Raman line broadening

FFM de Mul, C Otto, J Greve, J Arends, JJ ten Bosch, Calculation of the Raman line broadening on carbonation in synthetic hydroxyapatite. J Raman Spectrosc 19 13-21, 1998. 

The kinetics of ion-pair formation in concentrated aqueous NaN03 and of the protolysis of 2.0-14.7 mol liter nitric acid have been studied by Raman line broadening. Rate constants for the individual processes (15) and an equilibrium constant for the dissociation have been estimated, the latter having a value of 8.9 liter mol at 298 K ... 

Of great interest to physical chemists and chemical physicists are the broadening mechanisms of Raman lines in the condensed phase. Characterization of tliese mechanisms provides infomiation about the microscopic dynamical behaviour of material. The line broadening is due to the interaction between the Raman active chromophore and its environment. 

Stress in crystalline solids produces small shifts, typically a few wavenumbers, in the Raman lines that sometimes are accompanied by a small amount of line broadening. Measurement of a series of Raman spectra in high-pressure equipment under static or uniaxial pressure allows the line shifts to be calibrated in terms of stress level. This information can be used to characterize built-in stress in thin films, along grain boundaries, and in thermally stressed materials. Microfocus spectra can be obtained from crack tips in ceramic material and by a careful spatial mapping along and across the crack estimates can be obtained of the stress fields around the crack. ... 

Loader 38) studied the Raman spectra of styrene adsorbed on different silicas—chromatographic grade silica gel, Cab-O-Sil, and Aerosil 380. The author utilized the fact that chemisorption will bring about marked changes in the spectrum whereas physical adsorption will cause only a broadening of the Raman lines accompanied in some cases by a frequency... 

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

The behavior of the Raman spectrum under stress of the stretching vibration of the B—H complex has been reported recently by Stutzmann and Herrero (1988a,b) and by Herrero and Stutzmann (1988a,b). Spectra measured at 100 K are shown in Fig. 18 for several values of [100] stress. The dependence of the mode frequency on [100] and [112] stress is shown in Fig. 19. There were stress induced splittings observed for [100], [112], and [110] stress directions. For the [111] stress direction the line broadened for low stresses but did not split. Further, the stress-split component that shifts upward in frequency as the stress is increased decreases in intensity. 

The autput of a mode-locked ruby laser 729) producing a train of pulses of 5 psec duration with a maximum peak power of 5 GW was focused into a cell pressurized with the sample gas. Pulse-energy conversion efficiencies into the Raman lines of up to 70 % have been obtained. The induced rotational lines are broadened this could be due to a strong optical Stark effect 730)... 

FIGURE 5.5 (a) Components of the CARS signal. The last three terms in Equation 5.1 are plotted versus detuning A = C0p-co -O. O is the center frequency of a homogeneously broadened Raman line with linewidth F. The curves are calculated with an assumption that2 R = 1.2 = 0)- (b) Schematic of the FM CARS process. Solid curve, sum of the contribu-... 

Feshbach or compound resonances. These latter systems are bound rotovibra-tional supramolecular states that are coupled to the dissociation continuum in some way so that they have a finite lifetime these states will dissociate on their own, even in the absence of third-body collisions, unless they undergo a radiative transition first into some other pair state. The free-to-free state transitions are associated with broad profiles, which may often be approximated quite closely by certain model line profiles, Section 5.2, p. 270 If bound states are involved, the resulting spectra show more or less striking structures pressure broadened rotovibrational bands of bound-to-bound transitions, e.g., the sharp lines shown in Fig. 3.41 on p. 120, and more or less diffuse structures arising from bound-to-free and free-to-bound transitions which are also noticeable in that figure and in Figs. 6.5 and 6.19. At low spectroscopic resolution or at high pressures, these structures flatten, often to the point of disappearance. Spectral contributions of bound dimer states show absorption dips at the various monomer Raman lines, as in Fig. 6.5. 

We shall now briefly review the Kubo-Oxtoby theory of vibrational line-shape. The starting point for most theories of vibrational dephasing is the stochastic theory of lineshape first developed by Kubo [131]. This theory gives a simple expression for the broadened isotropic Raman line shape (/(< )) in terms of the Fourier transform of the normal coordinate time correlation function by... 

Because of the low symmetry at each point of trajectory after averaging the phonon frequencies of symmetry are split (Table 4). However, the value of gap is rather small to see distinct lines. That is why such splitting could give rise to the broadening of the Raman line, which was observed in experimental work [1,2]. 

An example is illustrated in Fig. 2. In case 1, there are two mechanisms operating one in the fast modulation limit, and one in the slow modulation limit. This is the classic case of combined homogeneous and inhomogeneous line broadening. In case 2, there is a single mechanism, but it is in the intermediate modulation region. The Raman hnewidths are identical... 

Figure 19 The VE prediction of the diffusive component of the vibrational coherence decay CpiD as a function of the solvent viscosity (ij = 1, 2, 4, 8, 16, 32 and oo cP) for typical parameters. At low viscosity, the decay is exponential, its rate is inversely proportional to the viscosity, and the corresponding Raman line is homogeneously broadened. At high viscosity, the decay becomes Gaussian, its decay time reaches a limiting value, and the Raman line is inhomogeneously broadened. (From Ref. 8.)...

Palese S, Mukamel S, Miller RJD, Lotshaw WT. Interrogation of vibrational structure and line broadening of liquid water by Raman-induced Kerr effect measurements within the multi-mode Brownian oscillator model. I Phys Chem 1996 100 10380-10388. 

Very few experiments have been performed on vibrational dynamics in supercritical fluids (47). A few spectral line experiments, both Raman and infrared, have been conducted (48-58). While some studies show nothing unique occurring near the critical point (48,51,53), other work finds anomalous behavior, such as significant line broadening in the vicinity of the critical point (52,54-60). Troe and coworkers examined the excited electronic state vibrational relaxation of azulene in supercritical ethane and propane (61-64). Relaxation rates of azulene in propane along a near-critical isotherm show the three-region dependence on density, as does the shift in the electronic absorption frequency. Their relaxation experiments in supercritical carbon dioxide, xenon, and ethane were done farther from the critical point, and the three-region behavior was not observed. The measured density dependence of vibrational relaxation in these fluids was... 

Powder X-ray diffraction (XRD) is performed on a Siemens D5005 diffractometer with Cu Ka radiation. The particle size is calculated from the X-Ray line broadening, using the Debye-Scherrer equation. DRS is measured by Perkin-Elmer Lambda 20 UV-visible spectophotometer at room temperature in the wavelength region between 200 and 800 nm. Raman spectra are recorded on a Broker RFS 100 with 2 cm resolution. 

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