, the intensity is proportional to the square of the molecular dipole moment. Section IVB.2 is concerned with this topic. 

In this section we consider the dipole transition intensity induced by permanent multimoments. Schnepp (1967) has ealculated the quadrupole-induced infrared absorption intensity of translational lattice modes in... 

The nature of intermolecular interactions can also be studied by analyzing the frequency and intensity of the external vibrations, or lattice modes, of the imit cell (49,54,55). The coupling of chains can be characterized by the whole chain segment movements which generally occur in the very low frequency region, ie, typically <100 cm. These modes are in addition to the internal modes of each chain. The translatory modes can be seen in far-infrared absorption spectra. Fourier transform instruments have improved the signal-to-noise ratio, making... 

The above approach has only been partially applied and this is reflected in the uncertainty which exists about the attribution broad band at 55 cm in the FIR spectrum PP, assigned tentatively in [%] to a lattice mode. It would be more reasonable, however, to ign this ateorption to disorcter-induced absorption or quasi-lattice mode [23]. The quasi-lattice absorption is inherent to the FIR spectra of all tte disordered condensed media We shall discuss it later. 

It is now well-established that the most general contribution in the FIR spectra of polymers in the range below tS0cm originates from the broadband absorption which is sometimes the background of the sharp lattice modes. Chantry and coworkers were the first to observe this broad and weak underlying absorption in the FIR spectra of PE, PP and TPX (a polyolefine based upon poly(4-methyl pentene-1) [2, 50]. It was supposed to be analogous to liquid-lattice type absorption observed in the far infrared spectra of polar and nonpolar liquids [51 -56]. 

An example (Fig. 7, curve 2) is the FIR spectrum of chlorobenz ie at 290 K [56]. Here, the broad absorption band at v ... = 45 cm was assigned to the quasi-lattice motion of chloroboizene molecules arising from the fact that the FIR spectrum of crystallized diloioben %ne at 130 K exhibits several sharp absorption bands corresponding to lattice modes observed in the same frequency range (Fig. 7, curve 3). 

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