Raman Scatterings

A Raman shift of -2310 cm was supposed for gaseous PH2 see Symmetric Stretching Vibration , p. 73. 

Raman scattering has been widely used to identify the molecular structure of glasses. With careful choice of sub-bandgap light as 

Our review of the application of Raman spectra will concentrate on three aspects [1] the VIR, [2] the implication for structural models, and [3] the correlation between Raman spectra and the IR 

However, some details need to be explained in Fig. 4.5. First this weak vibrational continuum is superimposed on the high-frequency tail of the Boson peak, a band generally observed at relatively low frequencies between 10 cm and 100 cm in the Raman spectra of glasses. Secondly, the peaklike feature at around 108 cm is an artifact associated with the cutoff of filters used in the experiments therefore, this is not a real Raman peak. However, as evident in Fig. 4.5, the high-frequency tail of the Boson peak has a different slope for the different spectra and a clear feature can be found around 130 crar, indicating that this continuum indeed provides some structural information on the glasses. 

Reprinted with permission from Lucas R, King E. A., Gulbiten 0., Yarger J. L., Soignard E., and Bureau B., Bimodal phase percolation model for the structure of Ge-Se glasses and the existence of the intermediate phase, Phys. Rev. B, 80,214114-8 (2009). Copyright (2009) by the American Physical Society. 

Raman vibrational frequencies as a function of Ge concentration in GeSe glasses. Reprinted with permission from FengX.,Bresser W. J., and Boolchand R, Direct evidence for stiffness threshold in chalcogenide glasses, Phys. Rev. Lett, 78,4422-4425 [1997). Copyright (1997) by the American Physical Society. 

The Raman scattering comes about through the polarization of the electron cloud of the molecule by the oscillating electric vector of the incident quantum. The important molecular property connected with Raman spectra is therefore the polarizability, and a vibration will give rise to a Raman line if it leads to a change in the polarizability of the molecule. We shall see in Section 8.5 that symmetry considerations allow us to decide which vibrational modes lead to Raman scattering. 

A Raman spectrometer is in principle very simple. An intense source of monochromatic visible radiation, i.e. a laser beam, is directed at the sample. Scattered radiation is observed at right angles to the incident beam. Frequencies close to that of the laser, which are due to inelastic Rayleigh scattering, are filtered out by use of a monochromator. If polarized laser excitation is used, with a polarization analyzer as part of the detector, then information about the symmetry of vibrations can also be obtained. This is described further in Section 8.6.1. Raman interferometers are also used, with the excitation being provided by a near-lR laser. 

The symmetry properties of resonance Raman lines can be predicted on the basis of Eq. 1.199. For totally symmetric vibrations, and Yaj = 0. Then, Eq. 20.15 

According to the quanmm mechanical theory of light scattering, the intensity per unit solid angle of scattered light arising from a transition between states m and n is given by 

Here Vq is the frequency of the incident light v, v, and are the frequencies corresponding to the energy differences between subscripted states terms of the type M )fnr are the Cartesian components of transition moments such as J Jx and 

E is the electric vector of the incident light. It should be noted here that the states denoted by m, n, and r represent vibronic states / (, g)(l)f (g), / (, g)(l) (g) and / (, g) (l)y (g), respectively, where / and / are electronic ground- and excited-state wavefunctions, respectively, and ( )f, and ( )y vibrational functions. The symbols  

Since the electric dipole operator acts only on the electronic wavefunctions, the (o pa)m term in Eq. 1.201 can be written in the form 

Surface-enhanced resonance Raman scattering (SERRS) has also been achieved using silver colloid aggregates produced in situ in the chip. This method was used to detect an azo dye, 5-(2,-methyl-3,5,-dinitrophenylazo)quinolin-8-ol, which is a derivative of the explosive, TNT. With this method, it was possible to detect 10 iL of 10 9 M dye (or 10 fmol). This represented a 20-fold increase in sensitivity over that achieved using a macro flow cell [739]. 

The Raman effect is due to the same vibrations that give rise to the infrared spectrum. Raman scattering describes the inelastic scattering of incident light by certain vibrational transitions (described as Raman active). Note that this is not a fluorescence effect. The molecule is not electronically excited and the incident photon interacts with the vibration of the molecule on a time-scale of the order of 10 seconds. The Raman effect is also weak—except for resonant transitions, no more than one photon in a million is inelastically scattered in this way. Hence the need for powerful sources of monochromatic radiation (lasers) and sensitive detectors (photo-multiplier tubes or charge-coupled devices). 

Raman spectra are a useful complement to infrared spectra. Some vibrations give rise to identical bands in infrared and Raman spectra, while others are weak or non-existent in one while being strong in the other. Polarisability of bonds determines Raman activity, not the strength of the electric dipole, as is the case for infrared. The interested reader is referred to [2] for full descriptions and applications of the technique. 

Most scattering events between photons and atoms or molecules are elastic (Rayleigh scattering). However, inelastic or Raman scattering can result when photons either 

In solids, Raman scattering results from inelastic interactions between photons and phonons in the optical mode. (Similar inelastic scattering from phonons in the acoustic mode is called Brillouin scattering.) Solids have characteristic phonon modes, which can be 

The RS of light is accompanied by the creation or annihilation of an elementary excitation in the sample. It may be an optical phonon in a crystal or a vibration of an adsorbed molecule. As a result, the frequency of the scattered light, co, is different from the frequency of the incident light, co. As follows from energy conservation in a scattering process of incident photons. 

RS originates from the coupling between electronic and vibrational motions in the material. This effect is described classically in terms of the linear susceptibility tensor, which relates the sample polarization, P, and the electric field of the light wave, E, as 

The susceptibility is a function of the normal coordinates, Qr, associated with the vibrational motion, and can be expanded in a Taylor series in them, i.e.. 

In quantum theory, the intensity of Raman scattering from the initial ground state g) to the final excited state e) is directly proportional to the incident light intensity as well as to the squared modulus of the scattering tensor component 

RS has a small cross-section typically, one Stokes photon is produced per 10 incident photons. This fact limits applications of Raman spectroscopy for surface and interface analysis. However, the RS efficiency can be considerably increased if the incident light frequency, w, is close to a transition frequency cokg- Then the corresponding term in the tensor (5.9) is enhanced, leading to resonance Raman scattering. In order to obtain a detectable Raman signal one has to apply a powerful light source. Therefore, in contrast to other linear optical techniques, the use of lasers is essential in Raman spectroscopy. 

If the vibrational frequency between the atomic nuclei constituting a molecule is v, the electronic state of the molecule will change periodically with a frequency v. Consequently, the polarization P of a molecule induced by an electric field is described by Eq. (4.16), obtained from Eqs. (4.14) and (4.15), in normal coordinates, assuming a periodical change of the molecular polarizability at the frequency v.  

The polarization P of a molecule has three frequency components v and v v and the vibrational polarization emits light with its frequency. Therefore in general light scattering experiments, scattered light with these frequencies can be observed. In contrast a Raman spectrum can be measured only in the case where there are changes in molecular polarizability in the various vibrational modes, since Eq. (4.16) is expected to hold at dA/dQ 0 (Raman active). 

Raman spectroscopy has played an important part in the study of molecular structure, often bringing information complementary to infrared spectroscopy. Over the recent years, it has also been the basis for the development of the field of nonlinear optics. 

For the molecular vibrations, the following wavenumbers (in cm ) and depolarization ratios q were observed with laser excitation  

Lattice vibrations were seen at 47,54,58, 73,77 (shoulder), 82 (shoulder), and 85 cm [3]. References  

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R. K. Chang and T. E. Furtek, eds.. Surface Enhanced Raman Scattering, Plenum, New York, 1982. 

In this section we will discuss more conventional spectroscopies absorption, emission and resonance Raman scattering. These spectroscopies are generally measured under single frequency conditions, and therefore our... 

We will now look at two-photon processes. We will concentrate on Raman scattering although two-photon absorption can be handled using the same approach. In Raman scattering, absorption of an incident photon of frequency coj carries... 

The only modification of equation (Al.6.90) for spontaneous Raman scattering is the multiplication by the density of states of the cavity, equation (Al.6.24). leading to a prefactor of the fonn cojCOg. ... 

Figure Al.6.15. Schematic diagram, showing the time-energy uncertainty principle operative in resonance Raman scattering. If the incident light is detuned from resonance by an amount Aco, the effective lifetime on the excited-state is i 1/Aco (adapted from [15]).

The more conventional, energy domain fonnula for resonance Raman scattering is the expression by Kramers-Heisenberg-Dirac (KHD). The differential cross section for Raman scattering into a solid angle dD can be written in the fomi... 

Lee S-Y and Heller E J 1979 Time-dependent theory of Raman scattering J. Chem. Rhys. 71 4777... 

Heller E J, Sundberg R L and Tanner D J 1982 Simple aspects of Raman scattering J. Rhys. Chem. 86 1822-33... 

Pausch R, Held M, Chen T, Schwoerer H and Kiefer W 2000 Quantum control by stimulated Raman scattering J. Raman Spectrosc. 31 7... 

Figure Bl.2.2. Schematic representation of the polarizability of a diatomic molecule as a fimction of vibrational coordinate. Because the polarizability changes during vibration, Raman scatter will occur in addition to Rayleigh scattering.

Raman scattering has been discussed by many authors. As in the case of IR vibrational spectroscopy, the interaction is between the electromagnetic field and a dipole moment, however in this case the dipole moment is induced by the field itself The induced dipole is pj j = a E, where a is the polarizability. It can be expressed in a Taylor series expansion in coordinate isplacement... 

The first temi results in Rayleigh scattering which is at the same frequency as the exciting radiation. The second temi describes Raman scattering. There will be scattered light at (Vq - and (Vq -i- v ), that is at sum and difference frequencies of the excitation field and the vibrational frequency. Since a. x is about a factor of 10 smaller than a, it is necessary to have a very efficient method for dispersing the scattered light. 

The light source must be highly monocln-omatic so that the Raman scattering occurs at a well-defined... 

Shreve A P and Mathies R A 1995 Thermal effects in resonance Raman-scattering—analysis of the Raman intensities of rhodopsin and of the time-resolved Raman-scattering of bacteriorhodopsin J. Phys. Chem. 99 7285-99... 

Measurement of the total Raman cross-section is an experimental challenge. More connnon are reports of the differential Raman cross-section, doj /dQ, which is proportional to the intensity of the scattered radiation that falls within the element of solid angle dQ when viewing along a direction that is to be specified [H]. Its value depends on the design of the Raman scattering experiment. 

Raman spectroscopy is pervasive and ever changing in modem physics and chemistry. In this section of the chapter, sources of up-to-date infonnation are given followed by brief discussions of a number of currently employed Raman based teclmiques. It is unpractical to discuss every possible technique and impossible to predict the many future novel uses of Raman scattering that are sure to come, but it is hoped that this section will provide a finu launching point into the modem uses of Raman spectroscopy for present and fiiture readers. 

Conventional spontaneous Raman scattering is the oldest and most widely used of the Raman based spectroscopic methods. It has served as a standard teclmique for the study of molecular vibrational and rotational levels in gases, and for both intra- and inter-molecular excitations in liquids and solids. (For example, a high resolution study of the vibrons and phonons at low temperatures in crystalline benzene has just appeared [38].)... 

Unlike the typical laser source, the zero-point blackbody field is spectrally white , providing all colours, CO2, that seek out all co - CO2 = coj resonances available in a given sample. Thus all possible Raman lines can be seen with a single incident source at tOp Such multiplex capability is now found in the Class II spectroscopies where broadband excitation is obtained either by using modeless lasers, or a femtosecond pulse, which on first principles must be spectrally broad [32]. Another distinction between a coherent laser source and the blackbody radiation is that the zero-point field is spatially isotropic. By perfonuing the simple wavevector algebra for SR, we find that the scattered radiation is isotropic as well. This concept of spatial incoherence will be used to explain a certain stimulated Raman scattering event in a subsequent section. 

Raman scattering and (b) anti-Stokes Raman scattering. In Stokes scattering, tlie cluomophore is initially in the ground vibrational state, g, and oi > CO2. hr spontaneous anti-Stokes scattering, the cluomophore must be initially m an excited vibrational state,/ Also note that in (b), M2 is (arbitrarily) defined as being greater than... 

RRS has also introduced the concept of a Raman excitation profile (REPy for thefth mode) [46, 4lZ, 48, 49, 50 and M]. An REP. is obtained by measuring the resonance Raman scattering strength of thefth mode as a fiinction of the excitation frequency [, 53]. Flow does the scattering intensity for a given (thefth) Raman active vibration vary with excitation frequency within an electronic absorption band In turn, this has led to transfomi theories that try to predict... 

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